1. Suppose a new nation decides to peg the value of its currency, the newbill, to a basket
consisting of 0.625 U.S. dollars and 0.25 British pounds. Further suppose the exchange
rate between the U.S. dollar and the British pound is 1.5 dollars per pound. If the basket
constitutes one newbill, what is the appropriate exchange value between the newbill and
the dollar, and between the newbill and the pound?
1 Newbill =
Exchange Rate $/£
Exchange Rate £/$
$ Value of £ portion of N
£ Value of $ portion of N
Exchange Rate N/£
Exchange Rate £/N
Exchange Rate N/$
Exchange Rate $/N
$0.6250
$1.5000
£0.6667
$0.3750
£0.4167
1.5000
£0.6667
1.0000
$1.0000
£0.2500
What is the weight assigned to the U.S. dollar in the currency basket? What is the weight
assigned to the British pound in the currency basket?
Weight $
Weight £
62.5%
37.5%
2. In 1990, a Japanese investor paid $100 million for an office building in downtown Los
Angeles. At the time, the exchange rate was ¥145/$1. When the investor went to sell the
building five years later, in early 1995, the exchange rate was ¥85/$1 and the building's
value had collapsed to $50 million. (3 points)
a. What exchange risk did the Japanese investor face at the time of his purchase?
ANSWER. The risk is that the value of the dollar would fall against the yen and that the dollar revenues
would not keep up with the decline in the value of the dollar.
b. How could the investor have hedged his risk?
ANSWER. The investor could have financed his purchase of the building by borrowing dollars, so that the
very same event that led to a decline in the yen value of his asset -- namely, a dollar decline -- would
simultaneously reduce the yen cost of the liability used to finance that asset. He could also have taken out
a long-dated forward contract to hedge the yen value of his building. Nothing would have protected the
investor from the decline in the building's dollar price.
c. Suppose the investor financed the building with a 10% down payment in yen and a
90% dollar loan accumulating interest at the rate of 8% per annum. Since this is a zerocoupon loan, the interest on it (along with the principal) is not due and payable until the
building is sold. How much has the investor lost in yen terms? In dollar terms?
ANSWER. Based on the 10% down payment, the investor's initial yen investment was ¥1.45 billion (0.10 x
100 million x 145). At an interest rate of 8%, the $90 million loan used to finance the balance of the
building's price will grow by the end of five years to $132,239,527 (1.085 x $90,000,000). Upon selling
the building and paying off the loan, the investor will have a dollar loss of $82,239,527 ($132,239,527 $50,000,000). At the current spot rate of ¥85/$1, this dollar loss translates into a yen loss of ¥6.99 billion.
Adding this loss to the investor's initial down payment of ¥1.45 billion yields a total yen loss for the
investor of ¥8.44 billion.
d. Suppose the investor financed the building with a 10% down payment in yen and a
90% yen loan accumulating interest at the rate of 3% per annum. Since this is a zerocoupon loan, the interest on it (along with the principal) is not due and payable until the
building is sold. How much has the investor lost in yen terms? In dollar terms?
ANSWER. If the investor had financed the building with the 90% yen loan, the investor would have had to
borrow 100,000,0000 x 0.90 x ¥145 = ¥13.05 billion. At an interest rate of 3%, the ¥13.05 billion loan will
grow by the end of five years to ¥15.13 billion (1.03 5 x ¥13.05 billion). The $50 million sale price
translates into ¥4.25 billion (50,000,000 x 85). After paying off the loan, the investor has a loss of ¥10.88
billion. Adding to this loss the initial down payment of ¥1.45 billion produces a total loss for the investor
of ¥12.33 billion. The answer to part c shows that the use of dollar financing reduced the investor's loss.
The investor, of course, lost anyway because the value of the building declined instead of increasing by at
least the rate of interest.
3. In 1990, Matsushita bought MCA Inc. for $6.1 billion. At the time of the purchase, the
exchange rate was about ¥145/$. By the time that Matsushita sold an 80% stake in MCA
to Seagram for $5.7 billion in 1995, the yen had appreciated to a rate of about ¥97/$.
a. Ignoring the time value of money, what was Matsushita's dollar gain or loss on its
investment in MCA?
ANSWER. If an 80% stake in MCA was worth $5.7 billion, then the entire firm was worth $7.125 billion.
Based on this valuation, Matsushita actually made $1.025 billion on its purchase of MCA. That is, by
buying MCA at a price of $6.1 billion and selling it for a price that valued the business at $7.125 billion,
Matsushita made $1.025 billion.
b. What was Matsushita's yen gain or loss on the sale?
ANSWER. Taking into account the differences in exchange rates, Matshushita paid ¥884,500,000,000
(6,100,000,000 x 145) for MCA in 1990 and sold MCA in 1995 for a price that valued it at
¥691,125,000,000 (7,125,000,000 x 97). The net result was a loss for Matsushita of ¥193,375,000,000 on
its purchase of MCA.
c. What did Matsushita's yen gain or loss translate into in terms of dollars? What
accounts for the difference between this figure and your answer to part a?
ANSWER. Matsushita's yen loss converts into a dollar loss of $1,999,382,000 (193,375,000,000/97). This
figure differs from the answer in part a, because it takes into account the change in exchange rates
between 1990 and 1995. In effect, it asks what would have happened if Matsushita had held onto its yen
instead of converting them into a dollar asset that didn't appreciate in line with the yen's appreciation. In
other words, this computed dollar loss represents an opportunity cost.
4. In May 1988, Walt Disney Productions sold Japanese investors a 20-year stream of
projected yen royalties from Tokyo Disneyland. The present value of that stream of
royalties, discounted at 6% (the return required by the Japanese investors), was ¥93
billion. Disney took the yen proceeds from the sale, converted them to dollars, and
invested the dollars in bonds yielding 10%
a. At the time of the sale, the exchange rate was ¥ 124 = $1. What dollar amount did
Disney realize from the sale of its yen proceeds?
ANSWER. Disney realized 93,000,000,000/124 = $750,000,000 from the sale of its future yen proceeds.
b. Demonstrate the equivalence between this transaction and a currency swap.
ANSWER. In a currency/interest rate swap, one party trades a stream of payments in one currency, at one
interest rate, for a stream of payments in a second currency, at a second interest rate. Disney's stream of
yen royalties can be treated as a yen bond, which it traded for a dollar bond, with dollar payments. The
only difference between the Disney swap and a traditional swap is that the latter usually involve cash
outflows whereas the Disney swap involves cash inflows.
c. Did Disney achieve the equivalent of a ‘free lunch’ through this transaction? Explain.
ANSWER. Gary Wilson, Disney's chief financial officer, committed an unpardonable analytical sin when
he claimed that: "In effect, we got money at a 6% discount rate, reinvested it at 10%, and hedged our
royalty stream against yen fluctuations -- all in one transaction." He was comparing apples with oranges:
in this case, a 6% yen interest rate with a 10% dollar interest rate. The international Fisher effect tells us
that the most likely reason that the yen interest rate is 4 percentage points less than the equivalent dollar
interest rate is because the market expects the dollar to depreciate by about 4% annually against the yen.
As it happens the exchange rate is currently ¥116 = $1. Corporate bond rates on AAA-rated, eight-year
maturities are about 6 percent in US and 2 percent in Japan.
5, Go to your textbook, answer question 3.10.
Current
Initial Investment
Profits
Spot rate
Year 1
Year 2
2,000,000
1,500,000
0.50
Germany
Risk-free rate
Rm
Beta
2,500,000
$/DM
US
3%
9.18%
0.9
6%
12.36%
0.9
Market S ecurity Line: CAPM r = rf+b(r m-rf)
a. Decentralized Method of capital budgeting
Germany
Cost of capital
US
8.56%
Current
Net Cash flow
NPV in DM
NPV in dollars
11.72%
Year 1
(2,000,000)
1,502,912 DM
751,456 $
1,500,000
Year 2
2,500,000
using the German cost of
capital
a. Centralized Method of capital budgeting
Current
Net Cash flow in DM
Expected Exchange rate
Net Cash flow in dollars
NPV
Year 1
(2,000,000)
0.50
(1,000,000)
751,456 $
1,500,000
0.515
771,845
Year 2
2,500,000
0.5296
1,323,876
Analysis: Giv en integrated capital markets, interest rate parity implies that the difference between the domestic
and foreign interest rates is the same as the expected percent change in exchange rates. Hence, both centralized
and decentralized method of capital budgeting produce the same v alue of NPV
assumming that UIP holds
6. Go to your text book, answer question 3.11.
Revenue
Year 1
200,000
$150.00
$30,000,000.00
Sales Volume (Units)
Price ($)
Total Revenue ($)
Year 2
220,000
$157.50
$34,650,000.00
Year 3
242,000
$165.38
$40,020,750.00
Year 4
266,200
$173.64
$46,223,966.25
Year 5
292,820
$182.33
$53,388,681.02
Costs
Year 1
Lcl. Mat. & Lbr. Costs (per Unit)
Manufacturing Overhead
Selling & admin. Costs
License Fee
Lcl. Mat. & Lbr. Costs
Total Costs
EBIT
Tax @ 34%
Net Income C $
$40.00
$9,000,000.00
$3,000,000.00
$0.00
$8,000,000.00
$20,000,000.00
$10,000,000.00
$3,400,000.00
$6,600,000.00
Year 2
$42.00
$9,180,000.00
$3,465,000.00
$0.00
$9,240,000.00
$21,885,000.00
$12,765,000.00
$4,340,100.00
$8,424,900.00
Year 3
$44.10
$9,363,600.00
$4,002,075.00
$0.00
$10,672,200.00
$24,037,875.00
$15,982,875.00
$5,434,177.50
$10,548,697.50
Year 4
$46.31
$9,550,872.00
$4,622,396.63
$0.00
$12,326,391.00
$26,499,659.63
$19,724,306.63
$6,706,264.25
$13,018,042.37
Year 5
$48.62
$9,741,889.44
$5,338,868.10
$0.00 This is revenue to parent
$14,236,981.61
$29,317,739.15
$24,070,941.87
$8,184,120.24
$15,886,821.64
$6,600,000.00
$8,424,900.00
$10,548,697.50
$13,018,042.37
$15,886,821.64
a)
Net Cash Flows C $
b)
Nom. Risk Free Interest rate, US
Nom. Risk Free Interest rate, Can.
Exchange Rate
10%
15.50%
$0.75
Forward Contract rates
Exg. Rate * (1+ US risk free rate) / (1+
Canada risk free rate)
Year 1
Year 2
$0.71
Year 3
$0.68
Year 4
$0.65
Year 5
$0.62
$0.59
c)
Required rate of return in US
Required rate of return in Canada
Beta for this project
All Equity Cost of Capital
Req. Rate Ret. + (Beta * (Req. rate of
return - riskfree rate)
16%
21.8%
1.2
US
Canada
17.20%
23.06%
There are various ways a firm can come up with a beta rate, if it is recurring project they can use the beta used in the previous project.
They could also use beta that other companies (industry) use for similar kind of projects.
d)
Present Value of the projects
Decentralized menthod
Year 1
$6,600,000.00
$5,363,237.45
$27,892,671.42
0.75
$20,919,503.57
Net Cash Flows
PV
Total
US Ex rate
Total
Year 2
$8,424,900.00
$5,563,280.19
Year 3
$10,548,697.50
$5,660,412.82
Year 4
$13,018,042.37
$5,676,465.96
Year 5
$15,886,821.64
$5,629,275.01
Year 2
$0.68
$5,731,224.49
$4,172,460.14
Year 3
$0.65
$6,834,271.14
$4,245,309.62
Year 4
$0.62
$8,032,481.76
$4,257,349.47
Year 5
$0.59
$9,335,805.34
$4,221,956.26
Centralized method
Year 1
Forward rates
PV
US rate
Total
$0.71
$4,714,285.71
$4,022,428.08
$20,919,503.57
The PV using the decentralized method or the centralized method is the same. The project should be undertaken as it is in the money.
e)
Future Expected spot rates with 2% risk premium
Year 1
Expected Future Spot Rates
Year 2
Year 3
Year 4
Year 5
$0.71
$0.68
$0.64
$0.61
$0.58
Year 1
$6,600,000.00
$5,363,237.45
$27,892,671.42
0.75
$20,919,503.57
Year 2
$8,424,900.00
$5,563,280.19
Year 3
$10,548,697.50
$5,660,412.82
Year 4
$13,018,042.37
$5,676,465.96
Year 5
$15,886,821.64
$5,629,275.01
Year 2
$0.68
$5,563,280.19
$3,764,310.54
Year 3
$0.64
$5,660,412.82
$3,637,887.30
Year 4
$0.61
$5,676,465.96
$3,465,179.97
Year 5
$0.58
$5,629,275.01
$3,263,975.18
Decentralized menthod
Net Cash Flows
PV
Total
US Ex rate
Total
Centralized method
Year 1
Forward rates
PV
US rate
Total
$0.71
$5,363,237.45
$3,820,629.39
$17,951,982.37
Even with the 2 % risk premuium the project should be accepted.