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# Finance Study Questions: Probability Distribution of Forecasts and Forecasting with a Forward Rate

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I wonder if you are using the textbook (Madura's) International Financial Management, which is a "standard text" for most instructors. The questions look familiar.

9.15 Probability Distribution of Forecasts. Assume that the following regression model was applied to historical quarterly data:

et = a0 + a1INTt + a2INFt 1 + t

where et = percentage change in the exchange rate of the Japanese yen in period t

INTt = average real interest rate differ¬ential (U.S. interest rate minus Japanese interest rate) over period t

INFt 1 = inflation differential (U.S. inflation rate minus Japanese inflation rate) in the previous period

a0, a1, a2 = regression coefficients

t = error term

Assume that the regression coefficients were estimated as follows:

a0 = 0.0
a1 = 0.9
a2 = 0.8

Also assume that the inflation differential in the most recent period was 3 percent. The real interest rate differential in the upcoming period is forecasted as follows:

Interest Rate
Differential Probability
0% 30%
1 60
2 10

If Stillwater, Inc., uses this information to forecast the Japanese yen's exchange rate, what will be the probability distribution of the yen's percentage change over the upcoming period?

Forecast of Forecast of the
Interest Rate Percentage Change
Differential in the Japanese Yen Probability
0% .9(0%) + .8(3%) = 2.4% 30%
1% .9(1%) + .8(3%) = 3.3% 60%
2% .9(2%) + .8(3%) = 4.2% 10%

9.16 Forecasting with a Forward Rate. Assume that the four year annualized interest rate in the United States is 9 percent and the four year annualized interest rate in Singapore is 6 percent. Assume interest rate parity holds for a four year horizon. Assume that the spot rate of the Singapore dollar is \$.60. If the forward rate is used to forecast exchange rates, what will be the forecast for the Singapore dollar's spot rate in four years? What percentage appreciation or depreciation does this forecast imply over the four year period?

Country Four Year Compounded Return
U.S. (1.09)4 - 1 = 41%
Singapore (1.06)4 - 1 = 26%

Premium =1.41 / 1.26 -1 = 11.9%
Thus, the four-year forward rate should contain an 11.9% premium above today's spot rate of \$.60, which means the forward rate is \$.60 × (1 + .119) = \$.6714. The forecast for the Singapore dollar's spot rate in four years is \$.6714, which represents an appreciation of 11.9% over the four-year period.

. 10.2 Your employer, a large MNC, has asked you to assess its transaction exposure. Its projected cash flows are as follows for the next year:

Currency
Total Inflow
Total Outflow Current Exchange Rate in U.S. Dollars
Danish krone (DK) DK50,000,000 DK40,000,000 \$.15
British pound (£) £2,000,000 £1,000,000 \$1.50
Assume that the movements in the Danish krone and the pound are highly correlated. Provide your assessment as to your firm's degree of transaction exposure (as to whether the exposure is high or low). Substantiate your answer.

ANSWER: The net exposure to each currency in U.S. dollars is derived below:

Foreign Currency Net Inflows in
Foreign Currency Current
Exchange Rate
Value of Exposure
Danish krone (DK) +DK10,000,000 \$.15 \$1,500,000
British pound (£) +£1,000,000 \$1.50 \$1,500,000

The krone and pound values move in tandem against the dollar. Both the krone and the pound exposure show positive net inflows. Thus, their exposure should be magnified if their exchange rates against the U.S. dollar continue to be highly correlated.

10.19 Using the following cost and revenue information shown for DeKalb, Inc., determine how the costs, revenue, and earnings items would be affected by three possible exchange rate scenarios for the New Zealand dollar (NZ\$): (1) NZ\$ = \$.50, (2) NZ\$ = \$.55, and (3) NZ\$ = \$.60. (Assume U.S. sales will be unaffected by the exchange rate.) Assume that NZ\$ earnings will be remitted to the U.S. parent at the end of the period.

Revenue and Cost Estimates: DeKalb Inc.
(in millions of U.S. dollars and New Zealand dollars)

New Zealand