Question

After all foreign and U.S. taxes, a U.S. corporation expects to receive 5 pounds of dividends per share from a British subsidiary this year. The exchange rate at the end of the year is expected to be $1.61 per pound, and the pound is expected to depreciate 5% against the dollar each year for an indefinite period. The dividend (in pounds) is expected to grow at 10% a year indefinitely. The parent U.S. corporation owns 6 million shares of the subsidiary.

What is the present value in dollars of its equity ownership of the subsidiary?

Assume a cost of equity capital of 10% for the subsidiary. Do not round intermediate calculations. Round your answer to the nearest dollar.

Answer 1

Expected Dividend = 5 pounds

Exchange rate at the end of the year is expected to be $1.61 per pound

i.e. 1 Pound = 1.61 Dollar

.

Pound is expected to depreciate 5% against the dollar each year for an indefinite period

.

The dividend (in pounds) is expected to grow at 10% a year indefinitely.

.

Therefore, net growth rate in dividend in dollar = (1+Dividend Growth Rate) * (1-Depreciation Rate in Pound) – 1

= (1+0.10) * (1-0.05) – 1

= 1.10*0.95 – 1

= 1.045 – 1

= 0.045

= 4.5%

.

.

Alternatively it can be calculated as follows:

Year	Dividend (Pound)	Exchange Rate ($/Pound)	Net Dividend in ($)	Working	Growth Rate
1	5	1.61	8.05
2	5.5	1.5295	8.41	(8.41-8.05)/8.05	4.50%
3	6.05	1.453025	8.79	(8.79-8.41)/8.41	4.50%

.

.

Therefore,

Growth rate (g) = 4.5%

Cost of equity capital (Re) = 10%

Expected Dividend in Dollars (D1) = 5*1.61 = $8.05

.

Therefore,

Present Value of each share in dollars = D1/(Re-g)

= 8.05/(0.10-0.045)

= 8.05/0.055

= $146.3636

.

.

Therefore,  present value in dollars of its equity ownership of the subsidiary = Present value of Each Share in Dollars * No. of shares owned

= 146.3636* 6 million shares

= $878 million dollars