Solutions to Assignment #2 Questions
CH 4
2.
Two countries, the United States and England, produce only one good, wheat. Suppose the price of
wheat is $3.25 in the United States and is £1.35 in England.
a.
According to the law of one price, what should the $:£ spot exchange rate be?
ANSWER. Since the price of wheat must be the same in both nations, the exchange rate, e, is 3.25/1.35
or e = $2.4074.
b.
Suppose the price of wheat over the next year is expected to rise to $3.50 in the United States and to
£1.60 in England. What should the one-year $:£ forward rate be?
ANSWER. In the absence of uncertainty, the forward rate, f, should be 3.50/1.60 or f = $2.1875.
c.
If the U.S. government imposes a tariff of $0.50 per bushel on wheat imported from England, what is
the maximum possible change in the spot exchange rate that could occur?
ANSWER. If e is the exchange rate, then wheat selling in England at £1.35 will sell in the United States for
1.35e + 0.5, where 0.5 is the U.S. tariff on English wheat. In order to eliminate the possibility of arbitrage,
1.35e + 0.5 must be greater than or equal to $3.25, the price of wheat in the U.S. or e > $2.0370. Thus the
maximum exchange rate change that could occur is (2.4074 - 2.0370)/2.4074 = 15.38%. This solution
assumes that the pound and dollar prices of wheat remain the same as before the tariff.
3.
If expected inflation is 100 percent and the real required return is 5 percent, what will the nominal
interest rate be according to the Fisher effect?
ANSWER. According to the Fisher effect, the relationship between the nominal interest rate, r, the real
interest rate a, and the expected inflation rate, i, is 1 + r = (1 + a)(1 + i). Substituting in the numbers in the
problem yields 1 + r = 1.05 x 2 = 2.1, or r = 110%.
4.
In early 1996, the short-term interest rate in France was 3.7%, and forecast French inflation was 1.8%.
At the same time, the short-term German interest rate was 2.6% and forecast German inflation was
1.6%.
1
a.
Based on these figures, what were the real interest rates in France and Germany?
ANSWER. The French real interest rate was 1.037/1.018 - 1 = 1.87%. The corresponding real rate in
Germany was 1.026/1.016 - 1 = 0.98%.
b.
To what would you attribute any discrepancy in real rates between France and Germany?
ANSWER. The most likely reason for the discrepancy is the inclusion of a higher inflation risk component
in the French real interest rate than in the German real rate. Other possibilities are the effects of currency
risk or transactions costs precluding this seeming arbitrage opportunity.
5.
In July, the one-year interest rate is 12% on British pounds and 9% on U.S. dollars.
a.
If the current exchange rate is $1.63:£1, what is the expected future exchange rate in one year?
ANSWER. According to the international Fisher effect, the spot exchange rate expected in one year
equals 1.63 x 1.09/1.12 = $1.5863.
b.
Suppose a change in expectations regarding future U.S. inflation causes the expected future spot rate
to decline to $1.52:£1. What should happen to the U.S. interest rate?
ANSWER. If rus is the unknown U.S. interest rate, and assuming that the British interest rate stayed at 12%
(because there has been no change in expectations of British inflation), then according to the IFE, 1.52/1.63
= (1+rus)/1.12 or rus = 4.44%.
7.
Chase Econometrics has just published projected inflation rates for the United States and Germany for
the next five years. U.S. inflation is expected to be 10 percent per year, and German inflation is
expected to be 4 percent per year.
1.
a.
If the current exchange rate is $0.95/€, what should the exchange rates for the next five years be?
ANSWER. According to PPP, the exchange rate for the euro at the end of year t should equal
0.95(1.10/1.04)t. Hence, projected exchange rates for the next 5 years are $1.0048, $1.0628, $1.1241,
$1.1889, $1.2575.
2
b.
Suppose that U.S. inflation over the next five years turns out to average 3.2%, German inflation
averages 1.5%, and the exchange rate in five years is $0.99/€. What has happened to the real value of
the euro over this five-year period?
ANSWER. According to Equation 4.7, the real value of the euro at the end of five years is
’
t
e = et
(1 + i f )t
1.015 5
= 0.99 x (
) = 0.9111
t
1.032
(1 + i h )
Hence, even though the euro has appreciated in nominal terms over this five-year period, it has fallen
in real terms by 4.09% [(0.9111 - 0.95)/0.95].
8.
During 1995, the Mexican peso exchange rate rose from Mex$5.33/U.S.$ to Mex$7.64/U.S.$. At the
same time, U.S. inflation was approximately 3% in contrast to Mexican inflation of about 48.7%.
a.
By how much did the nominal value of the peso change during 1995?
ANSWER. During 1995, the peso fell from $0.1876 (1/5.33) to $0.1309 (1/7.64), which is equivalent to a
devaluation of 30.24% ((0.1309 - 0.1876)/0.1876)
b.
By how much did the real value of the peso change over this period?
ANSWER. Using Equation 4.7, the real value of the peso by the end of 1995 was $0.1890:
’
t
e = et
(1 + i f )t
1.487
= 0.1309 x
= 0.1890
t
1.03
(1 + i h )
Based on this real exchange rate, the peso has appreciated during 1995 by 0.72% ((0.1890 0.1876)/0.1876). In other words, the real exchange rate stayed virtually constant, implying the purchasing
power parity held during the year.
Ch. 12
3
1.
A European company issues common shares that pay taxable dividends and bearer shares that pay an
identical dividend but offer an opportunity to evade taxes: Bearer shares come with a large supply of
coupons that can be redeemed anonymously at banks for the current value of the dividend.
a.
Suppose taxable dividends are taxed at the rate of 10 percent. What is the ratio between market
prices of taxable and bearer shares? If a new issue is planned, should taxable or bearer shares be sold?
ANSWER. Under these conditions, the taxable proceeds are 1 - 0.10 = 90% of the bearer proceeds.
Hence, the taxable shares will sell for 90% of the bearer shares. Bearer shares should be sold.
b.
Suppose, in addition, that it costs 10 percent of proceeds to issue a taxable dividend, whereas it costs
20 percent of the proceeds to issue bearer stocks because of the expense of distribution and coupon
printing. What type of share will the corporation prefer to issue?
ANSWER. In this case, the taxable proceeds are (1 - .10)(1 - .10) = 81% of gross bearer proceeds, and net
bearer proceeds are 1 - .20 = 80% of gross bearer proceeds. The firm will now prefer to issue taxable
equity.
c.
Suppose now that individuals pay 10 percent taxes on dividends, and corporations pay no taxes, but
bear an administrative cost of 10 percent of the value of any bearer dividends. Can you determine the
relative market prices for the two types of shares?
ANSWER. In this case, both issues yield 90% of gross bearer proceeds. Both types of shares will,
therefore, sell for the same price and the firm will be indifferent between the two.
Ch. 13
1.
Suppose that the current 180-day interbank Eurodollar rate is 9 percent (all rates are stated on an
annualized basis). If next period's rate is 9.5 percent, what will a Eurocurrency loan priced at LIBOR plus
1 percent cost?
ANSWER. Eurodollar loans are made on a floating rate basis, with the rate set at a fixed margin over
LIBOR. Thus, if next period's annualized LIBOR is 9.5%, then the Eurocurrency loan will be at 10.5% (9.5% +
1%) on an annualized basis.
4
2.
Citibank offers to syndicate a Eurodollar credit for the government of Poland
with the following terms:
Principal
US$1,000,000,000
Maturity
7 years
Interest rate
LIBOR + 1.5%, reset every six months
Syndication fee
1.75%
a.
What are the net proceeds to Poland from this syndicated loan?
ANSWER. Poland will receive $982,500,000, which equals the $1 billion less the 1.75% syndication fee.
b.
Assuming that six-month LIBOR is currently at 6.35 percent, what is the effective
annual interest cost to Poland for the first six months of this loan?
ANSWER. At 6-month LIBOR + 1.5%, Poland will pay interest at an annual rate of 7.85% (6.35% + 1.5%).
Interest = 1,000,000,000 × 7.85%/2 = $39,250,000
Effective rate =(39,250,000/982,500,000) × 2 = 7.99%
3.
IBM needs to raise $1 billion and is trying to decide between a domestic dollar
bond issue and a Eurobond issue. The U.S. bond can be issued at a coupon of 6.75 percent, paid
semiannually, with underwriting and other expenses totaling 0.95 percent of the issue size. The Eurobond
would cost only 0.55 percent to issue but would bear an annual coupon of 6.88 percent. Both issues would
mature in 10 years.
a.
Assuming all else is equal, which is the least expensive issue for IBM?
ANSWER. The least expensive issue can be found by comparing the yield to maturity (YTM) for each bond,
computed as the internal rate of return or IRR. For the domestic bond issue, the YTM is the solution r to the
following equation:
5
20
$990,500,000 = 
t=1
$33,750,000 $1,000,000,000
+
(1 + r )t
(1 + r )20
where the $990,500,000 in bond proceeds equals the billion dollar issue less 0.95% in issuance costs.
The solution turns out to be r = 3.44%. Since this is a semiannual yield, we must convert it to annualized
basis. The annualized YTM is found as (1.0344)2 - 1, or 7.00%.
For the Eurobond issue, the YTM is the solution k to the following equation:
10
$994,500,000 = 
t=1
$68,800,000 $1,000,000,000
+
(1 + r )t
(1 + r )10
The solution to this equation turns out to be k = 6.96%. Since this YTM is less than the annualized YTM
for the U.S. bond, the Eurobond is the less expensive bond to issue.
b.
What other factors might IBM want to consider before deciding which bond to
issue?
ANSWER. IBM might like to consider whether by issuing a Eurobond it can increase its investment
presence among a different class of investor. It should also take into account the terms of the call and other
provisions. Moreover, if it has any thoughts of revising the terms of the bond issue in the future, it should
consider the greater difficulty it would have with the Eurobond issue (because buyers are largely
anonymous).
4.
Daewoo Motors has been told it could issue $150 million face value in Euro-CP at
a discount rate of 8.9 percent based on a 360-day year.
a.
If the maturity of Daewoo's Euro-CP is 91 days, what will be its proceeds from the
issue?
ANSWER. Giving the discount pricing conventions for Euronotes and Euro-CP, the market price of an
issue is calculated using Equation 13.4 from the text:
The application of Equation 13.4 would yield a market price of $146,625,417 for the Daewoo issue:
6
Market price = Face value x [1 - ( Discount rate x
Market price = $150,000,000 x [1 - ( 0.089 x
b.
n
)]
360
91
)] = $146,625,417
360
What will be its annual yield on this issue?
ANSWER. The annual yield can be computed using Equation 13.6:
Annual yield = Discount rate x
Face value
Market price
In the case of the Daewoo issue, the annual yield would be 9.10%:
Annual yield = 8.9% x
5.
$150,000,000
= 9.10%
$146,625,417
Commerzbank in seeking to invest $100 million short term. It has the choice
between buying Euro-CP yielding 6.34 percent annually and a U.S. bank deposit yielding 6.36 percent
annually, both maturing in 150 days. The Euro-CP yield is calculated on a 360-day year, whereas the U.S.
bank-deposit yield is calculated on a 365-day year.
a.
How much Euro-CP in terms of face value can Commerzbank's $100 million buy?
ANSWER. We can reverse Equation 13.7 to solve for the face value of Euro-CP that $100 million can buy:
7
Face value = Market value x(1 + Annual yield x
= $100,000,000 x(1 + 0.0634 x
b.
n
)
360
150
) = $102,641,667
360
Assuming that all else is equal, which is Commerzbank's preferred investment?
Explain.
ANSWER. The Euro-CP will earn 6.34% x 150/360 or 2.64% for the 150-day period. The 150-day yield on
the U.S. bank deposit is 6.36% x 150/365, or 2.61%. Other things being equal, the higher yield on the EuroCP will dominate.
c.
What would be the annual yield on the U.S. bank deposit if it were quoted on a
360-day year?
ANSWER. To convert a yield from one based on a 365-day year to one based on a 360-day year, we must
multiply it by 360/365. Thus, the yield on the U.S. bank deposit quoted on a 360-day year equals 6.27%
(6.36% x 360/365).
d.
What would be the annual Euro-CP yield if it were quoted on a 365-day year?
ANSWER. To convert the Euro-CP yield to one based on a 365-day year, we must multiply it by 365/360.
Doing so generates a quoted yield based on a 365-day year of 6.43% (6.34% x 365/360). Based on the
answers to parts c and d, we can see that when quoted on an apples-to-apples basis, the annualized yield
on the Euro-CP exceeds the annualized yield on the U.S. bank deposit
CH 14
1.
A firm with a corporate-wide debt/equity ratio of 1:2, an after-tax cost of debt of 7 percent, and a
cost of equity capital of 15 percent is interested in pursuing a foreign project. The debt capacity of the
project is the same as for the company as a whole, but its systematic risk is such that the required return on
equity is estimated to be about 12 percent. The after-tax cost of debt is expected to remain at 7 percent.
a.
What is the project's weighted average cost of capital? How does it compare with the parent's
WACC?
8
ANSWER. The weighted average cost of capital for the project is
kI = (1 - w) x ke' + w x id(1 - t)
where w is the ratio of debt to total assets, k e' is the required risk-adjusted return on project equity,
and id(1 - t) is the after-tax cost of debt for the project. Substituting in the numbers provided yields
kI = 2/3 x 12% + 1/3 x 7% = 10.33%
2.
Suppose that a foreign project has a beta of 0.85, the risk-free return is 12 percent, and the
required return on the market is estimated at 19 percent. What is the cost of capital for the project?
ANSWER. The cost of capital for the project is
k* = Rf + β*[E(Rm) - Rf]
where Rf is the risk-free required return, β* is the project beta, and E(Rm) is the expected return on the
market. Substituting in the numbers provided in the problem yields
k* = .12 + .85(.19 - .12) = 17.95%
3. IBM is considering having its German affiliate issue a 10-year, $100 million bond denominated in euros
and priced to yield 7.5 percent. Alternatively, IBM’s German unit can issue a dollar-denominated bond of the
same size and maturity and carrying an interest rate of 6.7 percent..
a. If the euro is forecast to depreciate by 1.7 percent annually, what is the expected dollar cost of the eurodenominated bond? How does this compare to the cost of the dollar bond?
ANSWER. According to Chapter 14, the pre-tax dollar cost of borrowing in a foreign currency at an
interest rate of rL, where the currency is expected to appreciate (depreciate) against the dollar at an annual
rate of c, is rL(1 + c) + c. Substituting the numbers in the problem to this formula yields an expected dollar
cost of borrowing euros of 5.67% [7.5% x (1 - 0.017) - 1.7%). This figure is substantially below the 6.7% cost
of borrowing dollars.
b. At what rate of euro depreciation will the dollar cost of the euro-denominated bond equal the dollar cost
of the dollar-denominated bond?
9
ANSWER. The answer to this question is the solution to 7.5% x (1 + c) + c = 6.7%, or c = (6.7% 7.5%)/1.075 = -0.74%.
c. Suppose IBM’s German unit faces a 35 percent corporate tax rate. What is the expected after-tax dollar
cost of the euro-denominated bond?
ANSWER. According to Chapter 14, the effective after-tax dollar cost of borrowing a local currency at an
interest rate of rL, annual currency appreciation (depreciation) of c, and a corporate tax rate of ta, is r = rL(1
+ c)(1 - ta) + c. Substituting in the numbers from the question yields a solution of r = 7.5% x (1 - 0.017)(1 0.35) - 0.017 = 4.78%.
4. Suppose that the cost of borrowing restricted euros is 7 percent annually, whereas the market rate for
these funds is 12 percent. If a firm can borrow €10 million of restricted funds, how much will it save
annually in before-tax franc interest expense?
ANSWER. The annual interest savings on €10 million of restricted funds at 7% when the market rate is 12%
equals €10,000,000(0.12 - 0.07) or €500,000.
Ch 15:
1.
During the year the price of British gilts (government bonds) went from £102 to £106, while paying a
coupon of £9. At the same time, the exchange rate went from £1:$1.76 to £1:$1.62. What was the
total dollar return, in percent, on gilts for the year?
ANSWER. Rewriting Equation 15.4, the one-period total dollar return on a foreign bond investment
r$ can be calculated as follows:
Dollar
return
=
Local currency
return
x
Currency
gain (loss)
 B(1) B(0) + C 
1 + r $ = 1 +
 (1 + g)
B(0)


where B(t) = local currency bond price at time t
C
= local currency coupon income
G
= percent change in dollar value of LC
With an initial bond price of £102, coupon income of £9, end-of-period bond price of £106, and pound
depreciation of (1.62 - 1.76)/1.76 = -7.95%, the total dollar return is 3.79%:
10
r$ = [1 + (106 - 102 + 9)/102](1 - .0795) - 1= (1.1275)(0.9205) - 1= 3.79%
2.
During a recent six-month period, Swiss government bonds yielded a local-currency return of -1.6
percent. However, the Swiss franc rose by 8 percent against the dollar over this six-month period.
Corresponding figures for France were 1.8 percent and 2.6 percent. Which bond earned the higher U.S.
dollar return? What was the return?
ANSWER. The dollar return on Swiss bonds equaled (1 - .016)(1 + 0.08) - 1 = 6.27%. The return on
French bonds was lower at (1.018)(1.026) - 1 = 4.45%. In this case, Swiss franc appreciation more than
offset the lower local currency return on Swiss bonds.
3.
During the year Toyota Motor Company shares went from ¥9,000 to ¥11,200, while paying a dividend
of ¥60. At the same time, the exchange rate went from $1 = ¥145 to $1 = ¥120. What was the total
dollar return, in percent, on Toyota stock for the year?
ANSWER. Rewriting Equation 15.5, the one-period total dollar return on a foreign stock investment
R$ can be calculated as follows:
Dollar
return
=
Local currency Currency
x
return
gain(loss
 P(1) P(0) + DIV 
1 + R$ = 1 +
 (1 + g)
P(0)


where
P(t) = local currency stock price at time t
DIV = local currency dividend income
Substituting in the numbers yields a total dollar return on Toyota stock for the year of 51.17%:
R$ = [1 + (11,200 - 9,000 + 60)/9,000](1+.2083) - 1 = (1.2511)(1.2083) - 1 = 51.17%
Note that yen appreciation during the year was (145 - 120)/120 = 20.83%.
11
4.
During 1989, the Mexican stock market climbed 112 percent in peso terms while the peso depreciated
by 28.6 percent against the U.S. dollar. What was the dollar return on the Mexican stock market
during the year?
ANSWER. According to these data, the dollar return on the Mexican stock market during 1989 was
51.37%:
R$ = (1 + 1.12)(1 - 0.286) - 1 = 51.37%
5a. In 1992, the Brazilian market rose by 1,117 percent in cruzeiro terms, while the cruzeiro fell by 91.4
percent in dollar terms. Meanwhile, the U.S. market rose by 8.5 percent. Which market did better?
ANSWER. The dollar return on the Brazilian market can be calculated using Equation 15.5:
R$ = (1 + 11.17)(1 - 0.914) - 1 = 4.66%
The numbers reflect the fact that a return of 1,127% is equivalent to receiving an additional Cr11.17
for each Cr1 invested. Based on these figures, the U.S. market return of 8.5% bested the dollar return on
the Brazilian market by almost 4 percentage points.
b.
In 1993, the Brazilian market rose by 4,190 percent in cruzeiro terms, while the cruzeiro fell by 95.9
percent in dollar terms. Did the Brazilian market do better in dollar terms in 1992 or in 1993?
ANSWER. Redoing the numbers in the answer to part a, we see that the Brazilian market did far better
in 1993 than in 1992:
R$ = (1 + 41.90)(1 - 0.959) - 1 = 75.89%
In this case, the extraordinarily large local currency return more than offset the dramatic devaluation
of the cruzeiro.
9.
A portfolio manager is considering the benefits of increasing his diversification by investing overseas.
He can purchase shares in individual country funds with the following characteristics:
U.S.
U.K. (%)
12
Spain (%)
(%)
Expected return
Standard
deviation
of
return
15
12
5
10
9
4
1.0
0.33
0.06
Correlation with U.S.
a.
What is the expected return and standard deviation of return of a portfolio with 25 percent invested
in the United Kingdom and 75 percent in the United States?
ANSWER. Use the formulas rp = w1r1 + w2r2 and σp2 = w12σ12 + w22σ22 + 2w1w2r12σ1σ2 to calculate the
means and standard deviations of the portfolios.
% US
%UK
Expected
Standard
Return
b.
Deviation
25
75
12.75
7.93
50
50
13.50
7.75
75
25
14.25
8.51
What is the expected return and standard deviation of return of a portfolio with 25 percent invested
in Spain and 75 percent in the United States?
ANSWER. Using the same formulas as in the answer to part a, we can calculate the means and standard
deviations of the various portfolios as follows:
%US
%Spain
Expected
Return
c.
Standard
Deviation
25
75
7.50
4.02
50
50
10.00
5.50
75
25
12.50
7.63
Calculate the expected return and standard deviation of return of a portfolio with 50 percent invested
in the United States and 50 percent in the United Kingdom. With 50 percent invested in the United
States and 50 percent invested in Spain.
13
d.
Calculate the expected return and standard deviation of return of a portfolio with 25 percent invested
in the United States and 75 percent in the United Kingdom. With 25 percent invested in the United
States and 75 percent invested in Spain.
ANSWER. The answers to items a and b contain the answers to items c and d.
e.
Plot these two sets of risk-return combinations (a) through (d) as in Exhibit 15.5. Which leads to a
better set of risk-return choices, Spain or the United Kingdom?
ANSWER. As the following diagram shows, Spain offers better diversification opportunities because its
fund returns are less correlated with the U.S. market (corr. = 0.06) than U.K. funds (corr. = 0.33). However,
it also obvious that investors are sacrificing a significant amount of expected return by choosing to add
Spanish stocks to their portfolios.
Risk-Return Combinations for U.S., Spain, and the U.K.
15%
Expected return
14%
Portfolio Combinations of U.S. and Spanish Funds
13%
12%
Portfolio Combinations of U.S. and U.K. Funds
11%
10%
9%
8%
7%
6%
3%
4%
5%
6%
7%
8%
9%
Standard deviation
f.
How can you achieve an even better risk-return combination?
ANSWER. An investor can improve on the risk-return combination selected in the answer to part d by
including the U.K. fund in the portfolio. You can never do worse by expanding the set of portfolio assets.
The appropriate percent to invest in the U.K. fund depends on the correlation between the U.K. fund and
the Spain fund, which we don't know.
14
10. Suppose that the standard deviation of the return on Nestlé, a Swiss firm, in terms of Swiss francs is
19 percent and the standard deviation of the rate of change in the dollar-franc exchange rate is 15
percent. In addition, the estimated correlation between the Swiss franc return on Nestlé and the rate
of change in the exchange rate is 0.17. Given these figures, what is the standard deviation of the
dollar rate of return on investing in Nestlé stock?
ANSWER. According to Equation 15.8 in the text, we can write the standard deviation of the dollar
return, σ$, as
σ$ = [σf2 + σg2 + 2σfσgσf,g]½
where
σf2 = the variance (the standard deviation squared) of the foreign currency return
σg2 = the variance of the change in the exchange rate
σf,g = the correlation between the foreign currency return and the exchange rate change
Applying this equation, the standard deviation of the dollar rate of return on investing in Nestlé stock
is 27.33%:
 $ (Nestle) = (0.192 + 0.152 + 2 x .19 x .15 x .17) = 0.2733
1/2
Ch 17
2. Suppose a firm projects a $5 million perpetuity from an investment of $20 million in Spain. If the
required return on this investment is 20 percent, how large does the probability of expropriation in year 4
have to be before the investment has a negative NPV? Assume that all cash inflows occur at the end of each
year and that the expropriation, if it occurs, will occur prior to the year-4 cash inflow or not at all. There is
no compensation in the event of expropriation.
ANSWER. This problem can be solved by breaking the cash flow stream into two components--one
component if expropriation takes place and the other if no expropriation takes. The expected value of these
streams is found by multiplying the first component by the probability that expropriation will take place and
15
the other component by the probability that expropriation will not take place. Note that the cash flow
streams are identical prior to year 4. All numbers are in millions of dollars.
Year
0
1
2
3
4
5+
Cash Flow with expropriation
$20
$5
$5
$5
0
0
Cash
$20
$5
$5
$5
$5
$5
Flow
without
expropriation
If the probability of expropriation in year 4 is p, then the expected cash flows associated with this
investment are:
Year 0
1
2
3
4
5+
-$20
$5
$5
$5
$5(1 -
$5(1 -
p)
p)
The net present value of these cash flows, discounted at a 20% required return, is
-20 + 5/1.2 + 5/(1.2)2 + 5/(1.2)3 + 5(1 - p)/(1.2)4 + ... + 5(1 - p)/(1.2)t + ...
= -20 + 5/.2 - (5p/.2)/(1.2)3
= -20 + 25 - 14.68p
Setting this quantity equal to 0 yields a solution of p = 34.1%. This means that the probability of
expropriation has to be 34.1% before the investment no longer has a positive NPV.
Note. The summation of the terms in the NPV equation uses the fact that the sum of an infinite annuity
(a perpetuity) is a/r, where a is the annuity and r is the discount rate. Recognize also that the expected cash
flow can be split into two annuities--one beginning in year 1 and equal to 5 per annum and the other
beginning in year 4 and equal to -5p per annum.
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