Question

Assume that it is now Jan. 2018. AZDT Inc. (US) expects to receive cash dividends from a joint venture in India over the next five years. The first dividend of Rs 2 million will be paid in Dec. 2018. The dividend is then expected to grow at an annual rate of 10% over the following four years. Current exchange rate (Rs/$) is 45 (65.25) and AZDT’s average weighted cost of capital is 10%.

a. Compute the dollar present value of the expected rupee dividend stream if the dollar is expected to depreciate by 5% per year against the rupee over the investment period.

b. Obtain the dollar present value of the expected rupee dividend stream if the rupee is expected to depreciate by 10% per year against the dollar over the investment period

c. What is the dollar present value of the expected rupee dividend stream if the exchange rate remains constant over the investment period?

Answer 1

Since two exchange rates are given, we are assuming it a typo and do the problem assuming 65.25 as the correct rate. The reader can change it in the formulas below. The dollar present value without any change in interest rates will be given as:

PV(dollars) = 2/(1.1 x 65.25) + 2 x 1.1/(65.25 x 1.1^2) +... + 2 x 1.1^4/(65.25 x 1.1^5)

a. If dollar depreciates by 5%, the new exchange rate will be 65.25/1.05 and will be divided by 1.05 in each subsequent year.

PV(dollars) = 2 x 1.05/(1.1 x 65.25) + 2 x 1.1 x 1.05^2/(65.25 x 1.1^2) +... + 2 x 1.1^4 x 1.05^5/(65.25 x 1.1^5) = $0.16167 million.

b. Similarly, if it appreciates, the new exchange rate will be 65.25 x 1.1 and will be multiplied by 1.1 in each year.

PV(dollars) = 2/(1.1 x 65.25 x 1.1) + 2 x 1.1/(65.25 x 1.1^2 x 1.1^2) +... + 2 x 1.1^4/(65.25 x 1.1^5 x 1.1^5) = $0.10563 million.

c. If it remains constant, it will be given according to the first expression.

PV(dollars) = 2/(1.1 x 65.25) + 2 x 1.1/(65.25 x 1.1^2) +... + 2 x 1.1^4/(65.25 x 1.1^5) = $0.139324 million,