Question

Q No. 3: a. An investor in Canada purchased 100 shares of IBM on January 1st at $93.00/share. IBM paid an annual dividend of $0.72 on December 31st. The stock was sold that day as well for $100.25. The exchange rate is $0.68/Canadian dollar on January 1st and $0.7 1/Canadian dollar on December 31st.

What is the investor’s total return in Canadian dollars?

b. The British pound to U.S. dollar exchange rate is 1.36 and the New Zealand dollar to U.S. dollar exchange rate is 0.62. If you find that the British pound to New Zealand dollar is trading at 0.49, what would you do to earn a riskless profit?

c. The Mexican peso is trading at 10 pesos per dollar. If the expected U.S. Inflation rate is 23% while the Mexican inflation rate is 2% over the next year,

what is the expected exchange rate in one year?

Corporate Finance is subject

Answer 1

Solution

a)

The total return is the ratio of capital gain to the initial investment.

…… (1)

In the foreign exchange market, the currency exchange rate for currency is ratio of foreign currency to the unit of domestic currency.

The exchange rate is the ratio of foreign price of goods to the domestic price of same goods.

…… (2)

To compute the purchase price per share in Canadian dollar, substitute $93.00 for foreign value of investment and $0.68 per Canadian dollar for exchange rate in equation (2) as follows:

The purchase price of share is 136.7647 Canadian dollars per share on 1^st January.

To compute the dividend per share in Canadian dollar, substitute $0.72 for foreign value of investment and $0.71 per Canadian dollar for exchange rate in equation (2) as follows:

The dividend of share is 1.0140845 Canadian dollars per share on 31^st December.

To compute the selling price per share in Canadian dollar, substitute $100.25 for foreign value of investment and $0.71 per Canadian dollar for exchange rate in equation (2) as follows:

The selling price per share is 141.1972 Canadian dollars per share on 31^st December.

To compute the capital gain, substitute 136.7647 Canadian dollars per share for purchase price, selling price 141.1972 Canadian dollars per share, and 1.014084507 Canadian dollars per share for dividend in equation (1) as follows:

b)

In foreign exchange markets, various currencies are traded. One currency denominated in terms of various other currencies is known as cross rates.

The riskless profit can be earned from the arbitrage opportunity raised between two markets. The denomination of home currency in terms of one unit of foreign currency is known as direct quotation. The quotation of one unit of foreign currency in terms of home currency is known as indirect quotation.

The Country NZ dollar to Country U.S. exchange rate is 1.36. The Country B currency pound to Country U.S. currency exchange rate is 0.62. The Country B currency to Country N currency is trading at 0.49.

Calculate the riskless profit as follows:

Step 1: Exchange $1.00 with Country NZ exchange rate of 1.36:

Step 2: Exchange the Country NZ currency 1.36 with Country B currency pounds:

Step 3: Exchange the Country B currency 0.6664 with Country U.S. currency:

Step 4: Calculate the riskless profit:

Therefore, the riskless profit is $0.0748 .

c)

Inflation and interest rate are directly proportional. Hence, one can find that, high inflation rate depreciates the currency value. Countries having high inflation rates depreciate more with respect to countries having low inflation rates.

Mathematically,

To compute the current exchange rate, substitute 2% for expected inflation rate at home country, 23% for expected inflation rate at foreign country, and $10 for current exchange rate for peso and U.S. dollar.

Expected ER = 10*(1+0.02)/(1+0.23)

= 8.29 PESOS per dollar

Thus, the expected exchange rate is 8.29 pesos per dollar.