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tries merging their way into fresh woods and pastures new. What about diversification
as an end in itself? It is obvious that diversification reduces risk. Isn’t that a gain from
merging?
The trouble with this argument is that diversification is easier and cheaper for the
stockholder than for the corporation. Why should firm A buy firm B to diversify when
the shareholders of firm A can buy shares in firm B to diversify their own portfolios?
It is far easier and cheaper for individual investors to diversify than it is for firms to
combine operations.
THE BOOTSTRAP GAME
During the 1960s some conglomerate companies made acquisitions which offered no
evident economic gains. Nevertheless, the conglomerates’ aggressive strategy produced
several years of rising earnings per share. To see how this can happen, let us look at the
acquisition of Muck and Slurry by the well-known conglomerate World Enterprises.
(cid:1) EXAMPLE 2
The Bootstrap Game
The position before the merger is set out in the first two columns of Table 6.2. Notice
that because Muck and Slurry has relatively poor growth prospects, its stock sells at a
lower price-earnings ratio than World Enterprises (line 3). The merger, we assume, pro-
duces no economic benefits, so the firms should be worth exactly the same together as
apart. The value of World Enterprises after the merger is therefore equal to the sum of
the separate values of the two firms (line 6).
Since World Enterprises stock is selling for double the price of Muck and Slurry stock
4 This description of the Apex One purchase draws on M. Maremount, “How Converse Got Its Laces All Tan-
gled,” Business Week, September 4, 1995, p. 37, and A. Bernstein, “Converse, Apex Sellers Point Fingers in
Court Battle,” Sporting Goods Business, May 1996, p. 8.
576 SECTION SIX
TABLE 6.2
Impact of merger on market
value and earnings per share
of World Enterprises
1. Earnings per share
2. Price per share
3. Price-earnings ratio
4. Number of shares
5. Total earnings
6. Total market value
7. Current earnings per
dollar invested in stock
(line 1 divided by line 2)
World Enterprises
(before merger)
World Enterprises
(after acquiring
and Slurry Muck and Slurry)
Muck
$2.00
$40.00
20
100,000
$200,000
$4,000,000
$2.00
$20.00
10
100,000
$200,000
$2,000,000
$2.67
$40.00
15
150,000
$400,000
$6,000,000
$.05
$.10
$.067
Note: When World Enterprises purchases Muck and Slurry, there are no gains. Therefore, total earnings and
total market value should be unaffected by the merger. But earnings per share increase. World Enterprises
issues only 50,000 of its shares (priced at $40) to acquire the 100,000 Muck and Slurry shares (priced at
$20).
(line 2), World Enterprises can acquire the 100,000 Muck and Slurry shares for 50,000
of its own shares. Thus World will have 150,000 shares outstanding after the merger.
World’s total earnings double as a result of the acquisition (line 5), but the number
of shares increases by only 50 percent. Its earnings per share rise from $2.00 to $2.67.
We call this a bootstrap effect because there is no real gain created by the merger and
no increase in the two firms’ combined value. Since World’s stock price is unchanged
by the acquisition of Muck and Slurry, the price-earnings ratio falls (line 3).
Before the merger, $1 invested in World Enterprises bought 5 cents of current earn-
ings and rapid growth prospects. On the other hand, $1 invested in Muck and Slurry
bought 10 cents of current earnings but slower growth prospects. If the total market
value is not altered by the merger, then $1 invested in the merged firm gives World
shareholders 6.7 cents of immediate earnings but slower growth than before the merger.
Muck and Slurry shareholders get lower immediate earnings but faster growth. Neither
side gains or loses provided that everybody understands the deal.
Financial manipulators sometimes try to ensure that the market does not understand
the deal. Suppose that investors are fooled by the exuberance of the president of World
Enterprises and mistake the 33 percent postmerger increase in earnings per share for | Brealey |
sustainable growth. If they do, the price of World Enterprises stock rises and the share-
holders of both companies receive something for nothing.
You should now see how to play the bootstrap game. Suppose that you manage a
company enjoying a high price-earnings ratio. The reason it is high is that investors an-
ticipate rapid growth in future earnings. You achieve this growth not by capital invest-
ment, product improvement, or increased operating efficiency, but by purchasing slow-
growing firms with low price-earnings ratios. The long-run result will be slower growth
and a depressed price-earnings ratio, but in the short run earnings per share can increase
dramatically. If this fools investors, you may be able to achieve the higher earnings per
share without suffering a decline in your price-earnings ratio. But in order to keep fool-
ing investors, you must continue to expand by merger at the same compound rate. Ob-
viously you cannot do this forever; one day expansion must slow down or stop. Then
earnings growth will cease, and your house of cards will fall.
Mergers, Acquisitions, and Corporate Control 577
Buying a firm with a lower P/E ratio can increase earnings per share. But the
increase should not result in a higher share price. The short-term increase in
earnings should be offset by lower future earnings growth.
(cid:1) Self-Test 2
Suppose that Muck and Slurry has even worse growth prospects than in our example
and its share price is only $10. Recalculate the effects of the merger in this case. You
should find that earnings per share increase by a greater amount, since World Enter-
prises can now buy the same current earnings for fewer shares.
Evaluating Mergers
If you are given the responsibility for evaluating a proposed merger, you must think
hard about the following two questions:
1. Is there an overall economic gain to the merger? In other words, is the merger value-
enhancing? Are the two firms worth more together than apart?
2. Do the terms of the merger make my company and its shareholders better off? There
is no point in merging if the cost is too high and all the economic gain goes to the
other company.
Answering these deceptively simple questions is rarely easy. Some economic gains can
be nearly impossible to quantify, and complex merger financing can obscure the true
terms of the deal. But the basic principles for evaluating mergers are not too difficult.
MERGERS FINANCED BY CASH
We will concentrate on a simple numerical example. Your company, Cislunar Foods, is
considering acquisition of a smaller food company, Targetco. Cislunar is proposing to
finance the deal by purchasing all of Targetco’s outstanding stock for $19 per share.
Some financial information on the two companies is given in the left and center
columns of Table 6.3.
TABLE 6.3
Cislunar Foods is
considering an acquisition of
Targetco. The merger would
increase the companies’
combined earnings by $4
million.
Combined
Companies
$172
132
$ 40
(+2)
(–2)
(+4)
Cislunar Foods
Targetco
Revenues
Operating costs
Earnings
Cash
Other assets’ book value
Total assets
Price per share
Number of shares
Market value
$150
118
$ 32
$ 55
185
$240
$ 48
10.0
$480
Note: Figures in millions except price per share.
$ 20
16
$ 4
$ 2.5
17.0
$ 19.5
$ 16
2.5
$ 40
578 SECTION SIX
Question 1. Why would Cislunar and Targetco be worth more together than apart?
Suppose that operating costs can be reduced by combining the companies’ marketing,
distribution, and administration. Revenues can also be increased in Targetco’s region.
The rightmost column of Table 6.3 contains projected revenues, costs, and earnings for
the two firms operating together: annual operating costs postmerger will be $2 million
less than the sum of the separate companies’ costs, and revenues will be $2 million
more. Therefore, projected earnings increase by $4 million.5 We will assume that the in-
creased earnings are the only synergy to be generated by the merger.
The economic gain to the merger is the present value of the extra earnings. If the | Brealey |
earnings increase is permanent (a level perpetuity), and the cost of capital is 20 percent,
Economic gain = PV (increased earnings) =
4
.20
= $20 million
This additional value is the basic motivation for the merger.
Question 2. What are the terms of the merger? What is the cost to Cislunar and its
shareholders?
Targetco’s management and shareholders will not consent to the merger unless they
receive at least the stand-alone value of their shares. They can be paid in cash or by new
shares issued by Cislunar. In this case we are considering a cash offer of $19 per Tar-
getco share, $3 per share over the prior share price. Targetco has 2.5 million shares out-
standing, so Cislunar will have to pay out $47.5 million, a premium of $7.5 million over
Targetco’s prior market value. On these terms, Targetco stockholders will capture $7.5
million out of the $20 million gain from the merger. That ought to leave $12.5 million
for Cislunar.
This is confirmed in the Cash Purchase column of Table 6.4. Start at the bottom of
the column, where the total market value of the merged firms is $492.5 million. This is
derived as follows:
Cislunar market value prior to merger
Targetco market value
Present value of gain to merger
Less Cash paid out to Targetco shareholders
Postmerger market value
$480 million
40
20
–47.5
$492.5 million
Cash Purchase
Exchange of Shares
Earnings
Cash
Other assets’ book value
Total assets
Price per share
Number of shares
Market value
$ 40
$ 10
202
$212
$ 49.25
10.0
$492.5
Note: Figures in millions except price per share.
$ 40
$ 57.5
202
$259.5
$ 49.85
10.833
$540
TABLE 6.4
Financial forecasts after the
Cislunar–Targetco merger.
The left column assumes a
cash purchase at $19 per
Targetco share. The right
column assumes Targetco
stockholders receive one new
Cislunar share for every
three Targetco shares.
5 To keep things simple, the example ignores taxes and assumes that both companies are all-equity financed.
We also ignore the interest income that could have been earned by investing the cash used to finance the
merger.
Mergers, Acquisitions, and Corporate Control 579
The postmerger share price for Cislunar will be $49.25, an increase of $1.25 per share.
There are 10 million shares now outstanding, so the total increase in the value of Cis-
lunar shares is $12.5 million.
Now let’s summarize. The merger makes sense for Cislunar for two reasons. First, the
merger adds $20 million of overall value. Second, the terms of the merger give only $7.5
million of the $20 million overall gain to Targetco’s stockholders, leaving $12.5 million
for Cislunar. You could say that the cost of acquiring Targetco is $7.5 million, the differ-
ence between the cash payment and the value of Targetco as a separate company.
Cost = cash paid out – Targetco value = $47.5 – 40 = $7.5 million
Of course the Targetco stockholders are ahead by $7.5 million. Their gain is your cost.
As we’ve already seen, Cislunar stockholders come out $12.5 million ahead. This is the
merger’s NPV for Cislunar:
NPV = economic gain – cost = $20 – 7.5 = $12.5 million
Writing down the economic gain and cost of a merger in this way separates the mo-
tive for the merger (the economic gain, or value added) from the terms of the merger
(the division of the gain between the two merging companies).
(cid:1) Self-Test 3
Killer Shark Inc. makes a surprise cash offer of $22 a share for Goldfish Industries. Be-
fore the offer, Goldfish was selling for $18 a share. Goldfish has 1 million shares out-
standing. What must Killer Shark believe about the present value of the improvement it
can bring to Goldfish’s operations?
MERGERS FINANCED BY STOCK
What if Cislunar wants to conserve its cash for other investments, and therefore decides
to pay for the Targetco acquisition with new Cislunar shares? The deal calls for Targetco
shareholders to receive one Cislunar share in exchange for every three Targetco shares.
It’s the same merger, but the financing is different. The right column of Table 6.4
works out the consequences. Again, start at the bottom of the column. Note that the mar- | Brealey |
ket value of Cislunar’s shares after the merger is $540 million, $47.5 million higher than
in the cash deal, because that cash is kept rather than paid out to Targetco shareholders.
On the other hand, there are more shares outstanding, since 833,333 new shares have to
be issued in exchange for the 2.5 million Targetco shares (a 1 to 3 ratio). Therefore, the
price per share is 540/10.833 = $49.85, which is 60 cents higher than in the cash offer.
Why do Cislunar stockholders do better from the share exchange? The economic
gain from the merger is the same, but the Targetco stockholders capture less of it. They
get 833,333 shares at $49.85, or $41.5 million, a premium of only $1.5 million over
Targetco’s prior market value.
Cost = value of shares issued – Targetco value
= $41.5 – 40 = $1.5 million
The merger’s NPV to Cislunar’s original shareholders is
NPV = economic gain – cost = 20 – 1.5 = $18.5 million
Note that Cislunar stock rises by $1.85 from its prior value. The total increase in value
for Cislunar’s original shareholders, who retain 10 million shares, is $18.5 million.
580 SECTION SIX
SEE BOX
Evaluating the terms of a merger can be tricky when there is an exchange of shares.
The target company’s shareholders will retain a stake in the merged firms, so you have
to figure out what the firm’s shares will be worth after the merger is announced and its
benefits appreciated by investors. Notice that we started with the total market value of
Cislunar and Targetco postmerger, took account of the merger terms (833,333 new
shares issued), and worked back to the postmerger share price. Only then could we work
out the division of the merger gains between the two companies.
There is a key distinction between cash and stock for financing mergers. If cash is
offered, the cost of the merger is not affected by the size of the merger gains. If stock is
offered, the cost depends on the gains because the gains show up in the post-merger
share price, and these shares are used to pay for the acquired firm. The nearby box il-
lustrates how complex a stock offer can be. When Gillette offered to buy Duracell, giv-
ing Duracell shareholders about a 20 percent stake in the merged firm, the attractive-
ness of the deal depended on the stock market’s valuation of both firms.
Stock financing also mitigates the effects of over- or undervaluation of either firm.
Suppose, for example, that A overestimates B’s value as a separate entity, perhaps be-
cause it has overlooked some hidden liability. Thus A makes too generous an offer.
Other things equal, A’s stockholders are better off if it is a stock rather than a cash offer.
With a stock offer, the inevitable bad news about B’s value will fall partly on B’s for-
mer stockholders.
(cid:1) Self-Test 4
Suppose Targetco shareholders demand one Cislunar share for every 2.5 Targetco
shares. Otherwise they will not accept the merger. Under these revised terms, is the
merger still a good deal for Cislunar?
A WARNING
The cost of a merger is the premium the acquirer pays for the target firm over its value
as a separate company. If the target is a public company, you can measure its separate
value by multiplying its stock price by the number of outstanding shares. Watch out,
though: if investors expect the target to be acquired, its stock price may overstate the
company’s separate value. The target company’s stock price may already have risen in
anticipation of a premium to be paid by an acquiring firm.
ANOTHER WARNING
Some companies begin their merger analyses with a forecast of the target firm’s future
cash flows. Any revenue increases or cost reductions attributable to the merger are in-
cluded in the forecasts, which are then discounted back to the present and compared
with the purchase price:
Estimated net gain = DCF valuation of target including merger benefits
– cash required for acquisition
This is a dangerous procedure. Even the brightest and best-trained analyst can make
large errors in valuing a business. The estimated net gain may come up positive not be- | Brealey |
cause the merger makes sense, but simply because the analyst’s cash-flow forecasts are
too optimistic. On the other hand, a good merger may not be pursued if the analyst fails
to recognize the target’s potential as a stand-alone business.
FINANCE IN ACTION
Blades, Batteries, and a Fifth of Gillette
Back in 1988, when Kraft Inc. decided to unload its bat-
tery subsidiary, Gillette Co. was tempted. But the bid-
ding went up and up and out of Gillette’s reach.
Kohlberg Kravis Roberts & Co. eventually bought the
battery maker—
for a seem-
ingly extravagant $1.8 billion.
it was Duracell, of course—
After eight years of due diligence, Gillette has finally
agreed to fork over stock valued at more than $7 billion
for the very same Duracell International Inc. Just as
KKR now looks shrewd, rear-view analysts may snicker
at Gillette for buying dear what it could have had then
for, let us assume, only $2 billion in stock.
In fact, Gillette shareholders should thank their lucky
stars the earlier deal didn’t happen. In share-for-share
acquisitions, what you are getting is only half the pic-
ture; what you are giving up is just as important. The
standard analysis values such deals according to the
dollar value of the target, but that approach is flawed.
The key question isn’t whether Duracell is worth $7 bil-
lion, because Gillette isn’t giving up $7 billion. It is giv-
in this case 20%— of itself.
ing up a part—
Schematically, Gillette is trading razor blades for bat-
teries (not bucks for batteries), and the results can be
very different. Since 1988, for instance, the blade busi-
ness, at least under Gillette’s management, has per-
formed much better than batteries. While Duracell’s
stock has quadrupled, Gillette’s has multiplied eight
times. Thus if Gillette had in fact made that “ cheap” $2
billion acquisition, it would have acquired a jack rabbit
but given up a prize thoroughbred. The passed-over
purchase back then would have cost Gillette more than
one-third of its stock; today, it is buying the same busi-
ness for only a fifth of its stock.
Clearly, taking a pass was the right move. Duracell
was cheap in 1988, but Gillette was cheaper. And shop-
ping with inexpensive currency, meaning issuing under-
valued stock, amounts to selling the company (or a
piece of it) on the cheap.
Going forward, the same analysis holds. The im-
puted dollar value of the deal will forever drift with
Gillette’s share price; the one constant is that each
Gillette’s Stock
$80
60
40
20
0
1988
1989
1990
1991
1992
1993
1994
1995
1996
e
c
i
r
p
g
n
s
o
c
i
l
y
l
i
a
D
shareholder is trading away one-fifth of his interest in
the old Gillette. Whether Duracell will be worth it, a sub-
ject no analyst has addressed, is what matters.
Such deals are manna for investment bankers (and
bound to wind up in B-school texts) because you need
to size up two businesses instead of one.
On balance, the blade business is more distinct, and
better, than batteries. But how much better? Duracell
for one-fifth of Gillette works out to this: For each dollar
of Gillette earnings that shareholders are giving up, they
are getting roughly $1.30 in cash earnings from batter-
ies.
Blades should trade at a premium, but this one is
steep. That premium, of course, reflects the current
very high price of Gillette’s stock, which in turn reflects
a view that Gillette will forever keep profit growing twice
as fast as its sales. Gillette’s managers wouldn’t come
out and say that 34 times earnings reflects unwarranted
optimism, or even a bull-market joie de vivre, but if that
is what they thought, trading part of their company at
that price for a cheaper one would be a smart move.
And that is what they are doing.
Source: Republished with permission of Dow Jones, from “Blades,
Batteries, and a Fifth of Gillette,” from R. Lowenstein, “Intrinsic
Value,” The Wall Street Journal, September 19, 1996, p. C1; permis-
sion conveyed through Copyright Clearance Center.
| Brealey |
A better procedure starts with the target’s current and stand-alone market value and
concentrates instead on the changes in cash flow that would result from the merger. Al-
ways ask why the two firms should be worth more together than apart. Remember, you
add value only if you can generate additional economic benefits—some competitive
581
582 SECTION SIX
edge that other firms can’t match and that the target firm’s managers can’t achieve on
their own.
It makes sense to keep an eye on the value that investors place on the gains from merg-
ing. If A’s stock price falls when the deal is announced, investors are sending a message
that the merger benefits are doubtful or that A is paying too much for these benefits.
Merger Tactics
In recent years, most mergers have been agreed upon by both parties, but occasionally,
an acquirer goes over the heads of the target firm’s management and makes a tender
offer directly to its stockholders. The management of the target firm may advise share-
holders to accept the tender, or it may attempt to fight the bid in the hope that the ac-
quirer will either raise its offer or throw in the towel.
The rules of merger warfare are largely set by federal and state laws6 and the courts
act as referee to see that contests are conducted fairly. We will look at one recent con-
test that illustrates the tactics and weapons employed. Outside the English-speaking
countries hostile takeovers once were rare. But the world is changing, and the nearby
box describes a recent takeover battle between Italian companies.
SEE BOX
(cid:1) EXAMPLE 3
AlliedSignal Takes Over AMP
AMP was the world’s largest producer of cables for computers and other electronic
equipment. Its performance had disappointed investors, and the company was widely
viewed as ripe for change in operations and management.
AlliedSignal believed that it could make these changes faster and better than AMP’s
incumbent management. So in summer 1998, when AMP announced that its quarterly
profits were down 50 percent, AlliedSignal declared that it would bid $44.50 per share
for AMP’s stock. AMP’s stock price immediately bounded by nearly 50 percent to about
$43 per share.
AMP at first seemed impregnable. It was chartered in Pennsylvania, which had
passed tough antitakeover laws. Pennsylvania corporations could “just say no” to
takeovers that might adversely affect employees and local communities. AMP had also
protected itself against takeover by establishing a poison pill. This gave its sharehold-
ers the right to buy more shares at a bargain price if there was a bid.
AlliedSignal held out an olive branch, hinting that price was flexible if AMP was
ready to talk turkey. When its proposal was rebuffed, Allied decided to go ahead with
its offer and 72 percent of AMP shareholders accepted. However, there was still the
problem of the poison pill, and AlliedSignal’s offer stated that it was not obliged to buy
any shares until the poison pill was removed. This was not something that AMP’s man-
agement was likely to do voluntarily.
AMP fought back vigorously. It announced a plan to borrow $3 billion to repurchase
its shares at $55 per share—its management’s view of the true value of AMP stock. At
the same time it asked the Pennsylvania legislature to pass a law that would effectively
bar the merger. The governor gave his support and in October the bill was approved in
the Pennsylvania House of Representatives and sent to the Senate for consideration.
6 The principal federal act regulating takeovers is the Williams Act of 1968.
POISON PILL Measure
taken by a target firm to
avoid acquisition; for
example, the right for
existing shareholders to buy
additional shares at an
attractive price if a bidder
acquires a large holding.
FINANCE IN ACTION
An Italian Takeover Battle
Hostile takeovers were almost unheard of in Italy—
that
is, until 1999 when Olivetti made a takeover bid for Tele-
com Italia. What made this bid even more remarkable
was the fact that Telecom was seven times the size of
Olivetti.
| Brealey |
The recently privatized Telecom was Italy’s principal
fixed-line telecommunications firm. Its performance,
however, had been lackluster and Olivetti saw plenty of
room for improved efficiency. Therefore, in November
1998 Olivetti set about appointing advisers for a possi-
ble bid. These consisted of the Italian investment bank
Mediobanca and three American firms, Chase Manhat-
tan, Lehman Brothers, and Donaldson, Lufkin & Jen-
rette (DLJ).
Everybody agreed that Olivetti would have to offer
mainly cash to Telecom shareholders rather than
Olivetti’s shares. The company would need to borrow
this cash, and to pay it back it would have no choice
but to run a tight ship and keep costs under control.
Chase, therefore, set about signing up a syndicate of 25
major banks that would be prepared to lend 22.5 billion
euros, equivalent to nearly $24 billion.
Olivetti made its takeover bid for Telecom in Febru-
ary 1999. The bid was worth over 50 billion euros and
the cash would come from a mixture of the syndicated
bank loan, an issue of bonds, and an issue of shares.
Investors’ initial response to the offer was lukewarm.
Some doubted whether a minnow like Olivetti could
successfully swallow a whale like Telecom. Although
the offer price was more than a third higher than Tele-
com’s market price before the bid, many investors re-
garded it as too low.
Telecom began to prepare its defenses. It too ap-
pointed three advisers— Banca IMI, J. P. Morgan, and
Credit Suisse First Boston (CSFB). They ran through a
number of possible measures that the company could
take. One possibility was for Telecom to turn the tables
by making a bid for Olivetti. Another idea was that Tele-
com should buy the remaining shares of TIM, a com-
pany in which it already had a holding. This would make
Telecom a still larger bite for Olivetti to swallow. A third
possibility was for Telecom to borrow a large amount of
cash and use it to buy back some of its shares. In-
vestors would then know that Telecom had every incen-
tive to cut costs and generate the extra cash to pay off
this debt. Another potential defense was for Telecom to
look for a “ white knight” that would make a more con-
genial partner.
In the business plan that it sent to shareholders,
Telecom stated that it was proposing to acquire the re-
mainder of TIM shares and also to buy back some of its
shares. Soon afterwards it announced that it had found
a white knight in the form of a German company,
Deutsche Telekom, and would shortly submit the pro-
posal to shareholders. Investors were not convinced
that a takeover with Deutsche Telekom would make
sense, and The Wall Street Journal likened the prospect
to two elephants mating. There was a further potential
problem with such a merger. The German government
retained a large holding in Deutsche Telekom and would
therefore be the dominant shareholder in a merged firm.
The Italian government retained the right to veto any
merger involving Telecom Italia. It was unlikely to object
to Olivetti as a merger partner, but it might be unhappy
to see the country’s principal telecommunications com-
pany largely controlled by another government. So al-
though Deutsche Telekom’s offer was more generous
than Olivetti’s, investors were far from certain that it
would be allowed to proceed.
In March Olivetti upped its bid for Telecom by 15
percent. The new bid was worth 58 billion euros and of-
fered Telecom investors a profit of over 50 percent on
the January stock price. In May 1999 Telecom Italia’s
shareholders began to respond to Olivetti’s bid. At first
there was only a trickle of acceptances, but by the time
the offer closed 3 weeks later, the trickle had become a
flood and it was clear that Olivetti had won.
Source: The bid for Telecom Italia is described in M. Walker, “The
Sack of Telecom Italia,” Euromoney, July 1999, pp. 30–46. A record
of the offer, together with copies of press releases and other informa- | Brealey |
tion, is provided on www.olivetti.com/press/.
Meanwhile AlliedSignal was discovering that it too had powerful allies. About 80
percent of AMP’s shares were owned by mutual funds, pension funds, and other large
investors. Many of these institutions publicly disagreed with AMP’s stubbornness. The
College Retirement Equities Fund (CREF), one of the largest U.S. pension funds, then
took an extraordinary step: it filed a legal brief supporting AlliedSignal’s case in the
583
584 SECTION SIX
WHITE KNIGHT
Friendly potential acquirer
sought by a target company
threatened by an unwelcome
suitor.
SHARK REPELLENT
Amendments to a company
charter made to forestall
takeover attempts.
federal court. Then the Hixon family, descendants of AMP’s co-founder, made public a
letter to AMP’s management expressing “dismay” and asking, “Who do management
and the board work for? The central issue is that AMP’s management will not permit
shareholders to voice their will.”7
As the weeks passed, AMP’s defenses, while still intact, did not look quite so strong.
By mid-October, it became clear that AMP would not receive timely help from the
Pennsylvania legislature. In November, the federal court gave AlliedSignal the go-ahead
to ask shareholders to vote to remove the poison pill. Remember, 72 percent of its stock-
holders had already accepted AlliedSignal’s tender offer.
Then, suddenly, AMP gave up: management had found a white knight when Tyco
International came to its rescue. Tyco was prepared to offer stock worth $55 for each
AMP share. AlliedSignal dropped out of the bidding; it didn’t think AMP was worth
that much.
What are the lessons? First, the example illustrates some of the stratagems of merger
warfare. Firms like AMP that are worried about being taken over usually prepare their
defenses in advance. Often they will persuade shareholders to agree to shark-repellent
changes to the corporate charter. For example, the charter may be amended to require
that any merger must be approved by a supermajority of 80 percent of the shares rather
than the normal 50 percent.
Firms frequently deter potential bidders by devising poison pills, which make the
company unappetizing. For example, the poison pill may give existing shareholders the
right to buy the company’s shares at half price as soon as a bidder acquires more than
15 percent of the shares. The bidder is not entitled to the discount. Thus the bidder re-
sembles Tantalus—as soon as it has acquired 15 percent of the shares, control is lifted
away from its reach.
The battle for AMP demonstrates the strength of poison pills and other takeover de-
fenses. AlliedSignal’s offensive still gained ground, but with great expense and effort
and at a very slow pace.
The second lesson of the AMP story is the potential power of institutional investors.
The main reason that AMP caved in was not failure of its legal defenses but economic
pressure from its major shareholders.
Did AMP’s management and board act in the shareholders’ interests? In the end, yes.
They said that AMP was worth more than AlliedSignal’s offer, and they found another
buyer to prove them right. However, they would not have searched for a white knight
absent AlliedSignal’s bid.
WHO GETS THE GAINS?
Is it better to own shares in the acquiring firm or the target? In general, shareholders of
the target firm do best. Franks, Harris, and Titman studied 399 acquisitions by large
U.S. firms between 1975 and 1984. They found that shareholders who sold following
the announcement of the bid received a healthy gain averaging 28 percent.8 On the other
hand, it appears that investors expected acquiring companies to just about break even.
7 S. Lipin and G. Fairclothy, “AMP’s Antitakeover Tactics Rile Holder,” The Wall Street Journal, October 5,
1998, p. A18.
8 J. R. Franks, R. S. Harris, and S. Titman, “The Postmerger Share-Price Performance of Acquiring Firms,”
Journal of Financial Economics 29 (March 1991), pp. 81–96.
Mergers, Acquisitions, and Corporate Control 585
The prices of their shares fell by 1 percent.9 The value of the total package—buyer plus | Brealey |
seller—increased by 4 percent. Of course, these are averages; selling shareholders
sometimes obtain much higher returns. When IBM took over Lotus, it paid a premium
of 100 percent, or about $1.7 billion, for Lotus stock.
Why do sellers earn higher returns? The most important reason is the competition
among potential bidders. Once the first bidder puts the target company “in play,” one or
more additional suitors often jump in, sometimes as white knights at the invitation of
the target firm’s management. Every time one suitor tops another’s bid, more of the
merger gain slides toward the target. At the same time the target firm’s management
may mount various legal and financial counterattacks, ensuring that capitulation, if and
when it comes, is at the highest attainable price.
Of course, bidders and targets are not the only possible winners. Unsuccessful bid-
ders often win, too, by selling off their holdings in target companies at substantial prof-
its. Such shares may be sold on the open market or sold back to the target company.10
Sometimes they are sold to the successful suitor.
Other winners include investment bankers, lawyers, accountants, and in some cases
arbitrageurs, or “arbs,” who speculate on the likely success of takeover bids.
“Speculate” has a negative ring, but it can be a useful social service. A tender offer
may present shareholders with a difficult decision. Should they accept, should they
wait to see if someone else produces a better offer, or should they sell their stock in
the market? This quandary presents an opportunity for the arbitrageurs. In other words,
they buy from the target’s shareholders and take on the risk that the deal will not go
through.11
Leveraged Buyouts
Leveraged buyouts, or LBOs, differ from ordinary acquisitions in two ways. First, a
large fraction of the purchase price is debt-financed. Some, perhaps all, of this debt is
junk, that is, below investment grade. Second, the shares of the LBO no longer trade on
the open market. The remaining equity in the LBO is privately held by a small group of
(usually institutional) investors. When this group is led by the company’s management,
the acquisition is called a management buyout (MBO). Many LBOs are in fact MBOs.
In the 1970s and 1980s many management buyouts were arranged for unwanted di-
visions of large, diversified companies. Smaller divisions outside the companies’ main
lines of business often lacked top management’s interest and commitment, and divi-
sional management chafed under corporate bureaucracy. Many such divisions flowered
when spun off as MBOs. Their managers, pushed by the need to generate cash for debt
service and encouraged by a substantial personal stake in the business, found ways to
cut costs and compete more effectively.
During the 1980s MBO/LBO activity shifted to buyouts of entire businesses,
including large, mature public corporations. The largest, most dramatic, and best-
9 The small loss to the shareholders of acquiring firms is not statistically significant. Other studies using dif-
ferent samples have observed a small positive return.
10 When a potential acquirer sells the shares back to the target, the transaction is known as greenmail.
11 Strictly speaking, an arbitrageur is an investor who makes a riskless profit. Arbitrageurs in merger battles
often take very large risks indeed. Their activities are sometimes known as “risk arbitrage.”
586 SECTION SIX
documented LBO of them all was the $25 billion takeover of RJR Nabisco in 1988 by
Kohlberg Kravis Roberts (KKR). The players, tactics, and controversies of LBOs are
writ large in this case.
(cid:1) EXAMPLE 4
RJR Nabisco12
On October 28, 1988, the board of directors of RJR Nabisco revealed that Ross John-
son, the company’s chief executive officer, had formed a group of investors prepared to
buy all the firm’s stock for $75 per share in cash and take the company private. John-
son’s group was backed up and advised by Shearson Lehman Hutton, the investment | Brealey |
bank subsidiary of American Express.
RJR’s share price immediately moved to about $75, handing shareholders a 36 per-
cent gain over the previous day’s price of $56. At the same time RJR’s bonds fell, since
it was clear that existing bondholders would soon have a lot more company.
Johnson’s offer lifted RJR onto the auction block. Once the company was in play, its
board of directors was obliged to consider other offers, which were not long coming.
Four days later, a group of investors led by LBO specialists Kohlberg Kravis Roberts
bid $90 per share, $79 in cash plus preferred stock valued at $11.
The bidding finally closed on November 30, some 32 days after the initial offer was
revealed. In the end it was Johnson’s group against KKR. KKR offered $109 per share,
after adding $1 per share (roughly $230 million) at the last hour. The KKR bid was $81
in cash, convertible subordinated debentures valued at about $10, and preferred shares
valued at about $18. Johnson’s group bid $112 in cash and securities.
But the RJR board chose KKR. True, Johnson’s group had offered $3 per share more,
but its security valuations were viewed as “softer” and perhaps overstated. Also, KKR’s
planned asset sales were less drastic; perhaps their plans for managing the business in-
spired more confidence. Finally, the Johnson group’s proposal contained a management
compensation package that seemed extremely generous and had generated an avalanche
of bad press.
But where did the merger benefits come from? What could justify offering $109 per
share, about $25 billion in all, for a company that only 33 days previously had been sell-
ing for $56 per share?
KKR and other bidders were betting on two things. First, they expected to generate
billions of additional dollars from interest tax shields, reduced capital expenditures, and
sales of assets not strictly necessary to RJR’s core businesses. Asset sales alone were
projected to generate $5 billion. Second, they expected to make those core businesses
significantly more profitable, mainly by cutting back on expenses and bureaucracy. Ap-
parently there was plenty to cut, including the RJR “Air Force,” which at one point op-
erated 10 corporate jets.
In the year after KKR took over, new management was installed. This group sold as-
sets and cut back operating expenses and capital spending. There were also layoffs. As
expected, high interest charges meant a net loss of $976 million for 1989, but pretax op-
erating income actually increased, despite extensive asset sales, including the sale of
RJR’s European food operations.
While management was cutting costs and selling assets, prices in the junk bond mar-
12 The story of the RJR Nabisco buyout is reconstructed by B. Burrough and J. Helyar in Barbarians at the
Gate: The Fall of RJR Nabisco (New York: Harper & Row, 1990) and is the subject of a movie with the same
title.
Mergers, Acquisitions, and Corporate Control 587
ket were rapidly declining, implying much higher future interest charges for RJR and
stricter terms on any refinancing. In mid-1990 KKR made an additional equity invest-
ment, and later that year the company announced an offer of cash and new shares in ex-
change for $753 million of junk bonds. By 1993 the burden of debt had been reduced
from $26 billion to $14 billion. For RJR, the world’s largest LBO, it seemed that high
debt was a temporary, not permanent, virtue.
BARBARIANS AT THE GATE?
The buyout of RJR crystallized views on LBOs, the junk bond market, and the takeover
business. For many it exemplified all that was wrong with finance in the 1980s, espe-
cially the willingness of “raiders” to carve up established companies, leaving them with
enormous debt burdens, basically in order to get rich quick.
There was plenty of confusion, stupidity, and greed in the LBO business. Not all the
people involved were nice. On the other hand, LBOs generated enormous increases in
market value, and most of the gains went to selling stockholders, not raiders. For ex-
ample, the biggest winners in the RJR Nabisco LBO were the company’s stockholders. | Brealey |
We should therefore consider briefly where these gains may have come from before
we try to pass judgment on LBOs. There are several possibilities.
The Junk Bond Markets. LBOs and debt-financed takeovers may have been driven
by artificially cheap funding from the junk bond markets. With hindsight it seems that
investors in junk bonds underestimated the risks of default. Default rates climbed
painfully between 1989 and 1991. At the same time the junk bond market became much
less liquid after the demise of Drexel Burnham Lambert, the chief market maker. Yields
rose dramatically, and new issues dried up. Suddenly junk-financed LBOs seemed to
disappear from the scene.13
Leverage and Taxes. As we explained earlier, borrowing money saves taxes. But
taxes were not the main driving force behind LBOs. The value of interest tax shields
was just not big enough to explain the observed gains in market value.
Of course, if interest tax shields were the main motive for LBOs’ high debt, then
LBO managers would not be so concerned to pay off debt. We saw that this was one of
the first tasks facing RJR Nabisco’s new management.
Other Stakeholders.
It is possible that the gain to the selling stockholders is just
someone else’s loss and that no value is generated overall. Therefore, we should look at
the total gain to all investors in an LBO, not just the selling stockholders.
Bondholders are the obvious losers. The debt they thought was well-secured may
turn into junk when the borrower goes through an LBO. We noted how market prices of
RJR Nabisco debt fell sharply when Ross Johnson’s first LBO offer was announced.
But again, the value losses suffered by bondholders in LBOs are not nearly large
enough to explain stockholder gains.
Leverage and Incentives. Managers and employees of LBOs work harder and often
smarter. They have to generate cash to service the extra debt. Moreover, managers’
13 There was a sharp revival of junk bond sales in 1992 and 1993 and 1996 was a banner year. But many of
these issues simply replaced existing bonds. It remains to be seen whether junk bonds will make a lasting re-
covery.
588 SECTION SIX
personal fortunes are riding on the LBO’s success. They become owners rather than or-
ganization men or women.
It is hard to measure the payoff from better incentives, but there is some evidence of
improved operating efficiency in LBOs. Kaplan, who studied 48 management buyouts
between 1980 and 1986, found average increases in operating income of 24 percent over
the following 3 years. Ratios of operating income and net cash flow to assets and sales
increased dramatically. He observed cutbacks in capital expenditures but not in em-
ployment. Kaplan suggests that these operating changes “are due to improved incen-
tives rather than layoffs or managerial exploitation of shareholders through inside in-
formation.”14
Free Cash Flow. The free-cash-flow theory of takeovers is basically that mature firms
with a surplus of cash will tend to waste it. This contrasts with standard finance theory,
which says that firms with more cash than positive-NPV investment opportunities
should give the cash back to investors through higher dividends or share repurchases.
But we see firms like RJR Nabisco spending on corporate luxuries and questionable
capital investments. One benefit of LBOs is to put such companies on a diet and force
them to pay out cash to service debt.
The free-cash-flow theory predicts that mature, “cash cow” companies will be the
most likely targets of LBOs. We can find many examples that fit the theory, including
RJR Nabisco. The theory says that the gains in market value generated by LBOs are just
the present values of the future cash flows that would otherwise have been frittered
away.15
We do not endorse the free-cash-flow theory as the sole explanation for LBOs. We
have mentioned several other plausible rationales, and we suspect that most LBOs are
driven by a mixture of motives. Nor do we say that all LBOs are beneficial. On the con- | Brealey |
trary, there are many mistakes and even soundly motivated LBOs can be dangerous, as
the bankruptcies of Campeau, Revco, National Gypsum, and many other highly lever-
aged companies prove. However, we do take issue with those who portray LBOs simply
as Wall Street barbarians breaking up the traditional strengths of corporate America. In
many cases LBOs have generated true gains.
In the next section we sum up the long-run impact of mergers and acquisitions, in-
cluding LBOs, in the United States economy. We warn you, however, that there are no
neat answers. Our assessment has to be mixed and tentative.
Mergers and the Economy
MERGER WAVES
Mergers come in waves. The first episode of intense merger activity occurred at the turn
of the twentieth century and the second in the 1920s. There was a further boom from
1967 to 1969 and then again in the 1980s and 1990s. Each episode coincided with a pe-
14 S. Kaplan, “The Effects of Management Buyouts on Operating Performance and Value,” Journal of Finan-
cial Economics 24 (October 1989), pp. 217–254.
15 The free-cash-flow theory’s chief proponent is Michael Jensen. See M. C. Jensen, “The Eclipse of the Pub-
lic Corporation,” Harvard Business Review 67 (September–October 1989), pp. 61–74, and “The Agency
Costs of Free Cash Flow, Corporate Finance and Takeovers,” American Economic Review 76 (May 1986), pp.
323–329.
Mergers, Acquisitions, and Corporate Control 589
riod of buoyant stock prices, though in each case there were substantial differences in
the types of companies that merged and how they went about it.
We don’t really understand why merger activity is so volatile. If mergers are
prompted by economic motives, at least one of these motives must be “here today, gone
tomorrow,” and it must somehow be associated with high stock prices. But none of the
economic motives that we review in this material has anything to do with the general
level of the stock market. None of the motives burst on the scene in 1967, departed in
1970, reappeared for most of the 1980s, and reappeared again in the mid-1990s.
Some mergers may result from mistakes in valuation on the part of the stock market.
In other words, the buyer may believe that investors have underestimated the value of
the seller or may hope that they will overestimate the value of the combined firm. Why
don’t we see just as many firms hunting for bargain acquisitions when the stock market
is low? It is possible that “suckers are born every minute,” but it’s difficult to believe
that they can be harvested only in bull markets.
During the 1980s merger boom, only the very largest companies were immune from
attack from a rival management team. For example, in 1985 Pantry Pride, a small su-
permarket chain recently emerged from bankruptcy, made a bid for the cosmetics com-
pany Revlon. Revlon’s assets were more than five times those of Pantry Pride. What
made the bid possible (and eventually successful) was the ability of Pantry Pride to fi-
nance the takeover by borrowing $2.1 billion. The growth of leveraged buyouts during
the 1980s depended on the development of a junk bond market that allowed bidders to
place low-grade bonds rapidly and in high volume.
By the end of the decade the merger environment had changed. Many of the obvious
targets had disappeared, and the battle for RJR Nabisco highlighted the increasing cost
of victory. Institutions were reluctant to increase their holdings of junk bonds. More-
over, the market for these bonds had depended to a remarkable extent on one individ-
ual, Michael Milken, of the investment bank Drexel Burnham Lambert. By the late
1980s Milken and his employer were in trouble. Milken was indicted by a grand jury on
98 counts and was subsequently sentenced to jail and ordered to pay $600 million.
Drexel filed for bankruptcy, but by that time the junk bond market was moribund and
the finance for highly leveraged buyouts had largely dried up.16 Finally, in reaction to
the perceived excess of the merger boom, the state legislatures and the courts began to | Brealey |
lean against takeovers.
The decline in merger activity proved temporary; by the mid-1990s stock markets
and mergers were booming again. However, LBOs remained out of fashion, and rela-
tively few mergers were intended simply to replace management. Instead, companies
began to look once more at the possible benefits from combining two businesses.
DO MERGERS GENERATE NET BENEFITS?
There are undoubtedly good acquisitions and bad acquisitions, but economists find it
hard to agree on whether acquisitions are beneficial on balance. We do know that merg-
ers generate substantial gains to stockholders of acquired firms.
Since buyers seem roughly to break even and sellers make substantial gains, it seems
that there are positive gains to mergers. But not everybody is convinced. Some believe
that investors analyzing mergers pay too much attention to short-term earnings gains
and don’t notice that these gains are at the expense of long-term prospects.
16 For a history of the role of Milken in the development of the junk bond market, see C. Bruck, The Preda-
tor’s Ball: The Junk Bond Raiders and the Man Who Staked Them (New York: Simon and Schuster, 1988).
590 SECTION SIX
Since we can’t observe how companies would have fared in the absence of a merger,
it is difficult to measure the effects on profitability. Studies of recent merger activity
suggest that mergers do seem to improve real productivity. For example, Healy, Palepu,
and Ruback examined 50 large mergers between 1979 and 1983 and found an average
increase in the companies’ pretax returns of 2.4 percentage points.17 They argue that this
gain came from generating a higher level of sales from the same assets. There was no
evidence that the companies were mortgaging their long-term futures by cutting back
on long-term investments; expenditures on capital equipment and research and devel-
opment tracked the industry average.
If you are concerned with public policy toward mergers, you do not want to look only
at their impact on the shareholders of the companies concerned. For instance, we have
already seen that in the case of RJR Nabisco some part of the shareholders’ gain was at
the expense of the bondholders and the Internal Revenue Service (through the enlarged
interest tax shield). The acquirer’s shareholders may also gain at the expense of the tar-
get firm’s employees, who in some cases are laid off or are forced to take pay cuts after
takeovers.
Many people believe that the merger wave of the 1980s led to excessive debt levels
and left many companies ill-equipped to survive a recession. Also, many savings and
loan companies and some large insurance firms invested heavily in junk bonds. De-
faults on these bonds threatened, and in some cases extinguished, their solvency.
Perhaps the most important effect of acquisition is felt by the managers of compa-
nies that are not taken over. For example, one effect of LBOs was that the managers of
even the largest corporations could not feel safe from challenge. Perhaps the threat of
takeover spurs the whole of corporate America to try harder. Unfortunately, we don’t
know whether on balance the threat of merger makes for more active days or sleepless
nights.
We do know that merger activity is very costly. For example, in the RJR Nabisco
buyout, the total fees paid to the investment banks, lawyers, and accountants amounted
to over $1 billion.
Even if the gains to the community exceed these costs, one wonders whether the
same benefits could not be achieved more cheaply another way. For example, are lever-
aged buyouts necessary to make managers work harder? Perhaps the problem lies in the
way that many corporations reward and penalize their managers. Perhaps many of the
gains from takeover could be captured by linking management compensation more
closely to performance.
Summary
In what ways do companies change the composition of their ownership or man-
agement?
If the board of directors fails to replace an inefficient management, there are four ways to | Brealey |
effect a change: (1) shareholders may engage in a proxy contest to replace the board; (2)
the firm may be acquired by another; (3) the firm may be purchased by a private group of
investors in a leveraged buyout, or (4) it may sell off part of its operations to another
Mergers, Acquisitions, and Corporate Control 591
company. There are three ways for one firm to acquire another: (1) it can merge all the
assets and liabilities of the target firm into those of its own company; (2) it can buy the
stock of the target; or (3) it can buy the individual assets of the target. The offer to buy the
stock of the target firm is called a tender offer. The purchase of the stock or assets of
another firm is called an acquisition.
Why may it make sense for companies to merge?
A merger may be undertaken in order to replace an inefficient management. But sometimes
two business may be more valuable together than apart. Gains may stem from economies of
scale, economies of vertical integration, the combination of complementary resources, or
redeployment of surplus funds. We don’t know how frequently these benefits occur, but they
do make economic sense. Sometimes mergers are undertaken to diversify risks or artificially
increase growth of earnings per share. These motives are dubious.
How should the gains and costs of mergers to the acquiring firm be measured?
A merger generates an economic gain if the two firms are worth more together than apart.
The gain is the difference between the value of the merged firm and the value of the two
firms run independently. The cost is the premium that the buyer pays for the selling firm
over its value as a separate entity. When payment is in the form of shares, the value of this
payment naturally depends on what those shares are worth after the merger is complete. You
should go ahead with the merger if the gain exceeds the cost.
What are some takeover defenses?
Mergers are often amicably negotiated between the management and directors of the two
companies; but if the seller is reluctant, the would-be buyer can decide to make a tender
offer for the stock. We sketched some of the offensive and defensive tactics used in takeover
battles. These defenses include shark repellents (changes in the company charter meant to
make a takeover more difficult to achieve), poison pills (measures that make takeover of the
firm more costly), and the search for white knights (the attempt to find a friendly acquirer
before the unfriendly one takes over the firm).
Do mergers increase efficiency and how are the gains from mergers distributed be-
tween shareholders of the acquired and acquiring firms?
We observed that when the target firm is acquired, its shareholders typically win: target
firms’ shareholders earn abnormally large returns. The bidding firm’s shareholders roughly
break even. This suggests that the typical merger appears to generate positive net benefits,
but competition among bidders and active defense by management of the target firm pushes
most of the gains toward selling shareholders.
Mergers seem to generate economic gains, but they are also costly. Investment bankers,
lawyers, and arbitrageurs thrived during the 1980s merger and LBO boom. Many companies
were left with heavy debt burdens and had to sell assets or improve performance to stay
solvent. By the end of 1990, the new-issue junk bond market had dried up, and the
corporate jousting field was strangely quiet. But not for long. As we write this material early
in 2000, stock markets and mergers are again booming.
What are some of the motivations for leveraged and management buyouts of the
firm?
In a leveraged buyout (LBO) or management buyout (MBO), all public shares are
repurchased and the company “goes private.” LBOs tend to involve mature businesses with
ample cash flow and modest growth opportunities. LBOs and other debt-financed takeovers
592 SECTION SIX
are driven by a mixture of motives, including (1) the value of interest tax shields; (2)
transfers of value from bondholders, who may see the value of their bonds fall as the firm | Brealey |
piles up more debt; and (3) the opportunity to create better incentives for managers and
employees, who have a personal stake in the company. In addition, many LBOs have been
designed to force firms with surplus cash to distribute it to shareholders rather than plowing
it back. Investors feared such companies would otherwise channel free cash flow into
negative-NPV investments.
Related Web
Links
www.secdata.com/ Good source of merger data
www.mergernetwork.com/ Information about mergers and acquisitions
http://viking.som.yale.edu/will/finman540/acquira3.htm A sample case looking at an acquisi-
tion
www.lens-inc.com/ Active corporate governance strategies
www.corpgov.net/ The Corporate Governance Network
Key Terms
proxy contest
merger
tender offer
acquisition
leveraged buyout (LBO)
management buyout (MBO)
poison pill
white knight
shark repellent
Quiz
1. Merger Motives. Which of the following motives for mergers make economic sense?
a. Merging to achieve economies of scale.
b. Merging to reduce risk by diversification.
c. Merging to redeploy cash generated by a firm with ample profits but limited growth op-
portunities.
d. Merging to increase earnings per share.
2. Merger Motives. Explain why it might make good sense for Northeast Heating and North-
east Air Conditioning to merge into one company.
3. Empirical Facts. True or false?
a. Sellers almost always gain in mergers.
b. Buyers almost always gain in mergers.
c. Firms that do unusually well tend to be acquisition targets.
d. Merger activity in the United States varies dramatically from year to year.
e. On the average, mergers produce substantial economic gains.
f. Tender offers require the approval of the selling firm’s management.
g. The cost of a merger is always independent of the economic gain produced by the merger.
4. Merger Tactics. Connect each term to its correct definition or description:
A. LBO
B. Poison pill
C. Tender offer
D. Shark repellent
E. Proxy contest
1. Attempt to gain control of a firm by winning the votes of its
stockholders.
2. Changes in corporate charter designed to deter unwelcome
takeover.
3. Friendly potential acquirer sought by a threatened target firm.
Practice
Problems
Mergers, Acquisitions, and Corporate Control 593
F. White knight
4. Shareholders are issued rights to buy shares if bidder acquires
large stake in the firm.
5. Offer to buy shares directly from stockholders.
6. Company or business bought out by private investors, largely
debt-financed.
5. Empirical Facts. True or false?
a. One of the first tasks of an LBO’s financial manager is to pay down debt.
b. Shareholders of bidding companies earn higher abnormal returns when the merger is fi-
nanced with stock than in cash-financed deals.
c. Targets for LBOs in the 1980s tended to be profitable companies in mature industries
with limited investment opportunities.
6. Merger Gains. Acquiring Corp. is considering a takeover of Takeover Target Inc. Acquiring
has 10 million shares outstanding, which sell for $40 each. Takeover Target has 5 million
shares outstanding, which sell for $20 each. If the merger gains are estimated at $20 million,
what is the highest price per share that Acquiring should be willing to pay to Takeover Tar-
get shareholders?
7. Mergers and P/E Ratios. If Acquiring Corp. from problem 6 has a price-earnings ratio of
12, and Takeover Target has a P/E ratio of 8, what should be the P/E ratio of the merged
firm? Assume in this case that the merger is financed by an issue of new Acquiring Corp.
shares. Takeover Target will get one Acquiring share for every two Takeover Target shares
held.
8. Merger Gains and Costs. Velcro Saddles is contemplating the acquisition of Pogo Ski
Sticks, Inc. The values of the two companies as separate entities are $20 million and $10 mil-
lion, respectively. Velcro Saddles estimates that by combining the two companies, it will re-
duce marketing and administrative costs by $500,000 per year in perpetuity. Velcro Saddles
is willing to pay $14 million cash for Pogo. The opportunity cost of capital is 10 percent.
| Brealey |
a. What is the gain from merger?
b. What is the cost of the cash offer?
c. What is the NPV of the acquisition under the cash offer?
9. Stock versus Cash Offers. Suppose that instead of making a cash offer as in problem 8, Vel-
cro Saddles considers offering Pogo shareholders a 50 percent holding in Velcro Saddles.
a. What is the value of the stock in the merged company held by the original Pogo share-
holders?
b. What is the cost of the stock alternative?
c. What is its NPV under the stock offer?
10. Merger Gains. Immense Appetite, Inc., believes that it can acquire Sleepy Industries and
improve efficiency to the extent that the market value of Sleepy will increase by $5 million.
Sleepy currently sells for $20 a share, and there are 1 million shares outstanding.
a. Sleepy’s management is willing to accept a cash offer of $25 a share. Can the merger be
accomplished on a friendly basis?
b. What will happen if Sleepy’s management holds out for an offer of $28 a share?
11. Mergers and P/E Ratios. Castles in the Sand currently sells at a price-earnings multiple of
10. The firm has 2 million shares outstanding, and sells at a price per share of $40. Firm
594 SECTION SIX
Foundation has a P/E multiple of 8, has 1 million shares outstanding, and sells at a price per
share of $20.
a. If Castles acquires the other firm by exchanging one of its shares for every two of Firm
Foundation’s, what will be the earnings per share of the merged firm?
b. What should be the P/E of the new firm if the merger has no economic gains? What will
happen to Castles’s price per share? Show that shareholders of neither Castles nor Firm
Foundation realize any change in wealth.
c. What will happen to Castles’s price per share if the market does not realize that the P/E
ratio of the merged firm ought to differ from Castles’s premerger ratio?
d. How are the gains from the merger split between shareholders of the two firms if the mar-
ket is fooled as in part (c)?
12. Stock versus Cash Offers. Sweet Cola Corp. (SCC) is bidding to take over Salty Dog Pret-
zels (SDP). SCC has 3,000 shares outstanding, selling at $50 per share. SDP has 2,000
shares outstanding, selling at $17.50 a share. SCC estimates the economic gain from the
merger to be $10,000.
a. If SDP can be acquired for $20 a share, what is the NPV of the merger to SCC?
b. What will SCC sell for when the market learns that it plans to acquire SDP for $20 a
share? What will SDP sell for? What are the percentage gains to the shareholders of each
firm?
c. Now suppose that the merger takes place through an exchange of stock. Based on the
premerger prices of the firms, SCC sells for $50, so instead of paying $20 cash, SCC is-
sues .40 of its shares for every SDP share acquired. What will be the price of the merged
firm?
d. What is the NPV of the merger to SCC when it uses an exchange of stock? Why does
your answer differ from part (a)?
Challenge
Problems
13. Bootstrap Game. The Muck and Slurry merger has fallen through (see Section 6.3). But
World Enterprises is determined to report earnings per share of $2.67. It therefore acquires
the Wheelrim and Axle Company. You are given the following facts:
Earnings per share
Price per share
Price-earnings ratio
Number of shares
Total earnings
Total market value
World
Enterprises
$2.00
$40.00
20
100,000
$200,000
$4,000,000
Wheelrim
and Axle
$2.50
$25.00
10
200,000
$500,000
$5,000,000
Merged
Firm
$2.67
_____
_____
_____
_____
_____
Once again there are no gains from merging. In exchange for Wheelrim and Axle shares,
World Enterprises issues just enough of its own shares to ensure its $2.67 earnings per share
objective.
a. Complete the above table for the merged firm.
b. How many shares of World Enterprises are exchanged for each share of Wheelrim and
Axle?
c. What is the cost of the merger to World Enterprises?
d. What is the change in the total market value of those World Enterprises shares that were
outstanding before the merger?
Mergers, Acquisitions, and Corporate Control 595
14. Merger Gains and Costs. As treasurer of Leisure Products, Inc., you are investigating the
| Brealey |
possible acquisition of Plastitoys. You have the following basic data:
Leisure Products
Plastitoys
Forecast earnings per share
Forecast dividend per share
Number of shares
Stock price
$5.00
$3.00
1,000,000
$90.00
$1.50
$.80
600,000
$20.00
You estimate that investors currently expect a steady growth of about 6 percent in Plastitoys’s
earnings and dividends. You believe that Leisure Products could increase Plastitoys’s growth
rate to 8 percent per year, without any additional capital investment required.
a. What is the gain from the acquisition?
b. What is the cost of the acquisition if Leisure Products pays $25 in cash for each share of
Plastitoys?
c. What is the cost of the acquisition if Leisure Products offers one share of Leisure Prod-
ucts for every three shares of Plastitoys?
d. How would the cost of the cash offer and the share offer alter if the expected growth rate
of Plastitoys were not increased by the merger?
1 a. Horizontal merger. IBM is in the same industry as Apple Computer.
b. Conglomerate merger. Apple Computer and Stop & Shop are in different industries.
c. Vertical merger. Stop & Shop is expanding backward to acquire one of its suppliers,
Campbell Soup.
d. Conglomerate merger. Campbell Soup and IBM are in different industries.
2 Given current earnings of $2.00 a share, and a share price of $10, Muck and Slurry would
have a market value of $1,000,000 and a price-earnings ratio of only 5. It can be acquired
for only half as many shares of World Enterprises, 25,000 shares. Therefore, the merged
firm will have 125,000 shares outstanding and earnings of $400,000, resulting in earnings
per share of $3.20, higher than the $2.67 value in the third column of Table 6..2.
3 The cost of the merger is $4 million: the $4 per share premium offered to Goldfish share-
holders times 1 million shares. If the merger has positive NPV to Killer Shark, the gain
must be greater than $4 million.
4 Yes. Look again at Table 6.4. Total market value is still $540, but Cislunar will have to issue
1 million shares to complete the merger. Total shares in the merged firm will be 11 million.
The postmerger share price is $49.09, so Cislunar and its shareholders still come out ahead.
Solutions to
Self-Test
Questions
MINICASE
McPhee Food Halls operated a chain of supermarkets in the west
of Scotland. The company had had a lackluster record and, since
the death of its founder in late 1998, it had been regarded as a
prime target for a takeover bid. In anticipation of a bid, McPhee’s
share price moved up from £4.90 in March to a 12-month high
of £5.80 on June 10, despite the fact that the London stock mar-
ket index as a whole was largely unchanged.
Almost nobody anticipated a bid coming from Fenton, a di-
versified retail business with a chain of clothing and department
stores. Though Fenton operated food halls in several of its de-
partment stores, it had relatively little experience in food retail-
ing. Fenton’s management had, however, been contemplating a
merger with McPhee for some time. They not only felt that they
could make use of McPhee’s food retailing skills within their
596 SECTION SIX
department stores, but they believed that better management and
inventory control in McPhee’s business could result in cost sav-
ings worth £10 million.
Fenton’s offer of 8 Fenton shares for every 10 McPhee shares
was announced after the market close on June 10. Since McPhee
had 5 million shares outstanding, the acquisition would add an
additional 5 × (8/10) = 4 million shares to the 10 million Fenton
shares that were already outstanding. While Fenton’s manage-
ment believed that it would be difficult for McPhee to mount a
successful takeover defense, the company and its investment
bankers privately agreed that the company could afford to raise
the offer if it proved necessary.
Investors were not persuaded of the benefits of combining a
supermarket with a department store company, and on June 11
Fenton’s shares opened lower and drifted down £.10 to close the | Brealey |
day at £7.90. McPhee’s shares, however, jumped to £6.32 a share.
Fenton’s financial manager was due to attend a meeting with
the company’s investment bankers that evening, but before doing
so, he decided to run the numbers once again. First he reesti-
mated the gain and cost of the merger. Then he analyzed that
day’s fall in Fenton’s stock price to see whether investors be-
lieved there were any gains to be had from merging. Finally, he
decided to revisit the issue of whether Fenton could afford to
raise its bid at a later stage. If the effect was simply a further fall
in the price of Fenton stock, the move could be self-defeating.
INTERNATIONAL
FINANCIAL MANAGEMENT
Foreign Exchange Markets
Some Basic Relationships
Exchange Rates and Inflation
Inflation and Interest Rates
Interest Rates and Exchange Rates
The Forward Rate and the Expected Spot Rate
Some Implications
Hedging Exchange Rate Risk
International Capital Budgeting
Net Present Value Analysis
The Cost of Capital for Foreign Investment
Avoiding Fudge Factors
Summary
597
T
hus far we have talked principally about doing business at home. But
many companies have substantial overseas interests. Of course the ob-
jectives of international financial management are still the same. You
want to buy assets that are worth more than they cost, and you want to pay for
them by issuing liabilities that are worth less than the money raised. But when you
try to apply these criteria to an international business, you come up against some new
wrinkles.
You must, for example, know how to deal with more than one currency. Therefore
we open this material with a look at foreign exchange markets.
The financial manager must also remember that interest rates differ from country to
country. For example, in late 1999 the short-term rate of interest was about .1 percent
in Japan, 6 percent in the United States, and 3 percent in the euro countries. We will dis-
cuss the reasons for these differences in interest rates, along with some of the implica-
tions for financing overseas operations.
Exchange rate fluctuations can knock companies off course and transform black ink
into red. We will therefore discuss how firms can protect themselves against exchange
risks.
We will also discuss how international companies decide on capital investments.
How do they choose the discount rate? You’ll find that the basic principles of capital
budgeting are the same as for domestic projects, but there are a few pitfalls to watch for.
After studying this material you should be able to
(cid:1) Understand the difference between spot and forward exchange rates.
(cid:1) Understand the basic relationships between spot exchange rates, forward exchange
rates, interest rates, and inflation rates.
(cid:1) Formulate simple strategies to protect the firm against exchange rate risk.
(cid:1) Perform an NPV analysis for projects with cash flows in foreign currencies.
Foreign Exchange Markets
An American company that imports goods from Switzerland may need to exchange
its dollars for Swiss francs in order to pay for its purchases. An American company
exporting to Switzerland may receive Swiss francs, which it sells in exchange for
dollars. Both firms must make use of the foreign exchange market, where currencies
are traded.
The foreign exchange market has no central marketplace. All business is conducted
by computer and telephone. The principal dealers are the large commercial banks, and
598
EXCHANGE RATE
Amount of one currency
needed to purchase one unit
of another.
TABLE 6.5
Currency exchange rates on
October 6, 1999
International Financial Management 599
any corporation that wants to buy or sell currency usually does so through a commer-
cial bank.
Turnover in the foreign exchange markets is huge. In London alone about $640 bil-
lion of currency changes hands each day. That is equivalent to an annual turnover of
$159 trillion ($159,000,000,000,000). New York and Tokyo together account for a fur- | Brealey |
ther $500 billion of turnover per day. Compare this to trading volume of the New York
Stock Exchange, where no more than $30 billion of stock might change hands on a typ-
ical day.
Suppose you ask someone the price of bread. He may tell you that you can buy two
loaves for a dollar, or he may say that one loaf costs 50 cents. Similarly, if you ask a for-
eign exchange dealer to quote you a price for Ruritanian francs, she may tell you that
you can buy two francs for a dollar or that one franc costs $.50. The first quote (the
number of francs that you can buy for a dollar) is known as an indirect quote of the ex-
change rate. The second quote (the number of dollars that it costs to buy one franc) is
known as a direct quote. Of course, both quotes provide the same information. If you
can buy two francs for a dollar, then you can easily calculate that the cost of one franc
is 1/2.0 = $.50.
Now look at Table 6.5, which has been adapted from the daily table of exchange rates
in the London Financial Times. The first column of figures in the table shows the ex-
change rate for a number of countries on October 6, 1999. By custom, the prices of
most currencies are expressed as indirect quotes. Thus you can see that you could buy
9.438 Mexican pesos for one dollar. However, to make things confusing, the price of the
euro and the British pound are generally expressed as direct quotes. So Table 6.5 shows
that it cost $1.0707 to buy one euro ( 1).
Forward Rate
Spot Rate
3 Months
1 Year
Europe
EMU (euro)
Greece (drachma)
Sweden (krona)
Switzerland (franc)
U.K. (pound)
Americas
Canada
Mexico
Asia/Pacific
Australia (dollar)
Hong Kong (dollar)
Indonesia (rupiah)
Japan (yen)
Singapore (dollar)
1.0707
306.675
8.1400
1.4865
1.6566
1.4703
9.4380
1.5148
7.7681
7800.00
107.520
1.6790
1.0785
307.75
8.0875
1.471
1.6573
1.4662
9.853
1.5139
7.7687
7952.5
105.865
1.665
1.0979
314.125
7.988
1.4331
1.6535
1.4594
11.153
1.5133
7.896
8487.5
101.3
1.6358
Note: Rates show the number of units of foreign currency per dollar (indirect quotes), except for the euro
and the U.K. pound, which show the number of dollars per unit of foreign currency (direct quotes).
Source: From Financial Times, October 7, 1999. Used by permission of Financial Times.
600 SECTION SIX
(cid:1) EXAMPLE 5
A Yen for Trade
How many yen will it cost a Japanese importer to purchase $1,000 worth of oranges
from a California farmer? How many dollars will it take for that farmer to buy a Japa-
nese VCR priced in Japan at 30,000 yen (¥)?
The exchange rate is ¥107.52 per dollar. The $1,000 of oranges will require the
Japanese importer to come up with 1,000 × 107.52 = ¥107,520. The VCR will require
the American importer to come up with 30,000/107.52 = $279.
(cid:1) Self-Test 1
Use the exchange rates in Table 6.5. How many euros can you buy for one dollar (an in-
direct quote)? How many dollars can you buy for one yen (a direct quote)?
SPOT RATE OF
EXCHANGE Exchange
rate for an immediate
transaction.
(cid:1) Self-Test 2
The exchange rates in the first column of figures in Table 6.5 are the prices of cur-
rency for immediate delivery. These are known as spot rates of exchange. For exam-
ple, the spot rate of exchange for Mexican pesos is pesos9.4380/$. In other words, it
cost 9.438 Mexican pesos to buy one dollar.
Many countries allow their currencies to float, so that the exchange rate fluctuates
from day to day, and from minute to minute. When the currency increases in value,
meaning that you need less of the foreign currency to buy one dollar, the currency is
said to appreciate. When you need more of the currency to buy one dollar, the currency
is said to depreciate.
Table 6.5 shows the exchange rate for the Swiss franc on October 6, 1999. The next day
the spot rate of exchange for the Swiss franc was SFr1.4852/$. Thus you could buy
fewer Swiss francs for your dollar than one day earlier. Had the Swiss franc appreciated
or depreciated?
Some countries try to avoid fluctuations in the value of their currency and seek in-
stead to maintain a fixed exchange rate. But fixed rates seldom last forever. If every- | Brealey |
body tries to sell the currency, eventually the country will be forced to allow the cur-
rency to depreciate. When this happens, exchange rates can change dramatically. For
example, when Indonesia gave up trying to fix its exchange rate in fall 1997, the value
of the Indonesian rupiah fell by 80 percent in a few months.
These fluctuations in exchange rates can get companies into hot water. For example,
suppose you have agreed to buy a shipment of Japanese VCRs for ¥100 million and to
make the payment when you take delivery of the VCRs at the end of 12 months. You
could wait until the 12 months have passed and then buy 100 million yen at the spot ex-
change rate. If the spot rate is unchanged at ¥107.52/$, then the VCRs will cost you 100
million/107.52 = $930,060. But you are taking a risk by waiting, for the yen may be-
come more expensive. For example, if the yen appreciates to ¥100/$, then you will have
to pay out 100 million/100 = $1 million.
You can avoid exchange rate risk and fix the dollar cost of VCRs by “buying the yen
forward,” that is, by arranging now to buy yen in the future. A foreign exchange forward
contract is an agreement to exchange at a future date a given amount of currency at an
FORWARD EXCHANGE
RATE Exchange rate for a
forward transaction.
International Financial Management 601
exchange rate agreed to today. The forward exchange rate is the price of currency for
delivery at some time in the future. The second and third columns in Table 6.5 show 3-
month and 1-year forward exchange rates. For example, the 1-year forward rate for the
yen is quoted at 101.3 yen per dollar. If you buy 100 million yen forward, you don’t pay
anything today; you simply fix today the price which you will pay for your yen in the
future. At the end of the year you receive your 100 million yen and hand over 100 mil-
lion/101.3 = $987,167 in payment.
Notice that if you buy Japanese yen forward, you get fewer yen for your dollar than
if you buy spot. In this case, the yen is said to trade at a forward premium relative to the
dollar. Expressed as a percentage, the 1-year forward premium is
107.52 – 101.3 × 100 = 6.14%
101.3
You could also say that the dollar was selling at a forward discount of about 6.14 per-
cent.1
A forward purchase or sale is a made-to-order transaction between you and the bank.
It can be for any currency, any amount, and any delivery day. You could buy, say, 99,999
Vietnamese dong or Haitian gourdes for a year and a day forward as long as you can
find a bank ready to deal. Most forward transactions are for 6 months or less, but banks
are prepared to buy or sell the major currencies for up to 10 years forward.
There is also an organized market for currency for future delivery known as the cur-
rency futures market. Futures contracts are highly standardized versions of forward con-
tracts—they exist only for the main currencies, they are for specified amounts, and
choice of delivery dates is limited. The advantage of this standardization is that there is
a very low-cost market in currency futures. Huge numbers of contracts are bought and
sold daily on the futures exchanges.
(cid:1) Self-Test 3
A skiing vacation in Switzerland costs SFr1,500.
a. How many dollars does that represent? Use the exchange rates in Table 6.5.
b. Suppose that the dollar depreciates by 10 percent relative to the Swiss franc, so that
each dollar buys 10 percent fewer Swiss francs than before. What will be the new
value of the indirect exchange rate?
c. If the Swiss vacation continues to cost the same number of Swiss francs, what will
happen to the cost in dollars?
d. If the tour company that is offering the vacation keeps the price fixed in dollars, what
will happen to the number of Swiss francs that it will receive?
1 Here is a minor point that sometimes causes confusion. To calculate the forward premium, we divide by the
forward rate as long as the exchange quotes are indirect. If you use direct quotes, the correct formula is
Forward premium =
forward rate – spot rate
spot rate
In our example, the corresponding direct quote for spot yen is 1/107.52 = .009301, while the direct forward | Brealey |
quote is 1/101.3 = .009872. Substituting these rates in our revised formula gives
Forward premium =
.009872 – .009301
.009301
= .0614, or 6.14%
The two methods give the same answer.
602 SECTION SIX
Some Basic Relationships
The financial manager of an international business must cope with fluctuations in ex-
change rates and must be aware of the distinction between spot and forward exchange
rates. She must also recognize that two countries may have different interest rates. To
develop a consistent international financial policy, the financial manager needs to un-
derstand how exchange rates are determined and why one country may have a lower in-
terest rate than another. These are complex issues, but as a first cut we suggest that you
think of spot and forward exchange rates, interest rates, and inflation rates as being
linked as shown in Figure 6.1. Let’s explain.
EXCHANGE RATES AND INFLATION
Consider first the relationship between changes in the exchange rate and inflation
rates (the two boxes on the right of Figure 6.1). The idea here is simple: if country X
suffers a higher rate of inflation than country Y, then the value of X’s currency will de-
cline relative to Y’s. The decline in value shows up in the spot exchange rate for X’s cur-
rency.
But let’s slow down and consider why changes in inflation and spot interest rates are
linked. Think first about the prices of the same good or service in two different coun-
tries and currencies.
Suppose you notice that gold can be bought in New York for $300 an ounce and sold
in Mexico City for 4,000 pesos an ounce. If there are no restrictions on the import of
gold, you could be onto a good thing. You buy gold for $300 and put it on the first plane
to Mexico City, where you sell it for 4,000 pesos. Then (using the exchange rates from
Table 6.5) you can exchange your 4,000 pesos for 4,000/9.438 = $424. You have made
a gross profit of $124 an ounce. Of course, you have to pay transportation and insur-
ance costs out of this, but there should still be something left over for you.
You returned from your trip with a sure-fire profit. But sure-fire profits don’t exist—
not for long. As others notice the disparity between the price of gold in Mexico and the
FIGURE 6.1
Some simple theories linking
spot and forward exchange
rates, interest rates, and
inflation rates.
Difference in
interest rates
1 (cid:1) rpeso
1 (cid:1) r$
equals
Difference between forward
and spot exchange rates
fpeso/$
speso/$
equals
equals
Expected difference
in inflation rates
1 (cid:1) ipeso
1 (cid:1) i$
equals
Expected change in
spot exchange rates
E(speso/$)
speso/$
TABLE 6.6
Price of a Big Mac in
different countries
Price in Local
Currency
Exchange Rate
(currency/dollar)
Local Price
Converted to Dollars
International Financial Management 603
Australia
Canada
China
France
Germany
Hong Kong
Israel
Italy
Japan
Malaysia
Mexico
Poland
Russia
Switzerland
United Kingdom
United States
A$2.65
C$2.99
Yuan 9.90
FFr17.50
DM4.95
HK$10.2
Shekel 13.9
Lire4,500
¥294
M$4.52
Peso19.9
Zloty5.50
Ruble33.5
SFr5.90
£1.90
1.59
1.51
8.28
6.10
1.82
7.75
4.04
1,799
120
3.80
9.54
3.98
24.7
1.48
.621
1.66
1.98
1.20
2.87
2.72
1.32
3.44
2.50
2.44
1.19
2.09
1.38
1.35
3.97
3.07
2.43
Source: © 1999 The Economist Newspaper Group, Inc. Reprinted with permission. www.economist.com.
price in New York, the price will be forced down in Mexico and up in New York until
the profit opportunity disappears. This ensures that the dollar price of gold is about the
same in the two countries.2
Gold is a standard and easily transportable commodity, but to some degree you
might expect that the same forces would be acting to equalize the domestic and foreign
prices of other goods. Those goods that can be bought more cheaply abroad will be im-
ported, and that will force down the price of the domestic product. Similarly, those
goods that can be bought more cheaply in the United States will be exported, and that
will force down the price of the foreign product.
This conclusion is often called the law of one price. Just as the price of goods in
Safeway must be roughly the same as the price of goods in A&P, so the price of goods | Brealey |
in Mexico when converted into dollars must be roughly the same as the price in the
United States:
Dollar price of goods in USA =
peso price of goods in Mexico
number of pesos per dollar
$300 =
peso price of gold in Mexico
9.438
Price of gold in Mexico = 300 × 9.438 = 2,831 pesos
No one who has compared prices in foreign stores with prices at home really believes
that the law of one price holds exactly. Look at the first column of Table 6.6, which
2 Activity of this kind is known as arbitrage. The arbitrageur makes a riskless profit by noticing discrepan-
cies in prices.
LAW OF ONE PRICE
Theory that prices of goods
in all countries should be
equal when translated to a
common currency.
604 SECTION SIX
shows the price of a Big Mac in different countries in 1999. Using the exchange rates
at that time (second column), we can convert the local price to dollars (third column).
You can see that the price varies considerably across countries. For example, Big Macs
were 60 percent more expensive in Switzerland than in the United States, but they were
about half the price in Malaysia.3
This suggests a possible way to make a quick buck. Why don’t you buy a hamburger-
to-go in Malaysia for $1.19 and take it for resale to Switzerland where the price in dol-
lars is $3.97? The answer, of course, is that the gain would not cover the costs. The law
of one price works very well for commodities like gold where transportation costs are
relatively small; it works far less well for Big Macs and very badly indeed for haircuts
and appendectomies, which cannot be transported at all.
(cid:1) EXAMPLE 2
The Beer Standard
TABLE 6.7
The price of a beer in
different countries
There are very few McDonald’s branches in Africa, so we can’t use Big Macs to test the
law of one price there. But barley beer is a common and relatively homogeneous prod-
uct throughout Africa. So we can test the law of one price using the beer standard.
Table 6.7 shows the price of a bottle of beer in several African countries expressed
in local currencies and converted into South African rand using the spot exchange rate.
For example, beer in Kenya cost 41.25 shillings; at an exchange rate of 10.27 Kenyan
shillings per rand, this is equivalent to a price of 41.25/10.27 = 4.02 rand. This is 1.75
times the cost of beer in South Africa; for the costs to be equal, the shilling would need
to depreciate by 75 percent to a new exchange rate of 10.27 × 1.75 = 17.9 shillings per
rand. Therefore, we might say that this comparison suggests the shilling is 75 percent
overvalued against the rand.
Beer Prices
In Local
Currency
In
Rand
Actual Rand
Exchange Rate,
March 1999
Under(–)/Over(+)
Valuation
against the
Rand, %
Rand2.30
Pula2.20
Cedi1,200
Shilling41.25
Kwacha18.50
Rupee15.00
N$2.50
Kwacha1,200
Z$9.00
2.30
2.94
3.17
4.02
2.66
3.72
2.50
3.52
1.46
0.75
379.10
10.27
6.96
4.03
1.00
340.68
6.15
28
38
75
16
62
9
53
–36
Country
South Africa
Botswana
Ghana
Kenya
Malawi
Mauritius
Namibia
Zambia
Zimbabwe
Source: The Economist, May 8, 1999.
3 Of course, it could also be that Big Macs come with a bigger smile in Switzerland. If the quality of the ham-
burgers or the service differs, we are not comparing like with like.
International Financial Management 605
FIGURE 6.2
Countries with high inflation
rates tend to see their
currencies depreciate.
20
0
(cid:2)20
(cid:2)40
(cid:2)60
(cid:2)80
t
n
e
c
r
e
p
,
e
t
a
r
e
g
n
a
h
c
x
e
n
i
e
g
n
a
h
c
e
v
i
t
a
e
r
l
l
a
u
n
n
A
(cid:2)100
(cid:2)100
Russia
(cid:2)40
(cid:2)80
Annual relative change in purchasing power, percent
(cid:2)20
(cid:2)60
0
United
States
20
PURCHASING POWER
PARITY (PPP)
Theory
that the cost of living in
different countries is equal,
and exchange rates adjust to
offset inflation differentials
across countries.
A weaker version of the law of one price is known as purchasing power parity, or
PPP. PPP states that although some goods may cost different amounts in different coun-
tries, the general cost of living should be the same in any two countries.
Purchasing power parity implies that the relative costs of living in two
countries will not be affected by differences in their inflation rates. Instead, | Brealey |
the different inflation rates in local currencies will be offset by changes in the
exchange rate between the two currencies.
For example, between 1993 and 1998 Russia experienced high inflation. Each year
the purchasing power of the ruble declined by nearly 35 percent compared with other
countries’ currencies. As prices in Russia increased, Russian exporters would have
found it impossible to sell their goods if the exchange rate had not also changed. But,
of course, the exchange rate did adjust. In fact each year the ruble bought over 33 per-
cent less foreign currency than before. Thus a 35 percent annual decline in purchasing
power was offset by a 33 percent decline in the value of the Russian currency.
In Figure 6.2 we have plotted the relative change in purchasing power for a sample
of countries against the change in the exchange rate. Russia is toward the bottom left-
hand corner; the United States is closer to the top right. You can see that although the
relationship is far from exact, large differences in inflation rates are generally accom-
panied by an offsetting change in the exchange rate. In fact, if you have to make a long-
term forecast of the exchange rate, it is very difficult to do much better than to assume
that it will offset the effect of any differences in the inflation rates.
If purchasing power parity holds, then your forecast of the difference in inflation
rates is also your best forecast of the change in the spot rate of exchange. Thus the ex-
pected difference between inflation rates in Mexico and the United States is given by
the right-hand boxes in Figure 6.1:
606 SECTION SIX
(cid:1) Self-Test 4
INTERNATIONAL
FISHER EFFECT
Theory that real interest rates
in all countries should be
equal, with differences in
nominal rates reflecting
differences in expected
inflation.
Expected difference
in inflation rates
1 + ipeso
1 + i$
equals
Expected change in
spot exchange rate
E(speso/$)
speso/$
For example, if inflation is 2 percent in the United States and 20 percent in Mexico,
then purchasing power parity implies that the expected spot rate for the peso at the end
of the year is peso11.10/$:
Current × expected difference
in inflation rates
spot rate
9.438 × 1.20
1.02
= expected spot rate
= 11.10
Suppose that gold currently costs $330 an ounce in the United States and £220 an ounce
in Great Britain.
a. What must be the pound/dollar exchange rate?
b. Suppose that gold prices rise by 2 percent in the United States and by 5 percent in
Great Britain. What will be the price of gold in the two currencies at the end of the
year? What must be the exchange rate at the end of the year?
c. Show that at the end of the year each dollar buys about 3 percent more pounds, as
predicted by PPP.
INFLATION AND INTEREST RATES
Interest rates in Mexico in 1999 were about 25.25 percent. So why didn’t you (and a few
million other investors) put your cash in a Mexican bank deposit where the return
seemed to be so attractive?
The answer lies in the distinction that we made earlier between nominal and real
rates of interest. Bank deposits usually promise you a fixed nominal rate of interest but
they don’t promise what that money will buy. If you invested 100 pesos for a year at an
interest rate of 25.25 percent, you would have 25.25 percent more pesos at the end of
the year than you did at the start. But you wouldn’t be 25.25 percent better off. A good
part of the gain would be needed to compensate for inflation.
The nominal rate of interest in 1999 was much lower in the United States, but then so
was the inflation rate. The real rates of interest were much closer than the nominal rates.
There is a general law at work here. Just as water always flows downhill, so
capital always flows where returns are greatest. But it is the real returns that
concern investors, not the nominal returns. Two countries may have different
nominal interest rates but the same expected real interest rate.
Do you remember Irving Fisher’s theory that changes in the expected inflation rate | Brealey |
are reflected in the nominal interest rate? We have just described here the international
Fisher effect—international variations in the expected inflation rate are reflected in the
nominal interest rates:
International Financial Management 607
Difference in
interest rates
1 + rpeso
1 + r$
equals
Expected differences
in inflation rates
1 + ipeso
1 + i$
In other words, capital market equilibrium requires that real interest rates be the
same in any two countries.
(cid:1) EXAMPLE 3
International Fisher Effect
If the nominal interest rate in Mexico is 25.25 percent and the expected inflation is 20
percent, then
rpeso(real) =
1 + rpeso – 1 =
E(1 + ipeso)
1.2525
1.20
– 1 = .044, or 4.4%
In the United States, where the nominal interest rate is about 6 percent and the expected
inflation rate is about 2 percent,
r$(real) =
1 + r$ – 1 =
E(1 + i$)
1.06
1.02
– 1 = .039, or 3.9%
The real interest rate is higher in Mexico than in the United States, but the difference in
the real rates is much smaller than the difference in nominal rates.
How similar are real interest rates around the world? It is hard to say, because we can-
not directly observe expected inflation. In Figure 6.3 we have plotted the average interest
FIGURE 6.3
Countries with the highest
interest rates generally have
the highest subsequent
inflation rates. In this
diagram, each point
represents a different country.
)
8
9
9
1
–
4
9
9
1
(
t
n
e
c
r
e
p
,
e
t
a
r
t
s
e
r
e
t
n
i
e
g
a
r
e
v
A
40
35
30
25
20
15
10
5
0
0
10
20
30
40
Average inflation, percent (1994–1998)
608 SECTION SIX
(cid:1) Self-Test 5
rate in each of 40 countries against the inflation that in fact occurred. You can see that the
countries with the highest interest rates generally had the highest inflation rates.
American investors can invest $1,000 at an interest rate of 6.0 percent. Alternatively,
they can convert those funds to 306,675 drachma at the current exchange rate and in-
vest at 8.5 percent in Greece. If the expected inflation rate in the United States is 2 per-
cent, what must be investors’ forecast of the inflation rate in Greece?
INTEREST RATES AND EXCHANGE RATES
You are an investor with $1 million to invest for 1 year. The interest rate in Mexico is
25.25 percent and in the United States it is 6 percent. Is it better to make a peso loan or
a dollar loan?
The answer seems obvious: Isn’t it better to earn an interest rate of 25.25 percent
than 6 percent? But appearances may be deceptive. If you lend in Mexico, you first need
to convert your $1 million into pesos. When the loan is repaid at the end of the year,
you need to convert your pesos back into dollars. Of course you don’t know what the
exchange rate will be at the end of the year but you can fix the future value of your
pesos by selling them forward. If the forward rate of exchange is sufficiently low, you
may do just as well keeping your money in the United States.
Let’s use the data from Table 6.5 to check which loan is the better deal:
• Dollar loan: The rate of interest on a dollar loan is 6 percent. Therefore, at the end
of the year you get 1,000,000 × 1.06 = $1,060,000.
• Peso loan: The current rate of exchange (from Table 6.5) is peso9.438/$. Therefore,
for $1 million, you can buy 1,000,000 × 9.438 = peso9,438,000. The rate of interest
on a 1-year peso loan is 25.25 percent. So at the end of the year, you get
peso9,438,000 × 1.2525 = peso11,821,000. Of course, you don’t know what the ex-
change rate will be at the end of the year. But that doesn’t matter. You can nail down
the price at which you sell your pesos. The 1-year forward rate is peso11.153/$.
Therefore, by selling the peso11,821,000 forward, you make sure that you will get
11,821,000/11.153 = $1,059,900.
Thus the two investments offer almost exactly the same rate of return. They have to—
they are both risk-free. If the domestic interest rate were different from the “covered”
foreign rate, you would have a money machine: you could borrow in the market with
the lower rate and lend in the market with the higher rate.
A difference in interest rates must be offset by a difference between spot and | Brealey |
forward exchange rates. If the risk-free interest rate in country X is higher
than in country Y, then country X’s currency will buy less of Y’s in a forward
transaction than in a spot transaction.
When you make a peso loan, you gain because you get a higher interest rate. But you
lose because you sell the pesos forward at a lower price than you have to pay for them
today. The interest rate differential is
1 + rpeso =
1 + r$
1.2525
1.06
= 1.1816
INTEREST RATE
PARITY Theory that
forward premium equals
interest rate differential.
International Financial Management 609
and the differential between the forward and spot exchange rates is virtually identical:
fpeso/$ =
speso/$
11.153
9.438
= 1.1817
Interest rate parity theory says that the interest rate differential must equal the dif-
ferential between the forward and spot exchange rates. Thus
Difference in
interest rates
1 + rpeso
1 + r$
equals
Difference between
forward and spot rates
fpeso/$
speso/$
(cid:1) EXAMPLE 4
What Happens If Interest Rate Parity
Theory Does Not Hold?
(cid:1) Self-Test 6
Suppose that the forward rate on the peso is not peso11.153/$ but peso12.00/$. Here is
what you do. Borrow 1 million pesos at an interest rate of 25.25 percent and change
these pesos into dollars at the spot exchange rate of peso9.438/$. This gives you
$105,954, which you invest for a year at 6 percent. At the end of the year you will have
105,954 × 1.06 = $112,312. Of course, this is not money to spend because you must
repay your peso loan. The amount that you need to repay is 1,000,000 × 1.2525 =
peso1,252,500. If you buy these pesos forward, you can fix in advance the number of
dollars that you will need to lay out. With a forward rate of peso12.00/$, you need to
set aside 1,252,500/12.00 = $104,375. Thus, after paying off your peso loan, you walk
away with a risk-free profit of $112,312 – $104,375 = $7,937. It is a pity that in prac-
tice interest rate parity almost always holds and the opportunities for such easy profits
are rare.
Look at the exchange rates in Table 6.5. Does the Swiss franc sell at a forward
premium or discount on the dollar? Does this suggest that the interest rate in Switzer-
land is higher or lower than in the United States? Use the interest rate parity relation-
ship to estimate the 1-year interest rate in Switzerland. Assume the U.S. interest rate is
6 percent.
THE FORWARD RATE AND THE
EXPECTED SPOT RATE
If you buy pesos forward, you get more pesos for your dollar than if you buy them spot.
So the peso is selling at a forward discount. Now let us think how this discount is re-
lated to expected changes in spot rates of exchange.
The 1-year forward rate for the peso is peso11.153/$. Would you sell pesos at this
rate if you expected the peso to rise in value? Probably not. You would be tempted to
610 SECTION SIX
EXPECTATIONS
THEORY OF EXCHANGE
RATES Theory that
expected spot exchange rate
equals the forward rate.
wait until the end of the year and get a better price for your pesos in the spot market. If
other traders felt the same way, nobody would sell pesos forward and everybody would
want to buy. The result would be that the number of pesos that you could get for your
dollar in the forward market would fall. Similarly, if traders expected the peso to fall
sharply in value, they might be reluctant to buy forward and, in order to attract buyers,
the number of pesos that you could buy for a dollar in the forward market would need
to rise.4
This is the reasoning behind the expectations theory of exchange rates, which pre-
dicts that the forward rate equals the expected future spot exchange rate: fpeso/$ =
E(speso/$). Equivalently, we can say that the percentage difference between the forward
rate and today’s spot rate is equal to the expected percentage change in the spot rate:
Difference between
forward and spot rates
fpeso/$
speso/$
equals
Expected change in
spot exchange rate
E(speso/$)
speso/$
This is the final leg of our quadrilateral in Figure 6.1.
The expectations theory of forward rates does not imply that managers are | Brealey |
perfect forecasters. Sometimes the actual future spot rate will turn out to be
above the previous forward rate. Sometimes it will fall below. But if the theory
is correct, we should find that on the average the forward rate is equal to the
future spot rate.
The theory passes this simple test reasonably well. This is important news for the fi-
nancial manager; it means that a company which always covers its foreign exchange
commitments by buying or selling currency in the forward market does not have to pay
a premium to avoid exchange rate risk: on average, the forward price at which it agrees
to exchange currency will equal the eventual spot exchange rate, no better but no worse.
We should, however, warn you that the forward rate does not tell you very much
about the future spot rate. For example, when the forward rate appears to suggest that
the spot rate is likely to appreciate, you will find that the spot rate is about equally likely
to head off in the opposite direction.
SOME IMPLICATIONS
Our four simple relationships ignore many of the complexities of interest rates and ex-
change rates. But they capture the more important features and emphasize that interna-
tional capital markets and currency markets function well and offer no free lunches.
When managers forget this, it can be costly. For example, in the late 1980s, several Aus-
tralian banks observed that interest rates in Switzerland were about 8 percentage points
lower than those in Australia and advised their clients to borrow Swiss francs. Was this
advice correct? According to the international Fisher effect, the lower Swiss interest
4 This reasoning ignores risk. If a forward purchase reduces your risk sufficiently, you might be prepared to
buy forward even if you expected to pay more as a result. Similarly, if a forward sale reduces risk, you might
be prepared to sell forward even if you expected to receive less as a result.
(cid:1) Self-Test 7
International Financial Management 611
rate indicated that investors were expecting a lower inflation rate in Switzerland than in
Australia and this in turn would result in an appreciation of the Swiss franc relative to
the Australian dollar. Thus it was likely that the advantage of the low Swiss interest rate
would be offset by the fact that it would cost the borrowers more Australian dollars to
repay the loan. As it turned out, the Swiss franc appreciated very rapidly, the Australian
banks found that they had a number of very irate clients and agreed to compensate them
for the losses they had incurred. Moral: Don’t assume automatically that it is cheaper
to borrow in a currency with a low nominal rate of interest.
In October 1998 Stellar Corporation borrowed 100 million Japanese yen at an attractive
interest rate of 2 percent, when the exchange rate between the yen and U.S. dollar was
¥123.97/$. One year later when Stellar came to repay its loan, the exchange rate was
¥107.52/$. Calculate in U.S. dollars the amount that Stellar borrowed and the amounts
that it paid in interest and principal (assume annual interest payments). What was the
effective U.S. dollar interest rate on the loan?
Here is another case where our simple relationships can stop you from falling into a
trap. Managers sometimes talk as if you make money simply by buying currencies that
go up in value and selling those that go down. But if investors anticipate the change in
the exchange rate, then it will be reflected in the interest rate differential; therefore, what
you gain on the currency you will lose in terms of interest income. You make money
from currency speculation only if you can predict whether the exchange rate will change
by more or less than the interest rate differential. In other words, you must be able to pre-
dict whether the exchange rate will change by more or less than the forward premium.
(cid:1) EXAMPLE 5
Measuring Currency Gains
The financial manager of Universal Waffle is proud of his acumen. Instead of keeping
his cash in U.S. dollars, he for many years invested it in German deutschemark deposits. | Brealey |
He calculates that between the end of 1980 and 1998, the deutschemark increased in
value by nearly 47 percent, or about 2.1 percent a year. But did the manager really gain
from investing in foreign currency? Let’s check.
The compound rate of interest on dollar deposits during the period was 9.0 percent,
while the compound rate of interest on deutschemark deposits was only 6.9 percent. So
the 2.1 percent a year appreciation in the value of the deutschemark was almost exactly
offset by the lower rate of interest on deutschemark deposits.
The interest rate differential (which by interest rate parity is equal to the forward pre-
mium) is a measure of the market’s expectation of the change in the value of the cur-
rency. The difference between the German and United States interest rates during this
period suggests that the market was expecting the deutschemark to appreciate by just
over 2 percent a year,5 and that is almost exactly what happened.
5 If the interest rate is 9.0 percent on dollar deposits and 6.9 percent on deutschemark deposits, our simple re-
lationship implies that the expected change in the value of the deutschemark was (1 + r$)/(1 + rDM) – 1 =
1.090/1.069 – 1 = .020, or 2.0 percent per year.
612 SECTION SIX
Hedging Exchange Rate Risk
Firms with international operations are subject to exchange rate risk. As exchange rates
fluctuate, the dollar value of the firm’s revenues or expenses also fluctuates. It helps to
distinguish two types of exchange rate risk: contractual and noncontractual. By con-
tractual risk, we mean that the firm is committed either to pay or to receive a known
amount of foreign currency. For example, our VCR importer was committed to pay
¥100 million at the end of 12 months. If the value of the yen appreciates rapidly over
this period, those VCRs will cost more dollars than the firm expected.
Noncontractual risk arises because exchange rate fluctuations can affect the competi-
tive position of the firm. For example, during 1991 and 1992 the value of the deutsche-
mark appreciated relative to that of other major currencies. As a result, Porsche and other
German luxury car manufacturers found it increasingly difficult to compete in the United
States. American dealers that had a franchise to sell German luxury cars also took a bath.
Thus the German car producers and their dealers in the United States were exposed to ex-
change rate changes even if they had no fixed obligations to pay or receive dollars.
Exchange rate changes can get companies into big trouble and therefore most com-
panies aim to limit at least their contractual exposure to currency fluctuations. Let us
look at an example of how this can be done.
In 1989 a British company, Enterprise Oil, bought some oil properties from Texas
Eastern for $440 million.6 Since the payment was delayed a couple of months, Enter-
prise’s plans for financing the purchase could have been thrown out of kilter if the dol-
lar had strengthened during this period.
Enterprise therefore decided to avoid, or hedge, this risk. It did so by borrowing
pounds, which it converted into dollars at the current spot rate and invested for 2
months. In that way Enterprise guaranteed it would have just enough dollars available
to pay for the purchase. Of course it was possible that the dollar would depreciate over
the 2 months, in which case Enterprise would have regretted that it did not wait and buy
the dollars spot. Unfortunately, you cannot have your cake and eat it too. By fixing its
dollar cost, Enterprise forfeited the chance of pleasant as well as unpleasant surprises.
Was there any other way that Enterprise could hedge against exchange loss? Of
course. It could buy $440 million 2 months forward. No cash would change hands im-
mediately but Enterprise would fix the price at which it buys its dollars at the end of 2
months. It would therefore eliminate all exchange risk on the deal. Interest rate parity
theory tells us that the difference between buying spot and buying forward is equal to | Brealey |
the difference between the rate of interest that you pay at home and the interest that you
earn overseas. In other words, the two methods of eliminating risk should be equivalent.
Let us check this. In March 1989 the 2-month interest rate in the United States was
about 9.7 percent and the interest rate in the United Kingdom was 13.0 percent. The
spot exchange rate was $1.743 to the pound and the 2-month forward rate was $1.730/£.
Table 6.8 shows that the cash flows from the two methods of hedging the dollar pay-
ment for Texas Eastern were almost identical.7
What is the cost of such a hedge? You sometimes hear managers say that it is equal
to the difference between the forward rate and today’s spot rate. This is wrong. If En-
terprise did not hedge, it would pay the spot rate for dollars at the time that the payment
6 See “Enterprise Oil’s Mega Forex Option,” Corporate Finance 53 (April 1989), p. 13.
7 We are not sure of Enterprise’s borrowing rate but the company is rumored to have hedged at an effective
forward rate of $1.73/£.
International Financial Management 613
TABLE 6.8
Enterprise Oil could hedge
its future dollar payment
either by borrowing sterling
and lending dollars or by
buying dollars forward
Cash Flow, Millions
£
$
Method 1: Borrow sterling, convert proceeds
to dollars, and invest dollars until needed
Now:
Borrow £248.6m at 13%
Convert to $ at $1.743/£
Invest $433.3m for 2 months at 9.7%
Net cash flow now
Month 2:
Repay £ loan with interest
Receive payment on $ loan
Pay for oil properties
Net cash flow, Month 2
Method 2: Buy dollars forward
Now:
+248.6
–248.6
0
–253.7
–253.7
Buy $440m forward at $1.73/£
0
Month 2:
Pay for $
Pay for oil properties
Net cash flow, Month 2
–254.3
–254.3
+433.3
–433.3
0
+440
–440
0
0
+440
–440
0
for Texas Eastern was due. Therefore, the cost of hedging is the difference between the
forward rate and the expected spot rate when payment is received.
Hedge or speculate? We generally vote for hedging. First, it makes life simpler for
the firm and allows it to concentrate on its own business. Second, it does not cost much.
(In fact the cost is zero if the forward rate equals the expected spot rate, as our simple
relations imply.) Third, the foreign exchange market seems reasonably efficient, at least
for the major currencies. Speculation should be a zero-sum game unless financial man-
agers have superior information to the pros who make the market.
(cid:1) Self-Test 8
and that the 6-month forward
Suppose that the current spot rate for the euro is $1.05/
rate is $1.10/
. What is the cost to a U.S. company of hedging its future need for euros
by buying them in the forward market? Assume the expectations theory of exchange rates.
International Capital Budgeting
NET PRESENT VALUE ANALYSIS
KW Corporation is an American firm manufacturing flat-packed kit wardrobes. Its ex-
port business has risen to the point that it is considering establishing a small manufac-
turing operation overseas in Narnia. KW’s decision to invest overseas should be based
on the same criteria as a decision to invest in the United States—that is, the company
614 SECTION SIX
needs to forecast the incremental cash flows from the project, discount the cash flows
at the opportunity cost of capital, and accept those projects with a positive NPV.
Suppose KW’s Narnian facility is expected to generate the following cash flows in
Narnian leos:
Year
0
Cash flow (millions of leos)
–7.6
1
2.0
2
2.5
3
3.0
4
5
3.5
4.0
The interest rate in the United States is 5 percent. KW’s financial manager estimates
that the company requires an additional expected return of 10 percent to compensate for
the risk of the project, so the opportunity cost of capital for the project is 5 + 10 = 15
percent.
Notice that KW’s opportunity cost of capital is stated in terms of the return on a
dollar-denominated investment, but the cash flows are given in leos. A project that of-
fers a 15 percent expected return in leos could fall far short of offering the required re-
turn in dollars if the value of the leo is expected to decline. Conversely, a project that | Brealey |
offers an expected return of less than 15 percent in leos may be worthwhile if the leo is
likely to appreciate.
You cannot compare the project’s return measured in one currency with the
return that you require from investing in another currency. If the opportunity
cost of capital is measured as a dollar-denominated return, consistency
demands that the forecast cash flows should also be stated in dollars.
To translate the leo cash flows into dollars, KW needs a forecast of the leo/dollar ex-
change rate. Where does this come from? We suggest using the simple parity relation-
ships in Figure 6.1. These tell us that the expected annual change in the spot rate (the
southeast box in Figure 6.1) is equal to the difference between the interest rates in the
two countries (the northwest box). For example, suppose that the financial manager
looks in the newspaper and finds that the current exchange rate is 2 leos to the dollar
(sL/$ = 2.0), while the interest rate is 5 percent in the United States (r$ = .05) and 10 per-
cent in Narnia (rL = .10). Thus the manager sees right away that the leo is likely to de-
preciate by about 5 percent a year.8 For example, at the end of 1 year
Expected spot
rate in Year 1
=
spot rate × expected change
in Year 0
= 2.00 × 1.10
1.05
in spot rate
= L2.095/$
The forecast exchange rates for each year of the project are calculated in a similar
way as follows:
Year
Forecast Exchange Rate
0
1
2
3
4
5
Spot exchange rate = L2.00/$
2.00 × (1.10/1.05) = L2.095/$
2.00 × (1.10/1.05)2 = L2.195/$
2.00 × (1.10/1.05)3 = L2.300/$
2.00 × (1.10/1.05)4 = L2.409/$
2.00 × (1.10/1.05)5 = L2.524/$
8 The financial manager could equally well use the forward exchange rate (fL/$) to estimate the expected spot
rate. In practice it is usually easier to find interest rates in the financial press than yearly forward rates.
(cid:1) Self-Test 9
International Financial Management 615
The financial manager can use these projected exchange rates to convert the leo cash
flows into dollars:9
Year
Cash flow
($ millions)
0
–
7.6
2.00
= –$3.8
1
2.0
2.095
= $.95
2
3
4
5
2.5
2.195
= $1.14
3.0
2.300
= $1.30
3.5
2.409
= $1.45
4.0
2.524
= $1.58
Now the manager discounts these dollar cash flows at the 15 percent dollar cost of cap-
ital:
NPV = – 3.8 +
.95
1.15
+
1.14
1.152
+
1.30
1.153
+
1.45
1.154
+
1.58
1.155
= $.36 million, or $360,000
Notice that the manager discounted cash flows at 15 percent, not the United States
risk-free interest rate of 5 percent. The cash flows are risky, so a risk-adjusted interest
rate is appropriate. The positive NPV tells the manager that the project is worth under-
taking; it increases shareholder wealth by $360,000.
Suppose that the nominal interest rate in Narnia is 3 percent rather than 10 percent. The
spot exchange rate is still L2.00/$ and the forecast leo cash flows on KW’s project are
also the same as before.
a. What do you deduce about the likely difference in the inflation rates in Narnia and
the United States?
b. Would you now forecast that the leo will appreciate against the dollar or depreciate?
c. Do you think that the NPV of KW’s project will now be higher or lower than the fig-
ure we calculated above? Check your answer by calculating NPV under this new as-
sumption.
THE COST OF CAPITAL FOR
FOREIGN INVESTMENT
We did not say how KW arrived at a 15 percent dollar discount rate for its Narnian proj-
ect. That depends on the risk of overseas investment and the reward that investors re-
quire for taking this risk. These are issues on which few economists can agree, but we
will tell you where we stand.10
Remember that the risk of an investment cannot be considered in isolation; it de-
pends on the securities that the investor holds in his or her portfolio. For example, sup-
pose KW’s shareholders invest mainly in companies that do business in the United
9 Suppose KW’s managers do not go along with what market prices are telling them. For example, perhaps
they believe that the leo is likely to appreciate relative to the dollar. Should they plug their own currency fore-
casts into their present value calculations? We think not. It would be stupid to undertake what might be an un- | Brealey |
profitable investment just because management is optimistic about the currency. Given its exchange rate fore-
cast, KW would do better to pass up the investment in wardrobe manufacturing and buy leos instead.
10 Why don’t economists agree? One fundamental reason is that economists have never been able to agree on
what makes one country different from another. Is it just that they have different currencies? Or is it that their
citizens have different tastes? Or is it that they are subject to different regulations and taxes? The answer af-
fects the relationship between security prices in different countries.
FINANCE IN ACTION
Political Risk
When multinational companies invest abroad, their fi-
nancial managers need to consider the political risks
that are involved. By this, we mean the threat that gov-
ernments will change the rules of the game after an in-
vestment is made. At worst, the government may ex-
propriate the company’s assets without compensation.
Or it may simply insist that the company keep in the
country any profits that it makes.
Businesses in every country are exposed to the risk
of unanticipated actions by governments or the courts.
But in some parts of the world foreign companies are
particularly vulnerable. Several organizations publish
regular rankings of countries in terms of their political
risk. For example, the PRS Group places countries on a
scale
of
1 to 100 based on factors such as regime stability, fi-
nancial transfer, and turmoil. The following table pre-
sents the 10 least and most risky countries based on
these factors.
Least Risky
Most Risky
Finland
Belgium
Switzerland
Singapore
Denmark
Austria
Netherlands
Hong Kong
Australia
Ecuador
Iraq
Cuba
Russia
Myanmar
Sudan
Vietnam
Cameroon
Pakistan
Nigeria
Source: PRS Group (www.prsgroup.com), May 1, 2000.
States. They would find that the value of KW’s Narnian venture was relatively unaf-
fected by fluctuations in the value of United States shares. So an investment in the
Narnian furniture business would appear to be a relatively low-risk project to KW’s
shareholders. That would not be true of a Narnian company, whose shareholders are al-
ready exposed to the fortunes of the Narnian market. To them an investment in the
Narnian furniture business might seem a relatively high-risk project. They would there-
fore demand a higher return (measured in dollars) than KW’s shareholders.
AVOIDING FUDGE FACTORS
We certainly don’t pretend that we can put a precise figure on the cost of capital for for-
eign investment. But you can see that we disagree with the frequent practice of auto-
matically increasing the domestic cost of capital when foreign investment is considered.
We suspect that managers mark up the required return for foreign investment because
it is more costly to manage an operation in a foreign country and to cover the risk of ex-
propriation, foreign exchange restrictions, or unfavorable tax changes. The nearby box
discusses the sources of political risk. A fudge factor is added to the discount factor to
cover these costs.
We think managers should leave the discount rate alone and reduce expected cash
flows instead. For example, suppose that KW is expected to earn L2.5 million in the
first year if no penalties are placed on the operations of foreign firms. Suppose also that
SEE BOX
616
International Financial Management 617
there is a 20 percent chance that KW’s cash flow may be expropriated without com-
pensation. The expected cash flow is not L2.5 million but .8 × 2.5 million = L2.0 mil-
lion.
The end result may be the same if you pretend that the expected cash flow is L2.5
million but add a fudge factor to the discount rate. Nevertheless, adjusting cash flows
brings management’s assumptions about “political risks” out in the open for scrutiny
and sensitivity analysis.
Summary
What is the difference between spot and forward exchange rates?
The exchange rate is the amount of one currency needed to purchase one unit of another | Brealey |
currency. The spot rate of exchange is the exchange rate for an immediate transaction. The
forward rate is the exchange rate for a forward transaction, that is, a transaction at a
specified future date.
What are the basic relationships between spot exchange rates, forward exchange
rates, interest rates, and inflation rates?
To produce order out of chaos, the international financial manager needs some model of the
relationships between exchange rates, interest rates, and inflation rates. Four very simple
theories prove useful:
•
•
•
In its strict form, purchasing power parity states that $1 must have the same purchasing
power in every country. You only need to take a vacation abroad to know that this doesn’t
square well with the facts. Nevertheless, on average, changes in exchange rates match
differences in inflation rates and, if you need a long-term forecast of the exchange rate, it
is difficult to do much better than to assume that the exchange rate will offset the effect
of any differences in the inflation rates.
In an open world capital market real rates of interest would have to be the same. Thus
differences in nominal interest rates result from differences in expected inflation rates.
This international Fisher effect suggests that firms should not simply borrow where
interest rates are lowest. Those countries are also likely to have the lowest inflation rates
and the strongest currencies.
Interest rate parity theory states that the interest differential between two countries
must be equal to the difference between the forward and spot exchange rates. In the
international markets, arbitrage ensures that parity almost always holds.
• The expectations theory of exchange rates tells us that the forward rate equals the
expected spot rate (though it is very far from being a perfect forecaster of the spot rate).
What are some simple strategies to protect the firm against exchange rate risk?
Our simple theories about forward rates have two practical implications for the problem of
hedging overseas operations. First, the expectations theory suggests that hedging exchange
risk is on average costless. Second, there are two ways to hedge against exchange risk—one
is to buy or sell currency forward, the other is to lend or borrow abroad. Interest rate parity
tells us that the cost of the two methods should be the same.
How do we perform an NPV analysis for projects with cash flows in foreign cur-
rencies?
618 SECTION SIX
Related Web
Links
Overseas investment decisions are no different in principle from domestic decisions. You
need to forecast the project’s cash flows and then discount them at the opportunity cost of
capital. But it is important to remember that if the opportunity cost of capital is stated in
dollars, the cash flows must also be converted to dollars. This requires a forecast of foreign
exchange rates. We suggest that you rely on the simple parity relationships and use the
interest rate differential to produce these forecasts. In international capital budgeting the
return that shareholders require from foreign investments must be estimated. Adding a
premium for the “extra risks” of overseas investment is not a good solution.
www.cme.com/eurofx/ The Chicago Mercantile Exchange’s information center on managing Eu-
ropean foreign exchange risk with Euro contracts
www.bloomberg.com/markets Data on current exchange rates as well as securities
www.ms.com/msci.html Information for global investing from Morgan Stanley Capital Interna-
tional
www.global-investor.com Global Investor Directory with information about major international
markets
www.emgmkts.com/index.htm Analysis of economic, political, and financial events in emerg-
ing markets
www.jpmorgan.com/research Information about emerging markets
www.florin.com/v4/valore4.html Issues in currency risk management
Key Terms
exchange rate
spot rate of exchange
forward exchange rate
law of one price
purchasing power parity
(PPP)
international Fisher effect
interest rate parity
expectations theory of exchange rates
Quiz
1. Exchange Rates. Use Table 6.5 to answer these questions:
| Brealey |
a. How many euros can you buy for $100? How many dollars can you buy for 100 euros?
b. How many Swiss francs can you buy for $100? How many dollars can you buy for 100
Swiss francs?
c. If the euro depreciates with respect to the dollar, will the direct exchange rate quoted in
Table 6.5 increase or decrease? What about the indirect exchange rate?
d. Is a United States or an Australian dollar worth more?
2. Exchange Rate Relationships. Look at Table 6.5.
a. How many Japanese yen do you get for your dollar?
b. What is the 1-year forward rate for the yen?
c. Is the yen at a forward discount or premium on the dollar?
d. Calculate the annual percentage discount or premium on the yen.
e. If the interest rate on dollars is 6.5 percent, what do you think is the interest rate on yen?
f. According to the expectations theory, what is the expected spot rate for the yen in 1 year’s
time?
g. According to purchasing power parity, what is the expected difference in the rate of price
inflation in the United States and Japan?
3. Exchange Rate Relationships. Define each of the following theories in a sentence or sim-
ple equation:
International Financial Management 619
a. Interest rate parity theory.
b. Expectations theory of forward rates.
c. Law of one price.
d. International Fisher effect (relationship between interest rates in different countries).
4. International Capital Budgeting. Which of the following items do you need if you do all
your capital budgeting calculations in your own currency?
Forecasts of future exchange rates
Forecasts of the foreign inflation rate
Forecasts of the domestic inflation rate
Foreign interest rates
Domestic interest rates
5. Foreign Currency Management. Ms. Rosetta Stone, the treasurer of International Reprints,
Inc., has noticed that the interest rate in Switzerland is below the rates in most other coun-
tries. She is therefore suggesting that the company should make an issue of Swiss franc
bonds. What considerations ought she first take into account?
6. Hedging Exchange Rate Risk. An importer in the United States is due to take delivery of
silk scarves from Europe in 6 months. The price is fixed in euros. Which of the following
transactions could eliminate the importer’s exchange risk?
a. Buy euros forward.
b. Sell euros forward.
c. Borrow euros, buy dollars at the spot exchange rate.
d. Sell euros at the spot exchange rate, lend dollars.
7. Currency Risk. Sanyo produces audio and video consumer goods and exports a large frac-
tion of its output to the United States under its own name and the Fisher brand name. It
prices its products in yen, meaning that it seeks to maintain a fixed price in terms of yen.
Suppose the yen moves from ¥108.02/$ to ¥100/$. What currency risk does Sanyo face?
How can it reduce its exposure?
8. Managing Exchange Rate Risk. A firm in the United States is due to receive payment of
1 million Australian dollars in 8 years’ time. It would like to protect itself against a decline
in the value of the Australian dollar but finds it difficult to arrange a forward sale for such
a long period. Is there any other way that it can protect itself?
9. Interest Rate Parity. The following table shows interest rates and exchange rates for the
U.S. dollar and Mexican peso. The spot exchange rate is 9.5 pesos per dollar. Complete the
missing entries:
Dollar interest rate (annually compounded)
Peso interest rate (annually compounded)
Forward pesos per dollar
5.5
20%
____
7.0
___
11.2
1 Month
1 Year
Hint: When calculating the 1-month forward rate, remember to translate the annual interest
rate into a monthly interest rate.
10. Exchange Rate Risk. An American investor buys 100 shares of London Enterprises at a
price of £50 when the exchange rate is $1.60/£. A year later the shares are selling at £52. No
dividends have been paid.
Practice
Problems
620 SECTION SIX
a. What is the rate of return to an American investor if the exchange rate is still $1.60/£?
b. What if the exchange rate is $1.70/£?
c. What if the exchange rate is $1.50/£?
| Brealey |
11. Interest Rate Parity. Look at Table 6.5. If the 3-month interest rate on dollars is 6.0 percent
(annualized), what do you think is the 3-month sterling (U.K.) interest rate? Explain what
would happen if the rate were substantially above your figure. Hint: In your calculations re-
member to convert the annually compounded interest rate into a rate for 3 months.
12. Expectations Theory. Table 6.5 shows the 1-year forward rate on the Canadian dollar.
a. Is the Canadian dollar at a forward discount or a premium on the U.S. dollar?
b. What is the annualized percentage discount or premium?
c. If you have no other information about the two currencies, what is your best guess about
the spot rate in 1 year?
d. Suppose that you expect to receive 100,000 Canadian dollars in 1 year. How many U.S.
dollars is this likely to be worth?
13. Interest Rate Parity. Suppose the interest rate on 1-year loans in the United States is 5 per-
cent while in the United Kingdom the interest rate is 6 percent. The spot exchange rate is
$1.55/£ and the forward rate is $1.54/£. In what country would you choose to borrow? To
lend? Can you profit from this situation?
14. Purchasing Power Parity. Suppose that the inflation rate in the United States is 4 percent
and in Canada it is 5 percent. What would you expect is happening to the exchange rate be-
tween the United States and Canadian dollars?
15. Cross Rates. Look at Table 6.5. How many Swiss francs can you buy for $1? How many yen
can you buy? What rate do you think a Japanese bank would quote for buying or selling
Swiss francs? Explain what would happen if it quoted a rate that was substantially less than
your figure.
16. International Capital Budgeting. Suppose that you do use your own views about exchange
rates when valuing an overseas investment proposal. Specifically, suppose that you believe
that the leo will depreciate by 2 percent per year. Recalculate the NPV of KW’s project.
17. Currency Risk. You have bid for a possible export order that would provide a cash inflow
of ∼1 million in 6 months. The spot exchange rate is ∼1.06/$ and the 1-year forward rate is
∼1.07/$. There are two sources of uncertainty: (1) the euro could appreciate or depreciate,
and (2) you may or may not receive the export order. Illustrate in each case the profits or
losses that you would make if you sell ∼1 million forward by filling in the following table.
Assume that the exchange rate in 1 year will be either ∼1.02/$ or ∼1.12/$.
Profit/Loss
Spot Rate
∼1.12/$
∼1.02/$
Receive Order
Lose Order
__________
__________
__________
__________
18. Managing Currency Risk. General Gadget Corp. (GGC) is a United States–based multi-
national firm that makes electrical coconut scrapers. These gadgets are made only in the
United States using local inputs. The scrapers are sold mainly to Asian and West Indian
countries where coconuts are grown.
a. If GGC sells scrapers in Trinidad, what is the currency risk faced by the firm?
b. In what currency should GGC borrow funds to pay for its investment in order to mitigate
its foreign exchange exposure?
Challenge
Problem
Solutions to
Self-Test
Questions
International Financial Management 621
c. Suppose that GGC begins manufacturing its products in Trinidad using local (Trini-
dadian) inputs and labor. How does this affect its exchange rate risk?
19. Currency Risk. If investors recognize the impacts of inflation and exchange rate changes
on a firm’s cash flows, changes in exchange rates should be reflected in stock prices. How
would the stock price of each of the following Swiss companies be affected by an unantici-
pated appreciation in the Swiss franc of 10 percent, only 2 percent of which could be justi-
fied by comparing Swiss inflation to that in the rest of the world?
a. Swiss Air: More than two-thirds of its employees are Swiss. Most revenues come from in-
ternational fares set in U.S. dollars.
b. Nestlé: Fewer than 5 percent of its employees are Swiss. Most revenues are derived from
sales of consumer goods in a wide range of countries with competition from local pro-
ducers.
| Brealey |
c. Union Bank of Switzerland: Most employees are Swiss. All non–Swiss franc monetary
positions are fully hedged.
20. International Capital Budgeting. An American firm is evaluating an investment in In-
donesia. The project costs 500 billion Indonesian rupiah and it is expected to produce an in-
come of 250 billion Indonesian rupiah a year in real terms for each of the next 3 years. The
expected inflation rate in Indonesia is 12 percent a year and the firm estimates that an ap-
propriate discount rate for the project would be about 8 percent above the risk-free rate of
interest. Calculate the net present value of the project in U.S. dollars. Exchange rates are
given in Table 6.5. The interest rate is about 15.3 percent in Indonesia and 6 percent in the
United States.
1 Direct quote: $1.0707/
Indirect quote: 1/1.0707 =
Indirect quote: ¥107.520/$
Direct quote: $.0093/¥
.934/$.
2 The dollar buys fewer Swiss francs, so the franc has appreciated with respect to the dollar.
3 a. 1,500/1.4865 = $1,009
b. Indirect exchange rate: $1 = .9 × 1.4865 = 1.3379 francs.
c. 1,500/1.3379 = $1,121. The dollar price increases.
d. 1,009 × 1.3379 = 1,350 francs.
4 a. £220 = $330. Therefore £1 = 330/220 = $1.50.
b. In the United States, price = $330 × 1.02 = $336.60. In Great Britain, price = £220 × 1.05
= £231. The new exchange rate = $336.60/£231 = $1.457/£.
c. Initially $1 buys 1/1.50 = £.667. At the end of the year, $1 buys 1/1.457 = £.686, which
is about 3 percent higher than the original value of £.667.
5 The real interest rate in the United States is 1.06/1.02 – 1 = .039, or 3.9%. If the real rate
is the same in Greece, then expected inflation must be (1 + nominal rate)/(1 + real rate) –
1 = 1.085/1.039 – 1 = .044, or 4.4%.
6 The Swiss franc is at a forward premium (that is, you get fewer francs for $1 in the forward
market). This implies that interest rates in Switzerland are lower than in the United States.
The interest rate in the United States is 6 percent. Interest rate parity states
622 SECTION SIX
Therefore
1 + rfranc =
1 + r$
rfranc = 1.06 × 1.4331
1.4865
ffranc/$
sfranc/$
– 1 = .022, or 2.2%
7 Stellar borrows ¥100 million in 1998. It pays ¥2 million in interest at the end of 1999, when
it also repays the loan. Cash flows in dollars are:
1998:
1999:
+ 100 million
123.97
= +$806,647
2 million
107.52
100 million
107.52
Interest =
Principal =
Total
= $ 18,601
= 930,059
$948,661
To find the dollar interest rate, solve
806,647 × (1 + r$) = 948,661
r$ =
948,661
806,647
– 1 = .176 = 17.6%
8 According to the expectations theory of exchange rates, the forward rate equals the ex-
pected future spot exchange rate. Therefore, the expected cost of the hedge—the difference
between the forward rate and expected spot rate—is zero!
9 a. The lower interest rate in Narnia than in the United States suggests that forecast inflation
is lower in Narnia. If real interest rates are the same in the two countries, then the dif-
ference in inflation rates is about 5 – 3 = 2 percent.
b. The lower interest rate (and lower expected inflation rate) in Narnia suggests that in-
vestors are expecting the leo to appreciate against the dollar.
c. Since KW can now expect to change its leo cash flows into more dollars than before, the
project’s NPV is increased. Forecast exchange rates will be as follows:
Year
Forecast Exchange Rate
0
1
2
3
4
5
Spot exchange rate = L2.00/$
2.00 × (1.03/1.05) = L1.962/$
2.00 × (1.03/1.05)2 = L1.925/$
2.00 × (1.03/1.05)3 = L1.888/$
2.00 × (1.03/1.05)4 = L1.852/$
2.00 × (1.03/1.05)5 = L1.817/$
The expected dollar cash flows from the project are
Year
Cash flow
(millions
of dollars)
0
1
2
3
4
5
–7.6
2.00
= –$3.8
2.0
1.962
= $1.02
2.5
1.925
= $1.30
3.0
1.888
= $1.59
3.5
1.852
= $1.89
4.0
1.817
= $2.20
Discounting these dollar cash flows at the 15 percent dollar cost of capital gives
NPV = – 3.8 +
1.02
1.15
+
1.30
1.152
+
1.59
1.153
+
1.89
1.154
+
2.20
1.155
= $1.29 million, or $1,290,000
International Financial Management 623
The project is worth more because the reduced interest rate in Narnia suggests that investors
expect the leo to appreciate in value. Thus the dollar cash flows from the project are higher | Brealey |
than in Section 6.4.
MINICASE
“Jumping jackasses! Not another one!” groaned George Luger.
This was the third memo that he had received that morning from
the CEO of VCR Importers. It read as follows:
From:
To:
CEO’s Office
Company Treasurer
George,
I have been looking at some of our foreign exchange deals and they don’t seem to make sense.
First, we have been buying yen forward to cover the cost of our imports. You have explained that this insures us against the
risk that the dollar may depreciate over the next year, but it is incredibly expensive insurance. Each dollar buys only 101.3 yen when
we buy forward, compared with the current spot rate of 107.52 yen to the dollar. We could save a fortune by buying yen as and
when we need them rather than buying them forward.
Another possibility has occurred to me. If we are worried that the dollar may depreciate (or do I mean “appreciate”?), why
don’t we buy yen at the low spot rate of ¥107.52 to the dollar and then put them on deposit until we have to pay for the VCRs? That
way we can make sure that we get a good rate for our yen.
I am also worried that we are missing out on some cheap financing. We are paying about 8 percent to borrow dollars for one
year, but Ben Hur was telling me at lunch that we could get a one-year yen loan for about 1.75 percent. I find that a bit surprising,
but if that’s the case, why don’t we repay our dollar loans and borrow yen instead?
Perhaps we could discuss these ideas at next Wednesday’s meeting. I would be interested in your views on the matter.
Jill Edison
Appendix C
PRESENT VALUE TABLES
626 APPENDIX C Present Value Tables
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6
0
.
3
2
4
3
.
3
2
4
6
.
3
0
7
9
.
3
8
2
3
.
4
7
1
7
.
4
2
4
1
.
5
4
0
6
.
5
3
2
6
.
8
0
8
0
.
1
6
6
1
.
1
0
6
2
.
1
0
6
3
.
1
9
6
4
.
1
7
8
5
.
1
4
1
7
.
1
1
5
8
.
1
9
9
9
.
1
9
5
1
.
2
2
3
3
.
2
8
1
5
.
2
0
2
7
.
2
7
3
9
.
2
2
7
1
.
3
6
2
4
.
3
0
0
7
.
3
6
9
9
.
3
6
1
3
.
4
1
6
6
.
4
8
4
8
.
6
7
2
.
3
1
6
0
.
0
1
0
7
0
.
1
5
4
1
.
1
5
2
2
.
1
1
1
3
.
1
3
0
4
.
1
1
0
5
.
1
6
0
6
.
1
8
1
7
.
1
8
3
8
.
1
7
6
9
.
1
5
0
1
.
2
2
5
2
.
2
0
1
4
.
2
9
7
5
.
2
9
5
7
.
2
2
5
9
.
2
9
5
1
.
3
0
8
3
.
3
7
1
6
.
3
0
7
8
.
3
7
2
4
.
5
2
1
6
.
7
0
6
0
.
1
4
2
1
.
1
1
9
1
.
1
2
6
2
.
1
8
3
3
.
1
9
1
4
.
1
4
0
5
.
1
4
9
5
.
1
9
8
6
.
1
1
9
7
.
1
8
9
8
.
1
2
1
0
.
2
3
3
1
.
2
1
6
2
.
2
7
9
3
.
2
0
4
5
.
2
3
9
6
.
2
4
5
8
.
2
6
2
0
.
3
7
0
2
.
3
2
9
2
.
4
3
4
7
.
5
0
5
0
.
1
2
0
1
.
1
8
5
1
.
1
6
1
2
.
1
6
7
2
.
1
0
4
3
.
1
7
0
4
.
1
7
7
4
.
1
1
5
5
.
1
9
2
6
.
1
0
1
7
.
1
6
9
7
.
1
6
8
8
.
1
0
8
9
.
1
9
7
0
.
2
3
8
1
.
2
2
9
2
.
2
7
0
4
.
2
7
2
5
.
2
3
5
6
.
2
6
8
3
.
3
2
2
3
.
4
0
4
0
.
1
2
8
0
.
1
5
2
1
.
1
0
7
1
.
1
7
1
2
.
1
5
6
2
.
1
6
1
3
.
1
9
6
3
.
1
3
2
4
.
1
0
8
4
.
1
9
3
5
.
1
1
0
6
.
1
5
6
6
.
1
2
3
7
.
1
1
0
8
.
1
3
7
8
.
1
8
4
9
.
1
6
2
0
.
2
7
0
1
.
2
1
9
1
.
2
6
6
6
.
2
3
4
2
.
3
0
3
0
.
1
1
6
0
.
1
3
9
0
.
1
6
2
1
.
1
9
5
1
.
1
4
9
1
.
1
0
3
2
.
1
7
6
2
.
1
5
0
3
.
1
4
4
3
.
1
4
8
3
.
1
6
2
4
.
1
9
6
4
.
1
3
1
5
.
1
8
5
5
.
1
5
0
6
.
1
3
5
6
.
1
2
0
7
.
1
4
5
7
.
1
6
0
8
.
1
4
9
0
.
2
7
2
4
.
2
0
2
0
.
1
0
4
0
.
1
1
6
0
.
1
2
8
0
.
1
4
0
1
.
1
6
2
1
.
1
9
4
1
.
1
2
7
1
.
1
5
9
1
.
1
9
1
2
.
1
3
4
2
.
1
8
6
2
.
1
4
9
2
.
1
9
1
3
.
1
6
4
3
.
1
3
7
3
.
1
0
0
4
.
1
8
2
4
.
1
7
5
4
.
1
6
8
4
.
1
1
4
6
.
1
1
1
8
.
1
0
1
0
.
1
0
2
0
.
1
0
3
0
.
1
1
4
0
.
1
1
5
0
.
1
2
6
0
.
1
2
7
0
.
1
3
8
0
.
1
4
9
0
.
1
5
0
1
.
1
6
1
1
.
1
7
2
1
.
1
8
3
1
.
1
9
4
1
.
1
1
6
1
.
1
3
7
1
.
1
4
8
1
.
1
6
9
1
.
1
8
0
2
.
1
0
2
2
.
1
2
8
2
.
1
8
4
3
.
1
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
2
5
2
0
3
APPENDIX C Present Value Tables 627
%
0
3
%
9
2
%
8
2
%
7
2
0
0
3
1
.
0
9
6
1
.
7
9
1
2
.
6
5
8
2
.
3
1
7
3
.
7
2
8
4
.
5
7
2
6
.
7
5
1
8
.
0
6
0
1
.
9
7
3
1
.
2
9
7
1
.
0
3
3
2
.
9
2
0
3
.
7
3
9
3
.
9
1
1
5
.
4
5
6
6
.
0
5
6
8
.
.
5
2
1
1
.
2
6
4
1
.
0
0
9
1
.
6
5
0
7
0
9
2
1
.
4
6
6
1
.
7
4
1
2
.
9
6
7
2
.
2
7
5
3
.
8
0
6
4
.
5
4
9
5
.
9
6
6
7
.
3
9
8
9
.
6
7
2
1
.
6
4
6
1
.
4
2
1
2
.
9
3
7
2
.
4
3
5
3
.
9
5
5
4
.
1
8
8
5
.
6
8
5
7
.
6
8
7
9
.
0
8
2
1
.
8
3
6
1
.
7
9
0
2
.
4
8
6
2
.
6
3
4
3
.
8
9
3
4
.
9
2
6
5
.
6
0
2
7
.
3
2
2
9
.
1
8
1
1
.
1
1
5
1
.
4
3
9
1
.
6
7
4
2
.
9
6
1
3
.
6
5
0
4
.
2
9
1
5
.
6
4
6
6
.
7
0
5
8
.
.
2
6
2
1
.
9
2
6
1
.
8
1
8
5
.
9
8
0
1
.
4
9
3
1
.
9
8
7
4
0
7
2
1
.
3
1
6
1
.
8
4
0
2
.
1
0
6
2
.
4
0
3
3
.
6
9
1
4
.
9
2
3
5
.
8
6
7
6
.
5
9
5
8
.
2
9
0
1
.
6
8
3
1
.
1
6
7
1
.
6
3
2
2
.
0
4
8
2
.
6
0
6
3
.
0
8
5
4
.
7
1
8
5
.
7
8
3
7
.
1
8
3
9
.
%
6
2
0
6
2
1
.
8
8
5
1
.
0
0
0
2
.
0
2
5
2
.
6
7
1
3
.
2
0
0
4
.
2
4
0
5
.
3
5
3
6
.
5
0
0
8
.
9
0
0
1
.
1
7
2
1
.
1
0
6
1
.
8
1
0
2
.
2
4
5
2
.
3
0
2
3
.
6
3
0
4
.
5
8
0
5
.
7
0
4
6
.
3
7
0
8
.
%
5
2
0
5
2
.
1
3
6
5
.
1
3
5
9
.
1
1
4
4
.
2
2
5
0
.
3
5
1
8
.
3
8
6
7
.
4
0
6
9
.
5
1
5
4
.
7
3
1
3
.
9
4
6
.
1
1
5
5
.
4
1
9
1
.
8
1
4
7
.
2
2
2
4
.
8
2
3
5
.
5
3
1
4
.
4
4
1
5
.
5
5
9
3
.
9
6
4
7
.
6
8
.
1
9
1
1
.
6
3
9
3
.
7
1
0
1
.
0
3
2
3
r
a
e
Y
r
e
p
e
t
a
R
t
s
e
r
e
t
n
I
%
4
2
%
3
2
%
2
2
%
1
2
%
0
2
%
9
1
%
8
1
%
7
1
%
6
1
r
e
b
m
u
N
s
r
a
e
Y
f
o
0
4
2
.
1
8
3
5
.
1
7
0
9
.
1
4
6
3
.
2
2
3
9
.
2
5
3
6
.
3
8
0
5
.
4
0
9
5
.
5
1
3
9
.
6
4
9
5
.
8
6
6
.
0
1
1
2
.
3
1
9
3
.
6
1
2
3
.
0
2
0
2
.
5
2
4
2
.
1
3
4
7
.
8
3
4
0
.
8
4
7
5
.
9
5
6
8
.
3
7
0
3
2
.
1
3
1
5
.
1
1
6
8
.
1
9
8
2
.
2
5
1
8
.
2
3
6
4
.
3
9
5
2
.
4
9
3
2
.
5
4
4
4
.
6
6
2
9
.
7
9
4
7
.
9
9
9
.
1
1
5
7
.
4
1
4
1
.
8
1
1
3
.
2
2
5
4
.
7
2
6
7
.
3
3
2
5
.
1
4
7
0
.
1
5
2
8
.
2
6
0
2
2
.
1
8
8
4
.
1
6
1
8
.
1
5
1
2
.
2
3
0
7
.
2
7
9
2
.
3
3
2
0
.
4
8
0
9
.
4
7
8
9
.
5
5
0
3
.
7
2
1
9
.
8
7
8
.
0
1
6
2
.
3
1
8
1
.
6
1
4
7
.
9
1
9
0
.
4
2
8
3
.
9
2
5
8
.
5
3
4
7
.
3
4
6
3
.
3
5
0
1
2
.
1
4
6
4
.
1
2
7
7
.
1
4
4
1
.
2
4
9
5
.
2
8
3
1
.
3
7
9
7
.
3
5
9
5
.
4
0
6
5
.
5
8
2
7
.
6
0
4
1
.
8
0
5
8
.
9
2
9
.
1
1
2
4
.
4
1
5
4
.
7
1
1
1
.
1
2
5
5
.
5
2
1
9
.
0
3
0
4
.
7
3
6
2
.
5
4
0
0
2
.
1
0
4
4
.
1
8
2
7
.
1
4
7
0
.
2
8
8
4
.
2
6
8
9
.
2
3
8
5
.
3
0
0
3
.
4
0
6
1
.
5
2
9
1
.
6
0
3
4
.
7
6
1
9
.
8
0
7
.
0
1
4
8
.
2
1
1
4
.
5
1
9
4
.
8
1
9
1
.
2
2
2
6
.
6
2
5
9
.
1
3
4
3
.
8
3
0
9
1
.
1
6
1
4
.
1
5
8
6
.
1
5
0
0
.
2
6
8
3
.
2
0
4
8
.
2
9
7
3
.
3
1
2
0
.
4
5
8
7
.
4
5
9
6
.
5
7
7
7
.
6
4
6
0
.
8
6
9
5
.
9
2
4
.
1
1
9
5
.
3
1
7
1
.
6
1
4
2
.
9
1
0
9
.
2
2
5
2
.
7
2
3
4
.
2
3
0
8
1
.
1
2
9
3
.
1
3
4
6
.
1
9
3
9
.
1
8
8
2
.
2
0
0
7
.
2
5
8
1
.
3
9
5
7
.
3
5
3
4
.
4
4
3
2
.
5
6
7
1
.
6
8
8
2
.
7
9
9
5
.
8
5
1
.
0
1
7
9
.
1
1
3
1
.
4
1
7
6
.
6
1
7
6
.
9
1
1
2
.
3
2
9
3
.
7
2
0
7
1
.
1
9
6
3
.
1
2
0
6
.
1
4
7
8
.
1
2
9
1
.
2
5
6
5
.
2
1
0
0
.
3
1
1
5
.
3
8
0
1
.
4
7
0
8
.
4
4
2
6
.
5
0
8
5
.
6
9
9
6
.
7
7
0
0
.
9
4
5
.
0
1
3
3
.
2
1
3
4
.
4
1
8
8
.
6
1
5
7
.
9
1
1
1
.
3
2
0
6
1
.
1
6
4
3
.
1
1
6
5
.
1
1
1
8
.
1
0
0
1
.
2
6
3
4
.
2
6
2
8
.
2
8
7
2
.
3
3
0
8
.
3
1
1
4
.
4
7
1
1
.
5
6
3
9
.
5
6
8
8
.
6
8
8
9
.
7
6
6
2
.
9
5
7
.
0
1
7
4
.
2
1
6
4
.
4
1
8
7
.
6
1
6
4
.
9
1
7
8
.
0
4
5
8
.
5
8
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
2
5
2
0
3
0
2
6
2
8
7
0
2
6
4
6
1
1
0
3
1
6
2
0
1
7
.
4
6
2
8
.
7
0
8
5
.
6
1
2
8
.
4
3
6
9
.
6
7
1
9
.
7
9
4
2
.
4
4
1
8
.
9
8
3
4
.
7
1
1
5
.
4
0
3
0
4
.
5
9
9
3
.
7
7
7
6
.
2
6
6
6
.
0
5
4
.
7
3
2
7
.
4
8
1
4
.
3
4
1
1
.
1
1
1
.
5
r
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t
f
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,
.
g
.
e
| Brealey |
628 APPENDIX C Present Value Tables
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Y
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S
E
R
P
:
S
R
O
T
C
A
F
T
N
U
O
C
S
I
D
%
5
1
%
4
1
%
3
1
%
2
1
%
1
1
%
0
1
%
9
%
8
0
7
8
.
6
5
7
.
8
5
6
.
2
7
5
.
7
9
4
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2
3
4
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6
7
3
.
7
2
3
.
4
8
2
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7
4
2
.
5
1
2
.
7
8
1
.
3
6
1
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1
4
1
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3
2
1
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7
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3
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0
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1
8
0
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0
7
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1
6
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7
7
8
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9
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7
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5
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6
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2
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5
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9
1
5
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6
5
4
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4
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1
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3
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3
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0
7
2
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7
3
2
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8
0
2
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2
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1
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0
6
1
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0
4
1
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3
2
1
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8
0
1
.
5
9
0
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3
8
0
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3
7
0
.
8
3
0
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0
2
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5
8
8
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3
8
7
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3
9
6
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3
1
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3
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0
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3
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1
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8
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3
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1
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3
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1
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6
4
1
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0
3
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6
1
1
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4
0
1
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9
5
0
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3
3
0
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1
0
9
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2
1
8
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1
3
7
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9
5
6
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3
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5
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5
3
5
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2
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4
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4
3
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3
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2
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3
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3
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6
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0
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4
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2
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2
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7
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8
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2
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2
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0
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2
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2
3
2
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1
2
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6
4
1
.
9
9
0
.
%
7
5
3
9
.
3
7
8
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6
1
8
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3
6
7
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3
1
7
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6
6
6
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3
2
6
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2
8
5
.
4
4
5
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8
0
5
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5
7
4
.
4
4
4
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5
1
4
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8
8
3
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2
6
3
.
9
3
3
.
7
1
3
.
6
9
2
.
7
7
2
.
8
5
2
.
4
8
1
.
1
3
1
.
%
6
3
4
9
.
0
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0
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2
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7
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4
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3
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0
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1
3
3
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2
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3
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3
3
2
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1
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5
2
5
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7
0
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4
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3
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4
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6
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4
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3
1
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9
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3
4
9
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8
8
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3
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7
3
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3
1
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9
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6
6
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4
4
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2
2
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0
7
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1
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6
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1
6
6
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2
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3
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6
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7
8
5
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0
7
5
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4
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4
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2
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1
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2
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3
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3
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2
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%
1
0
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9
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0
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1
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1
6
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1
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2
4
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3
3
9
.
3
2
9
.
4
1
9
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5
0
9
.
6
9
8
.
7
8
8
.
9
7
8
.
0
7
8
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1
6
8
.
3
5
8
.
4
4
8
.
6
3
8
.
8
2
8
.
0
2
8
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0
8
7
.
2
4
7
.
r
e
b
m
u
N
s
r
a
e
Y
f
o
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
2
5
2
0
3
APPENDIX C Present Value Tables 629
9
6
7
.
2
9
5
.
5
5
4
.
0
5
3
.
9
6
2
.
7
0
2
.
9
5
1
.
3
2
1
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4
9
0
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3
7
0
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6
5
0
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3
4
0
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3
3
0
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5
2
0
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0
2
0
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5
1
0
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2
1
0
.
9
0
0
.
7
0
0
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5
0
0
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1
0
0
.
0
0
0
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5
7
7
.
1
0
6
.
6
6
4
.
1
6
3
.
0
8
2
.
7
1
2
.
8
6
1
.
0
3
1
.
1
0
1
.
8
7
0
.
1
6
0
.
7
4
0
.
7
3
0
.
8
2
0
.
2
2
0
.
7
1
0
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3
1
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0
1
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8
0
0
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6
0
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2
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0
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1
8
7
.
0
1
6
.
7
7
4
.
3
7
3
.
1
9
2
.
7
2
2
.
8
7
1
.
9
3
1
.
8
0
1
.
5
8
0
.
6
6
0
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2
5
0
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0
4
0
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2
3
0
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5
2
0
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9
1
0
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5
1
0
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2
1
0
.
9
0
0
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7
0
0
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2
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1
0
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7
8
7
.
0
2
6
.
8
8
4
.
4
8
3
.
3
0
3
.
8
3
2
.
8
8
1
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8
4
1
.
6
1
1
.
2
9
0
.
2
7
0
.
7
5
0
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5
4
0
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5
3
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8
2
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2
2
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1
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4
1
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1
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8
0
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3
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4
9
7
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3
6
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5
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7
9
3
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1
3
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8
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1
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7
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1
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5
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9
9
0
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2
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1
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8
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6
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1
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4
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8
2
3
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2
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2
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8
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1
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4
3
1
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7
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6
8
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9
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5
5
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4
4
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4
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6
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4
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3
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5
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2
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9
7
1
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4
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3
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1
6
6
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7
3
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7
3
4
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9
8
2
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5
3
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1
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3
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3
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3
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3
3
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4
9
6
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9
7
5
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2
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4
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2
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4
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5
3
3
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9
7
2
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3
3
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4
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1
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2
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3
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8
7
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5
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4
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5
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6
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3
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5
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9
9
4
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9
1
4
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2
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3
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6
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2
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9
4
2
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2
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6
7
1
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8
4
1
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4
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4
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8
8
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4
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2
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2
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4
4
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7
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1
3
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5
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4
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1
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9
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7
3
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6
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1
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7
3
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6
1
0
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7
0
0
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5
5
8
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1
3
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4
2
6
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4
3
5
.
6
5
4
.
0
9
3
.
3
3
3
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5
8
2
.
3
4
2
.
8
0
2
.
8
7
1
.
2
5
1
.
0
3
1
.
1
1
1
.
5
9
0
.
1
8
0
.
9
6
0
.
9
5
0
.
1
5
0
.
3
4
0
.
0
2
0
.
9
0
0
.
2
6
8
.
3
4
7
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1
4
6
.
2
5
5
.
6
7
4
.
0
1
4
.
4
5
3
.
5
0
3
.
3
6
2
.
7
2
2
.
5
9
1
.
8
6
1
.
5
4
1
.
5
2
1
.
8
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1
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3
9
0
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0
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0
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9
6
0
.
0
6
0
.
1
5
0
.
4
2
0
.
2
1
0
.
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
2
5
2
0
3
r
a
e
Y
r
e
p
e
t
a
R
t
s
e
r
e
t
n
I
%
0
3
%
9
2
%
8
2
%
7
2
%
6
2
%
5
2
%
4
2
%
3
2
%
2
2
%
1
2
%
0
2
%
9
1
%
8
1
%
7
1
%
6
1
r
e
b
m
u
N
s
r
a
e
Y
f
o
.
1
2
6
.
$
s
i
5
r
a
e
y
t
a
d
e
v
i
e
c
e
r
1
$
f
o
e
u
l
a
v
t
n
e
s
e
r
p
e
h
t
,
r
a
e
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e
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t
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e
c
r
e
p
0
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i
e
t
a
r
t
s
e
r
e
t
n
i
e
h
t
f
i
,
.
g
.
e
630 APPENDIX C Present Value Tables
3
.
C
E
L
B
A
T
X
I
D
N
E
P
P
A
]
t
)
r
+
1
(
r
[
/
1
–
r
/
1
=
S
R
A
E
Y
t
F
O
H
C
A
E
R
O
F
R
A
E
Y
R
E
P
1
$
F
O
E
U
L
A
V
T
N
E
S
E
R
P
:
E
L
B
A
T
Y
T
I
U
N
N
A
%
5
1
%
4
1
%
3
1
%
2
1
0
7
8
.
6
2
6
1
.
3
8
2
2
.
5
5
8
2
.
2
5
3
3
.
4
8
7
3
.
0
6
1
4
.
7
8
4
4
.
2
7
7
4
.
9
1
0
5
.
4
3
2
5
.
1
2
4
5
.
3
8
5
5
.
4
2
7
5
.
7
4
8
5
.
4
5
9
5
.
7
4
0
6
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8
2
1
6
.
8
9
1
6
.
9
5
2
6
.
4
6
4
6
.
6
6
5
6
.
7
7
8
.
7
4
6
1
.
2
2
3
2
.
4
1
9
2
.
3
3
4
3
.
9
8
8
3
.
8
8
2
4
.
9
3
6
4
.
6
4
9
4
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6
1
2
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3
5
4
5
.
0
6
6
5
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2
4
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5
.
2
0
0
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2
4
1
6
.
5
6
2
6
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3
7
3
6
.
7
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6
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0
5
5
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3
2
6
6
.
3
7
8
6
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3
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5
8
8
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8
6
6
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1
6
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2
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4
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2
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7
1
5
3
.
8
9
9
3
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3
2
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4
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9
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2
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6
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9
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0
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3
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.
6
9
4
7
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3
9
8
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0
9
6
1
.
2
0
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2
.
7
3
0
3
.
5
0
6
3
.
1
1
1
4
.
4
6
5
4
.
8
6
9
4
.
8
2
3
5
.
0
5
6
5
.
8
3
9
5
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4
9
1
6
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4
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8
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6
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4
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9
6
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0
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0
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2
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6
6
3
7
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9
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4
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3
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7
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5
5
0
8
.
%
1
1
1
0
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3
1
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1
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4
4
4
2
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3
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6
9
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3
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1
3
2
4
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7
4
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6
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5
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7
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5
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9
8
8
5
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7
0
2
6
.
2
9
4
6
.
0
5
7
6
.
2
8
9
6
.
1
9
1
7
.
9
7
3
7
.
9
4
5
7
.
2
0
7
7
.
9
3
8
7
.
3
6
9
7
.
2
2
4
8
.
4
9
6
8
.
%
0
1
9
0
9
.
6
3
7
.
1
7
8
4
.
2
0
7
1
.
3
1
9
7
.
3
5
5
3
.
4
8
6
8
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4
5
3
3
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5
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7
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5
5
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6
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4
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6
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1
8
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6
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.
7
7
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3
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7
6
0
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7
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9
r
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Y
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t
a
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e
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t
n
I
%
9
%
8
%
7
%
6
%
5
%
4
%
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2
%
1
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e
b
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N
s
r
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o
7
1
9
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9
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1
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3
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4
3
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5
5
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.
5
5
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5
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1
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7
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4
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6
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1
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3
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1
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2
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3
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4
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5
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2
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0
1
7
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6
9
3
1
.
7
6
3
5
.
7
4
0
9
.
7
4
4
2
.
8
9
5
5
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1
5
8
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8
2
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9
2
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4
0
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9
8
1
8
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9
7
6
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1
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1
1
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3
9
.
8
0
8
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1
4
2
6
.
2
7
8
3
.
3
0
0
1
.
4
7
6
7
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4
9
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3
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5
1
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9
.
5
5
1
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6
4
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7
9
9
4
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7
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7
8
5
3
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8
5
4
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8
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9
7
4
4
.
9
3
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7
.
9
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3
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5
.
0
1
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6
.
1
1
1
4
.
2
1
3
4
9
.
3
3
8
.
1
3
7
6
.
2
5
6
4
.
3
2
1
2
.
4
7
1
9
.
4
2
8
5
.
5
0
1
2
.
6
2
0
8
.
6
0
6
3
.
7
7
8
8
.
7
4
8
3
.
8
3
5
8
.
8
5
9
2
.
9
2
1
7
.
9
1
1
.
0
1
8
4
.
0
1
3
8
.
0
1
6
1
.
1
1
7
4
.
1
1
8
7
.
2
1
6
7
.
3
1
2
5
9
.
9
5
8
.
1
3
2
7
.
2
6
4
5
.
3
9
2
3
.
4
6
7
0
.
5
6
8
7
.
5
3
6
4
.
6
8
0
1
.
7
2
2
7
.
7
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3
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6
.
1
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0
.
2
1
6
4
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2
1
9
0
.
4
1
7
3
.
5
1
2
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9
.
6
8
8
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1
5
7
7
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2
0
3
6
.
3
2
5
4
.
4
2
4
2
.
5
2
0
0
.
6
3
3
7
.
6
5
3
4
.
7
1
1
1
.
8
0
6
7
.
8
5
8
3
.
9
6
8
9
.
9
6
5
.
0
1
2
1
.
1
1
5
6
.
1
1
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1
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1
6
6
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2
1
3
1
.
3
1
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5
.
3
1
2
6
.
5
1
9
2
.
7
1
1
7
9
.
3
1
9
.
1
9
2
8
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2
7
1
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3
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5
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4
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1
4
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0
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2
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6
0
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0
.
7
6
8
7
.
7
0
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5
.
8
3
5
2
.
9
4
5
9
.
9
3
6
.
0
1
0
3
.
1
1
4
9
.
1
1
6
5
.
2
1
7
1
.
3
1
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7
.
3
1
2
3
.
4
1
8
8
.
4
1
1
4
.
7
1
0
6
.
9
1
0
8
9
.
2
4
9
.
1
4
8
8
.
2
8
0
8
.
3
3
1
7
.
4
1
0
6
.
5
2
7
4
.
6
5
2
3
.
7
2
6
1
.
8
3
8
9
.
8
7
8
7
.
9
8
5
.
0
1
5
3
.
1
1
1
1
.
2
1
5
8
.
2
1
8
5
.
3
1
9
2
.
4
1
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4
1
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6
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1
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1
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1
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4
.
2
2
0
9
9
.
0
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1
1
4
9
.
2
2
0
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.
3
3
5
8
.
4
5
9
7
.
5
8
2
7
.
6
2
5
6
.
7
6
6
5
.
8
1
7
4
.
9
7
3
.
0
1
6
2
.
1
1
3
1
.
2
1
0
0
.
3
1
7
8
.
3
1
2
7
.
4
1
6
5
.
5
1
0
4
.
6
1
3
2
.
7
1
5
0
.
8
1
2
0
.
2
2
1
8
.
5
2
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
2
5
2
0
3
| Brealey |
APPENDIX C Present Value Tables 631
%
0
3
%
9
2
%
8
2
%
7
2
9
6
7
.
1
6
3
1
.
6
1
8
1
.
6
6
1
2
.
6
3
4
2
.
3
4
6
2
.
2
0
8
2
.
5
2
9
2
.
9
1
0
3
.
2
9
0
3
.
7
4
1
3
.
0
9
1
3
.
3
2
2
3
.
9
4
2
3
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8
6
2
3
.
3
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3
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9
2
3
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4
0
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3
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1
1
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3
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6
1
3
3
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9
2
3
3
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2
3
3
3
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5
7
7
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6
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3
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1
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3
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2
2
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3
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2
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8
6
8
2
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9
9
9
2
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0
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3
.
8
7
1
3
.
9
3
2
3
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6
8
2
3
.
2
2
3
3
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1
5
3
3
.
3
7
3
3
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0
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3
3
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3
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3
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3
1
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3
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1
2
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3
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2
4
3
.
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4
3
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7
4
4
3
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1
8
7
.
2
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3
1
.
8
6
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1
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1
4
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1
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9
6
2
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3
3
3
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7
8
3
3
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7
2
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3
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9
5
4
3
.
3
8
4
3
.
3
0
5
3
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8
1
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3
.
9
2
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3
.
9
3
5
3
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6
4
5
3
.
4
6
5
3
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9
6
5
3
.
7
8
7
.
7
0
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1
.
6
9
8
1
.
0
8
2
2
.
3
8
5
2
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1
2
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2
.
9
0
0
3
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6
5
1
3
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3
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2
3
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4
6
3
3
.
7
3
4
3
.
3
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4
3
.
8
3
5
3
.
3
7
5
3
.
1
0
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3
.
3
2
6
3
.
0
4
6
3
.
4
5
6
3
.
4
6
6
3
.
3
7
6
3
.
4
9
6
3
.
1
0
7
3
.
%
6
2
4
9
7
.
4
2
4
1
.
3
2
9
1
.
0
2
3
2
.
5
3
6
2
.
5
8
8
2
.
3
8
0
3
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1
4
2
3
.
6
6
3
3
.
5
6
4
3
.
3
4
5
3
.
6
0
6
3
.
6
5
6
3
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9
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3
.
8
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5
2
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1
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9
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3
r
a
e
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r
e
p
e
t
a
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t
s
e
r
e
t
n
I
%
4
2
%
3
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%
2
2
%
1
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%
0
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9
1
%
8
1
%
7
1
%
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b
m
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1
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3
$
s
i
s
r
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5
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f
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1
$
f
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a
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t
,
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,
.
g
.
e
632 APPENDIX C Present Value Tables
4
.
C
E
L
B
A
T
X
I
D
N
E
P
P
A
r
/
]
1
–
t
)
r
+
1
(
[
=
S
R
A
E
Y
t
F
O
H
C
A
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R
O
F
R
A
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Y
R
E
P
1
$
F
O
E
U
L
A
V
E
R
U
T
U
F
:
E
L
B
A
T
Y
T
I
U
N
N
A
%
5
1
%
4
1
%
3
1
%
2
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1
.
0
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3
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3
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%
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.
%
0
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8
.
6
2
4
1
.
8
9
4
5
.
9
7
2
0
.
1
1
8
7
5
.
2
1
7
0
2
.
4
1
7
1
9
.
5
1
3
1
7
.
7
1
9
9
5
.
9
1
9
7
5
.
1
2
7
5
6
.
3
2
0
4
8
.
5
2
2
3
1
.
8
2
9
3
5
.
0
3
6
6
0
.
3
3
7
2
7
.
7
4
9
3
4
.
6
6
0
0
0
.
1
0
4
0
.
2
2
2
1
.
3
6
4
2
.
4
6
1
4
.
5
3
3
6
.
6
8
9
8
.
7
4
1
2
.
9
3
8
5
.
0
1
6
0
0
.
2
1
6
8
4
.
3
1
6
2
0
.
5
1
7
2
6
.
6
1
2
9
2
.
8
1
4
2
0
.
0
2
5
2
8
.
1
2
8
9
6
.
3
2
5
4
6
.
5
2
1
7
6
.
7
2
8
7
7
.
9
2
6
4
6
.
1
4
5
8
0
.
6
5
0
0
0
.
1
0
3
0
.
2
1
9
0
.
3
4
8
1
.
4
9
0
3
.
5
8
6
4
.
6
2
6
6
.
7
2
9
8
.
8
9
5
1
.
0
1
4
6
4
.
1
1
8
0
8
.
2
1
2
9
1
.
4
1
8
1
6
.
5
1
6
8
0
.
7
1
9
9
5
.
8
1
7
5
1
.
0
2
2
6
7
.
1
2
4
1
4
.
3
2
7
1
1
.
5
2
0
7
8
.
6
2
9
5
4
.
6
3
5
7
5
.
7
4
0
0
0
.
1
0
2
0
.
2
0
6
0
.
3
2
2
1
.
4
4
0
2
.
5
8
0
3
.
6
4
3
4
.
7
3
8
5
.
8
5
5
7
.
9
0
0
0
.
1
0
1
0
.
2
0
3
0
.
3
0
6
0
.
4
1
0
1
.
5
2
5
1
.
6
4
1
2
.
7
6
8
2
.
8
9
6
3
.
9
0
5
9
.
0
1
2
6
4
.
0
1
9
6
1
.
2
1
2
1
4
.
3
1
0
8
6
.
4
1
4
7
9
.
5
1
3
9
2
.
7
1
9
3
6
.
8
1
2
1
0
.
0
2
2
1
4
.
1
2
1
4
8
.
2
2
7
9
2
.
4
2
0
3
0
.
2
3
8
6
5
.
0
4
7
6
5
.
1
1
3
8
6
.
2
1
9
0
8
.
3
1
7
4
9
.
4
1
7
9
0
.
6
1
8
5
2
.
7
1
0
3
4
.
8
1
5
1
6
.
9
1
1
1
8
.
0
2
9
1
0
.
2
2
3
4
2
.
8
2
5
8
7
.
4
3
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
2
5
2
0
3
r
a
e
Y
r
e
p
e
t
a
R
t
s
e
r
e
t
n
I
%
9
%
8
%
7
%
6
%
5
%
4
%
3
%
2
%
1
r
e
b
m
u
N
s
r
a
e
Y
f
o
| Brealey |
APPENDIX C Present Value Tables 633
%
0
3
%
9
2
%
8
2
%
7
2
0
0
0
1
.
0
0
3
2
.
0
9
9
3
.
7
8
1
6
.
3
4
0
9
.
6
5
7
2
1
.
3
8
5
7
1
.
8
5
8
3
2
.
5
1
0
2
3
.
9
1
6
2
4
.
5
0
4
6
5
.
7
2
3
4
7
.
5
2
6
7
9
.
0
0
0
1
.
0
9
2
2
.
4
5
9
3
.
1
0
1
6
.
0
7
8
8
.
2
4
4
2
1
.
1
5
0
7
1
.
5
9
9
2
2
.
4
6
6
0
3
.
6
5
5
0
4
.
8
1
3
3
5
.
0
8
7
9
6
.
6
1
0
1
9
.
0
0
0
1
.
0
8
2
2
.
8
1
9
3
.
6
1
0
6
.
0
0
7
8
.
6
3
1
2
1
.
4
3
5
6
1
.
3
6
1
2
2
.
9
6
3
9
2
.
3
9
5
8
3
.
8
9
3
0
5
.
0
1
5
5
6
.
3
5
8
4
8
.
0
0
0
1
.
0
7
2
2
.
3
8
8
3
.
1
3
9
5
.
3
3
5
8
.
7
3
8
1
1
.
2
3
0
6
1
.
1
6
3
1
2
.
9
2
1
8
2
.
3
2
7
6
3
.
9
3
6
7
4
.
1
0
5
1
6
.
7
0
1
9
7
.
3
1
9
7
2
1
.
6
8
2
7
6
1
.
1
1
4
8
1
1
.
0
5
7
3
5
1
.
2
1
6
9
0
1
.
3
0
3
1
4
1
.
5
6
4
1
0
1
.
1
6
8
9
2
1
.
%
6
2
0
0
0
1
.
0
6
2
2
.
8
4
8
3
.
8
4
8
5
.
8
6
3
8
.
4
4
5
1
1
.
6
4
5
5
1
.
8
8
5
0
2
.
0
4
9
6
2
.
5
4
9
4
3
.
1
3
0
5
4
.
9
3
7
7
5
.
1
5
7
3
7
.
6
2
9
3
9
.
%
5
2
0
0
0
.
1
0
5
2
.
2
3
1
8
.
3
6
6
7
.
5
7
0
2
.
8
9
5
2
.
1
1
3
7
0
.
5
1
2
4
8
.
9
1
2
0
8
.
5
2
3
5
2
.
3
3
6
6
5
.
2
4
8
0
2
.
4
5
0
6
7
.
8
6
9
4
9
.
6
8
0
0
0
.
1
0
4
2
.
2
8
7
7
.
3
4
8
6
.
5
8
4
0
.
8
0
8
9
.
0
1
5
1
6
.
4
1
3
2
1
.
9
1
2
1
7
.
4
2
3
4
6
.
1
3
8
3
2
.
0
4
5
9
8
.
0
5
0
1
1
.
4
6
6
9
4
.
0
8
0
0
0
.
1
0
3
2
.
2
3
4
7
.
3
4
0
6
.
5
3
9
8
.
7
8
0
7
.
0
1
1
7
1
.
4
1
0
3
4
.
8
1
9
6
6
.
3
2
3
1
1
.
0
3
9
3
0
.
8
3
8
8
7
.
7
4
9
7
7
.
9
5
8
2
5
.
4
7
9
6
6
.
2
9
2
7
4
8
1
2
.
4
1
0
5
8
2
.
8
1
5
1
7
3
.
3
7
9
3
8
4
.
5
6
1
0
3
6
.
7
3
3
9
9
1
.
5
4
1
8
5
2
.
7
0
0
4
3
3
.
0
7
8
1
3
4
.
2
1
1
8
5
5
.
8
6
8
1
8
1
.
1
9
7
3
3
2
.
2
5
2
0
0
3
.
3
2
3
5
8
3
.
3
1
2
4
9
4
.
4
2
9
5
6
1
.
3
2
7
1
1
2
.
8
8
8
9
6
2
.
8
5
7
3
4
3
.
3
7
5
7
3
4
.
7
7
3
1
5
1
.
5
3
7
1
9
1
.
5
8
5
2
4
2
.
8
5
6
6
0
3
.
9
8
3
7
8
3
.
9
0
1
.
8
3
1
6
3
6
.
3
7
1
5
4
0
.
8
1
2
6
5
5
.
3
7
2
5
4
9
.
2
4
3
1
1
0
.
6
2
1
3
5
2
.
7
5
1
4
9
9
.
5
9
1
3
3
0
.
4
4
2
1
0
6
.
3
0
3
3
8
9
.
4
1
1
0
3
4
.
2
4
1
8
8
1
.
6
7
1
2
1
7
.
7
1
2
5
8
7
.
8
6
2
7
4
3
9
1
1
.
7
8
6
.
9
0
1
5
1
8
.
0
0
1
0
0
0
.
1
0
2
2
.
2
8
0
7
.
3
4
2
5
.
5
0
4
7
.
7
2
4
4
.
0
1
0
4
7
.
3
1
2
6
7
.
7
1
0
7
6
.
2
2
7
5
6
.
8
2
2
6
9
.
5
3
4
7
8
.
4
4
6
4
7
.
5
5
0
1
0
.
9
6
2
9
1
.
5
8
0
0
0
.
1
0
1
2
.
2
4
7
6
.
3
6
4
4
.
5
9
8
5
.
7
3
8
1
.
0
1
1
2
3
.
3
1
9
1
1
.
7
1
4
1
7
.
1
2
4
7
2
.
7
2
1
0
0
.
4
3
2
4
1
.
2
4
1
9
9
.
1
5
9
0
9
.
3
6
0
3
3
.
8
7
0
0
0
.
1
0
0
2
.
2
0
4
6
.
3
8
6
3
.
5
2
4
4
.
7
0
3
9
.
9
6
1
9
.
2
1
9
9
4
.
6
1
9
9
7
.
0
2
9
5
9
.
5
2
0
5
1
.
2
3
1
8
5
.
9
3
7
9
4
.
8
4
6
9
1
.
9
5
5
3
0
.
2
7
0
0
0
.
1
0
9
1
.
2
6
0
6
.
3
1
9
2
.
5
7
9
2
.
7
3
8
6
.
9
3
2
5
.
2
1
2
0
9
.
5
1
3
2
9
.
9
1
9
0
7
.
4
2
4
0
4
.
0
3
0
8
1
.
7
3
4
4
2
.
5
4
1
4
8
.
4
5
1
6
2
.
6
6
5
3
9
.
4
0
1
0
8
7
.
5
9
2
4
4
.
7
8
0
5
8
.
9
7
0
2
0
.
9
2
1
4
9
8
.
6
1
1
1
3
9
.
5
0
1
2
2
0
.
6
9
0
0
0
.
1
0
8
1
.
2
2
7
5
.
3
5
1
2
.
5
4
5
1
.
7
2
4
4
.
9
2
4
1
.
2
1
7
2
3
.
5
1
6
8
0
.
9
1
1
2
5
.
3
2
5
5
7
.
8
2
1
3
9
.
4
3
9
1
2
.
2
4
8
1
8
.
0
5
5
6
9
.
0
6
9
3
9
.
2
7
8
6
0
.
7
8
0
0
0
.
1
0
7
1
.
2
9
3
5
.
3
1
4
1
.
5
4
1
0
.
7
7
0
2
.
9
2
7
7
.
1
1
3
7
7
.
4
1
5
8
2
.
8
1
3
9
3
.
2
2
0
0
2
.
7
2
4
2
8
.
2
3
4
0
4
.
9
3
3
0
1
.
7
4
0
1
1
.
6
5
9
4
6
.
6
6
9
7
9
.
8
7
5
0
4
.
8
5
1
1
4
4
.
2
4
1
7
1
1
.
8
2
1
6
6
2
.
5
1
1
0
4
7
.
3
0
1
6
0
4
.
3
9
0
0
0
.
1
0
6
1
.
2
6
0
5
.
3
6
6
0
.
5
7
7
8
.
6
7
7
9
.
8
4
1
4
.
1
1
0
4
2
.
4
1
9
1
5
.
7
1
1
2
3
.
1
2
3
3
7
.
5
2
0
5
8
.
0
3
6
8
7
.
6
3
2
7
6
.
3
4
0
6
6
.
1
5
5
2
9
.
0
6
3
7
6
.
1
7
1
4
1
.
4
8
4
5
2
.
4
9
1
4
5
3
.
3
7
1
0
4
7
.
4
5
1
6
6
1
.
8
3
1
4
1
4
.
3
2
1
5
8
2
.
0
1
1
3
0
6
.
8
9
9
8
9
.
7
3
2
8
5
7
.
0
1
2
8
8
6
.
6
8
1
8
1
4
.
5
6
1
8
2
6
.
6
4
1
3
3
0
.
0
3
1
0
8
3
.
5
1
1
.
0
8
8
4
3
2
.
9
9
9
2
7
8
.
2
6
2
0
0
2
.
2
8
2
6
1
7
.
0
8
6
0
7
1
.
3
2
3
7
8
5
.
0
2
4
5
4
1
.
8
9
2
1
8
4
.
4
6
8
3
2
1
.
3
0
2
4
9
3
9
7
.
4
5
0
1
7
1
.
7
2
2
3
9
0
.
8
9
8
1
6
.
4
6
7
6
9
.
0
5
6
4
2
.
4
5
5
8
9
.
1
7
4
2
4
0
.
2
0
4
3
0
6
.
2
4
3
5
0
1
.
2
9
2
4
1
2
.
9
4
2
2
9
.
0
4
6
2
9
4
.
0
6
1
2
8
0
.
7
6
7
1
5
1
.
5
4
4
1
8
8
.
1
8
1
1
2
1
7
.
6
6
9
8
4
9
.
0
9
7
9
3
4
.
7
4
6
2
1
3
.
0
3
5
1
2
3
4
5
6
7
8
9
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
0
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Glossary
acquisition: Takeover of a firm by purchase of that firm’s com-
mon stock or assets.
additional paid-in capital: Difference between issue price and
par value of stock. Also called capital surplus.
agency problems: Conflicts of interest between the firm’s own-
between risk and return which states that the expected risk
premium on any security equals its beta times the market risk
premium.
capital budget: List of planned investment projects.
capital budgeting decision: Decision as to which real assets the
ers and managers.
firm should acquire.
aging schedule: Classification of accounts receivable by time
outstanding.
capital markets: Markets for long-term financing.
capital rationing: Limit set on the amount of funds available for
annual percentage rate (APR): Interest rate that is annualized
investment.
using simple interest.
annuity: Equally spaced level stream of cash flows.
annuity due: Level stream of cash flows starting immediately.
annuity factor: Present value of an annuity of $1 per period.
authorized share capital: Maximum number of shares that the
company is permitted to issue, as specified in the firm’s arti-
cles of incorporation.
capital structure: Firm’s mix of long-term financing.
CAPM: See capital asset pricing model.
carrying costs: Costs of maintaining current assets, including
opportunity cost of capital.
cash conversion cycle: Period between firm’s payment for mate-
rials and collection on its sales.
cash cow: Business that produces a lot of cash but few growth
availability float: Checks already deposited that have not yet
prospects.
been cleared.
average tax rate: Total taxes owed divided by total income.
balance sheet: Financial statement that shows the value of the
| Brealey |
firm’s assets and liabilities at a particular time.
cash dividend: Payment of cash by the firm to its shareholders.
CEO: Acronym for chief executive officer.
CFO: See chief financial officer.
chief financial officer (CFO): Officer who oversees the treas-
balancing item: Variable that adjusts to maintain the consistency
urer and controller and sets overall financial strategy.
of a financial plan. Also called plug.
bankruptcy: The reorganization or liquidation of a firm that can-
not pay its debts.
collection policy: Procedures to collect and monitor receivables.
commercial paper: Short-term unsecured notes issued by firms.
common-size balance sheet: Balance sheet that presents items
bear market: A market in which stock or bond prices are gener-
as a percentage of total assets.
ally falling.
common-size income statement: Income statement that presents
beta: Sensitivity of a stock’s return to the return on the market
items as a percentage of revenues.
portfolio.
bond: Security that obligates the issuer to make specified pay-
ments to the bondholder.
book rate of return: Accounting income divided by book value.
Also called accounting rate of return.
book value: Net worth of the firm’s assets or liabilities accord-
ing to the balance sheet.
break-even analysis: Analysis of the level of sales at which the
company breaks even.
bull market: A market in which stock or bond prices are gener-
ally rising.
common stock: Ownership shares in a publicly held corporation.
company cost of capital: Expected rate of return demanded by
investors in a company, determined by the average risk of the
company’s assets and operations.
compound interest: Interest earned on interest.
concentration banking: System whereby customers make pay-
ments to a regional collection center which transfers funds to
a principal bank.
constant-growth dividend discount model: Version of the divi-
dend discount model in which dividends grow at a constant rate.
controller: Officer responsible for budgeting, accounting, and
call option: Right to buy an asset at a specified exercise price on
auditing.
or before the exercise date.
convertible bond: Bond that the holder may exchange for a spec-
callable bond: Bond that may be repurchased by the issuer be-
ified number of shares.
fore maturity at specified call price.
corporation: Business owned by stockholders who are not per-
capital asset pricing model (CAPM): Theory of the relationship
sonally liable for the business’s liabilities.
635
636 GLOSSARY
costs of financial distress: Costs arising from bankruptcy or dis-
exchange rate: Amount of one currency needed to purchase one
torted business decisions before bankruptcy.
unit of another.
coupon: The interest payments paid to the bondholder.
coupon rate: Annual interest payment as a percentage of face
value.
ex-dividend date: Date that determines whether a stockholder is
entitled to a dividend payment; anyone holding stock before
this date is entitled to a dividend.
credit analysis: Procedure to determine the likelihood a cus-
expectations theory of exchange rates: Theory that expected
tomer will pay its bills.
spot exchange rate equals the forward rate.
credit policy: Standards set to determine the amount and nature
face value: Payment at the maturity of the bond. Also called par
of credit to extend to customers.
cumulative voting: Voting system in which all the votes one
shareholder is allowed to cast can be cast for one candidate for
the board of directors.
current yield: Annual coupon payments divided by bond price.
decision tree: Diagram of sequential decisions and possible out-
comes.
default premium: Difference in promised yields between a
default-free bond and a riskier bond.
degree of operating leverage (DOL): Percentage change in prof-
its given a 1 percent change in sales.
depreciation tax shield: Reduction in taxes attributable to the
depreciation allowance.
discount factor: Present value of a $1 future payment.
discount rate: Interest rate used to compute present values of fu-
| Brealey |
ture cash flows.
value or maturity value.
Fed: See Federal Reserve.
Federal Reserve (the Fed): The central bank in the United
States, responsible for setting interest rates.
financial assets: Claims to the income generated by real assets.
Also called securities.
financial intermediary: Firm that raises money from many
small investors and provides financing to businesses or other
organizations by investing in their securities.
financial leverage: Debt financing amplifies the effects of
changes in operating income on the returns to stockholders.
financial markets: Markets in which financial assets are traded.
financial risk: Risk to shareholders resulting from the use of
debt.
financial slack: Ready access to cash or debt financing.
financing decision: Decision as to how to raise the money to
diversification: Strategy designed to reduce risk by spreading
pay for investments in real assets.
the portfolio across many investments.
dividend: Periodic cash distribution from the firm to its share-
fixed costs: Costs that do not depend on the level of output.
floating-rate security: Security paying dividends or interest that
holders.
dividend discount model: Computation of today’s stock price
which states that share value equals the present value of all
expected future dividends.
vary with short-term interest rates.
forex: Abbreviation for foreign exchange; also abbreviated fx.
forward contract: Agreement to buy or sell an asset in the future
at an agreed price.
dividend payout ratio: Percentage of earnings paid out as divi-
forward rate of exchange: Exchange rate for a forward transac-
dends.
tion.
Dow Jones Industrial Average: Index of the investment per-
formance of a portfolio of 30 “blue-chip” stocks.
Du Pont system: A breakdown of ROE and ROA into compo-
nent ratios.
economic order quantity: Order size that minimizes total inven-
fundamental analysts: Analysts who attempt to find under- or
overvalued securities by analyzing fundamental information,
such as earnings, asset values, and business prospects.
funded debt: Debt with more than 1 year remaining to maturity.
future value: Amount to which an investment will grow after
tory costs.
earning interest.
economic value added (EVA): Term used by the consulting firm
Stern Stewart for profit remaining after deduction of the cost
of the capital employed.
effective annual interest rate: Interest rate that is annualized
using compound interest.
efficient capital markets: Financial markets in which security
prices rapidly reflect all relevant information about asset val-
ues.
futures contract: Exchange-traded promise to buy or sell an
asset in the future at a prespecified price.
fx: Abbreviation for foreign exchange; also abbreviated forex.
GAAP: See generally accepted accounting principles.
general cash offer: Sale of securities open to all investors by an
already-public company.
generally accepted accounting principles (GAAP): Procedures
for preparing financial statements.
equivalent annual cost: The cost per period with the same pres-
ent value as the cost of buying and operating a machine.
income statement: Financial statement that shows the revenues,
expenses, and net income of a firm over a period of time.
eurobond: Bond that is marketed internationally.
eurodollars: Dollars held on deposit in a bank outside the
United States.
EVA: See economic value added.
inflation: Rate at which prices as a whole are increasing.
information content of dividends: Dividend increases send good
news about cash flow and earnings. Dividend cuts send bad
news.
GLOSSARY 637
initial public offering (IPO): First offering of stock to the gen-
eral public.
interest rate parity: Theory that forward premium equals inter-
est rate differential.
interest tax shield: Tax savings resulting from deductibility of
interest payments.
internal growth rate: Maximum rate of growth without external
financing.
market risk: Economywide (macroeconomic) sources of risk that | Brealey |
affect the overall stock market. Also called systematic risk.
market risk premium: Risk premium of market portfolio. Dif-
ference between market return and return on risk-free Trea-
sury bills.
market value added: Market value of equity minus book value.
market-value balance sheet: Financial statement that uses the
market value of all assets and liabilities.
internal rate of return (IRR): Discount rate at which project
maturity premium: Extra average return from investing in long-
NPV = 0.
versus short-term Treasury securities.
internally generated funds: Cash reinvested in the firm; depre-
merger: Combination of two firms into one, with the acquirer
ciation plus earnings not paid out as dividends.
assuming assets and liabilities of the target firm.
international Fisher effect: Theory that real interest rates in all
countries should be equal, with differences in nominal rates
reflecting differences in expected inflation.
MM dividend-irrelevance proposition: Theory that under ideal
conditions, the value of the firm is unaffected by dividend
policy.
in the black: Making a profit.
in the red: Making a loss.
investment grade: Bonds rated Baa or above by Moody’s or
BBB or above by Standard & Poor’s.
issued shares: Shares that have been issued by the company.
IPO: See initial public offering.
IRR: See internal rate of return.
junk bond: Bond with a rating below Baa or BBB.
law of one price: Theory that prices of goods in all countries
should be equal when translated to a common currency.
lease: Long-term rental agreement.
leveraged buyout (LBO): Acquisition of the firm by a private
MM’s proposition I (debt irrelevance proposition): The value of
a firm is unaffected by its capital structure.
MM’s proposition II: The required rate of return on equity in-
creases as the firm’s debt-equity ratio increases.
Modified Accelerated Cost Recovery System (MACRS): Depre-
ciation method that allows higher tax deductions in early years
and lower deductions later.
money market: Market for short-term financial assets.
mutually exclusive projects: Two or more projects that cannot be
pursued simultaneously.
net float: Difference between payment float and availability
float.
group using substantial borrowed funds.
net present value (NPV): Present value of cash flows minus ini-
limited liability: The owners of the corporation are not person-
tial investment.
ally responsible for its obligations.
line of credit: Agreement by a bank that a company may borrow
at any time up to an established limit.
liquidation: Sale of bankrupt firm’s assets.
liquidation value: Net proceeds that would be realized by selling
the firm’s assets and paying off its creditors.
liquidity: Ability of an asset to be converted to cash quickly at
net working capital: Current assets minus current liabilities.
net worth: Book value of common stockholders’ equity plus pre-
ferred stock.
nominal interest rate: Rate at which money invested grows.
NPV: See net present value.
NYSE: New York Stock Exchange.
open account: Agreement whereby sales are made with no for-
low cost.
mal debt contract.
lock-box system: System whereby customers send payments to a
post office box and a local bank collects and processes
checks.
operating leverage: Degree to which costs are fixed.
operating risk (business risk): Risk in firm’s operating income.
opportunity cost of capital: Expected rate of return given up by
long position: Purchase of an investment.
majority voting: Voting system in which each director is voted
investing in a project.
opportunity cost: Benefit or cash flow forgone as a result of an
on separately.
action.
management buyout (MBO): Acquisition of the firm by its own
management in a leveraged buyout.
M&A: Abbreviation for mergers and acquisitions.
marginal tax rate: Additional taxes owed per dollar of addi-
tional income.
market index: Measure of the investment performance of the
overall market.
market portfolio: Portfolio of all assets in the economy. In prac-
tice a broad stock market index, such as the Standard & Poor’s | Brealey |
Composite, is used to represent the market.
OTC: See over-the-counter.
outstanding shares: Shares that have been issued by the com-
pany and are held by investors.
over-the-counter (OTC): Shares traded off an organized ex-
change. Also used to refer to the Nasdaq market.
par value: Value of security shown on certificate.
partnership: Business owned by two or more persons who are
personally responsible for all its liabilities.
payback period: Time until cash flows recover the initial invest-
ment of the project.
638 GLOSSARY
payment float: Checks written by a company that have not yet
reorganization: Restructuring of financial claims on failing
cleared.
firm to allow it to keep operating.
payout ratio: Fraction of earnings paid out as dividends.
P/E: See price-earnings multiple.
pecking order theory: Firms prefer to issue debt rather than eq-
residual income: Also called economic value added. Profit
minus cost of capital employed.
restructuring: Process of changing the firm’s capital structure
uity if internal finance is insufficient.
without changing its assets.
percentage of sales models: Planning model in which sales fore-
casts are the driving variables and most other variables are
proportional to sales.
perpetuity: Stream of level cash payments that never ends.
planning horizon: Time horizon for a financial plan.
plowback ratio: Fraction of earnings retained by the firm.
poison pill: Measure taken by a target firm to avoid acquisition;
for example, the right for existing shareholders to buy addi-
tional shares at an attractive price if a bidder acquires a large
holding.
preferred stock: Stock that takes priority over common stock in
regard to dividends.
present value (PV): Value today of a future cash flow.
present value of growth opportunities (PVGO): Net present
value of a firm’s future investments.
price-earnings (P/E) multiple: Ratio of stock price to earnings
per share.
primary market: Market for the sale of new securities by corpo-
rations.
prime rate: Benchmark interest rate charged by banks.
private placement: Sale of securities to a limited number of in-
vestors without a public offering.
pro formas: Projected or forecasted financial statements.
profitability index: Ratio of net present value to initial invest-
ment.
project cost of capital: Minimum acceptable expected rate of re-
turn on a project given its risk.
prospectus: Formal summary that provides information on an
issue of securities.
protective covenant: Restriction on a firm to protect bond-
holders.
proxy contest: Takeover attempt in which outsiders compete
with management for shareholders’ votes. Also called proxy
fight.
purchasing power parity (PPP): Theory that the cost of living in
different countries is equal, and exchange rates adjust to off-
set inflation differentials across countries.
put option: Right to sell an asset at a specified exercise price on
or before the exercise date.
PV: See present value.
random walk theory: Security prices change randomly, with no
predictable trends or patterns.
rate of return: Total income per period per dollar invested.
real assets: Assets used to produce goods and services.
real interest rate: Rate at which the purchasing power of an in-
vestment increases.
real options: Options embedded in real assets.
real value of $1: Purchasing power–adjusted value of a dollar.
retained earnings: Earnings not paid out as dividends.
rights issue: Issue of securities offered only to current stock-
holders.
risk premium: Expected return in excess of risk-free return as
compensation for risk.
S&P: Abbreviation for Standard & Poor’s stockmarket index.
scenario analysis: Project analysis given a particular combina-
tion of assumptions.
seasoned offering: Sale of securities by a firm that is already
publicly traded.
SEC: See Securities and Exchange Commission.
secondary market: Market in which already issued securities are
traded among investors.
secured debt: Debt that has first claim on specified collateral in
| Brealey |
the event of default.
Securities and Exchange Commission (SEC): Federal agency
responsible for regulation of securities markets in the United
States.
security market line: Relationship between expected return and
beta.
semi-strong-form efficiency: Market prices reflect all publicly
available information.
sensitivity analysis: Analysis of the effects of changes in sales,
costs, and so on, on project profitability.
shark repellent: Amendments to a company charter made to
forestall takeover attempts.
shelf registration: A procedure that allows firms to file one reg-
istration statement for several issues of the same security.
shortage costs: Costs incurred from shortages in current assets.
short position: The sale of an investment, particularly by some-
one who does not yet own it.
simple interest: Interest earned only on the original investment;
no interest is earned on interest.
simulation analysis: Estimation of the probabilities of different
possible outcomes, e.g., from an investment project.
sinking fund: Fund established to retire debt before maturity.
sole proprietor: Sole owner of a business which has no partners
and no shareholders. The proprietor is personally liable for all
the firm’s obligations.
spot rate of exchange: Exchange rate for an immediate transac-
tion.
spread: Difference between public offer price and price paid by
underwriter.
stakeholder: Anyone with a financial interest in the firm.
Standard & Poor’s Composite Index: Index of the investment
performance of a portfolio of 500 large stocks. Also called the
S&P 500.
GLOSSARY 639
standard deviation: Square root of variance. Another measure of
treasury stock: Stock that has been repurchased by the company
volatility.
statement of cash flows: Financial statement that shows the
firm’s cash receipts and cash payments over a period of time.
stock dividend: Distribution of additional shares to a firm’s
stockholders.
stock repurchase: Firm buys back stock from its shareholders.
stock split: Issue of additional shares to firm’s stockholders.
straight-line depreciation: Constant depreciation for each year
of the asset’s accounting life.
strong-form efficiency: Market prices rapidly reflect all infor-
mation that could in principle be used to determine true value.
subordinated debt: Debt that may be repaid in bankruptcy only
after senior debt is paid.
and held in its treasury.
underpricing: Issuing securities at an offering price set below
the true value of the security.
underwriter: Firm that buys an issue of securities from a com-
pany and resells it to the public.
unique risk: Risk factors affecting only that firm. Also called di-
versifiable risk.
variable costs: Costs that change as the level of output changes.
variance: Average value of squared deviations from mean. A
measure of volatility.
venture capital: Money invested to finance a new firm.
WACC: See weighted-average cost of capital.
warrant: Right to buy shares from a company at a stipulated
sunk costs: Costs that have been incurred and cannot be recov-
price before a set date.
ered.
sustainable growth rate: Steady rate at which a firm can grow
without changing leverage; plowback ratio × return on equity.
swap: Arrangement by two counterparties to exchange one
stream of cash flows for another.
technical analysts: Investors who attempt to identify over- or
undervalued stocks by searching for patterns in past prices.
tender offer: Takeover attempt in which outsiders directly offer
to buy the stock of the firm’s shareholders.
terms of sale: Credit, discount, and payment terms offered on a
sale.
weak-form efficiency: Market prices rapidly reflect all informa-
tion contained in the history of past prices.
weighted-average cost of capital (WACC): Expected rate of re-
turn on a portfolio of all the firm’s securities, adjusted for tax
savings due to interest payments.
white knight: Friendly potential acquirer sought by a target com-
pany threatened by an unwelcome suitor.
workout: Agreement between a company and its creditors estab- | Brealey |
lishing the steps the company must take to avoid bankruptcy.
yield curve: Graph of the relationship between time to maturity
and yield to maturity.
trade-off theory: Debt levels are chosen to balance interest tax
yield to maturity: Interest rate for which the present value of the
shields against the costs of financial distress.
bond’s payments equals the price.
treasurer: Manager responsible for financing, cash manage-
ment, and relationships with financial markets and institu-
tions.
zero-balance account: Regional bank account to which just
enough funds are transferred daily to pay each day’s bills.
| Brealey |