Question

Jacksonville Corp. is a U.S. based firm that needs $500,000. It has no business in Japan but is considering one year financing with Japanese yen, because the annual interest rate would be 5 percent versus 9 percent in the United States. Assume that interest rate parity exists.
1. Can Jacksonville benefit from borrowing Japanese yen and simultaneously purchasing yen one year forward to avoid exchange rate risk? Explain.
2. Assume that Jacksonville does not cover its exposure and uses the forward rate to forecast the future spot rate. Determine the expected effective financing rate. Should Jacksonville finance with Japanese yen? Explain.
3. Assume that Jacksonville does not cover its exposure and expects that the Japanese yen will appreciate by either 5 percent, 3 percent, or 2 percent, and with equal probability of each occurrence. Use this information to determine the probability distribution of the effective financing rate. Should Jacksonville finance with Japanese yen? Explain.

Answer 1

Total Fund Requirement = $ 500000 or $ 0.5 million

US Interest Rate = 9 % per annum and Japanese Interest Rate = 5 % per annum

Let us assume that the current spot exchange rate is 100 Yen / $ where Yen is assumed to be the domestic currency and the USD is the foreign currency.

(1) - If the firm borrows in Japanese Yen, then fund requirement becomes = ($ 0.5 million x 100) = Y 50 million

- This Japanese Yen borrowing creates a one-year debt liability of (50 x 1.05) = Y 52.5 million.

- As interest rate parity is valid, the future spot exchange rate one-year from now would be S(f) = 100 x [(1.05) / (1.09)] = 96.3303 Yen / $

- The debt liability one-year from now in $ terms would be 96.3303 x 52.5 = $ 0.544999 million or $ 0.5445 million approximately.

- If the firm would have made borrowings in the US market, the debt obligation would have been $ (0.5 x 1.09) = $ 0.545 million which is approximately equal to the liability created by the Japanese Yen borrowing.

- As is observable, the company does not benefit by borrowing in Japanese Yen, owing to the existence of Interest Rate Parity.

(2) If the original assumption of the spot exchange rate being 100 Yen / $ is made again, then by Interest Rate Parity the one-year forward rate would be: 100 x [(1.05) / (1.09)] = 96.3303 Yen / $. If the Interest Rate Parity is believed to exist then the future spot exchange rate and forecasted (by the interest rate parity relationship) forward rate would both be equal one-year from now.In such a situation, the effective financing rate would be 5 % in Japanese Yen terms and 9 % in US $ terms, thereby making borrowings in either currency equivalent to each other. Further, owing to this equivalence, borrowing in Yen will have no extra benefit (as demonstrated in par(1)).

(3) The initial assumption of the exchange rate being 100 Yen/$ is still considered valid. Therefore, if the Japanese Yen is expected to appreciate by different extent with different probabilities, then one would be able to purchase lesser Japanese Yen for a $, one-year from now as compared to today.

Probability Distribution of Possible Exchange Rates:

5 % Appreciation - 95 Yen / $ - 0.33 probability

3 % Appreciation - 97 Yen / $ - 0.33 probability

2 % Appreciation - 98 Yen / $ - 0.33 probability

Therefore, expected exchange rate = (1/3) x 95 + (1/3) x 97 + (1/3) x 98 = 95.7 Yen / $

Under these three exchange rates, the $ value of the Yen borrowing of 50 million one year from now would be:

(a) 52.5 / 95 = $ 552631.6 , Effective Financing Rate = (552631.6 / 500000) - 1 = 0.10526 or 10.53%

(b) 52.5 / 97 = $ 541237.11 , Effective Financing Rate = (541237.11 / 500000) - 1 = 0.08247 or 8.247 %

(c) 52.5 / 98 = $ 535714.29, Effective Financing Rate = (535714.29 / 500000) - 1 = 0.07143 or 7.143 %

Borrowing $ 500000 at the US Rate of 9 % would have created a debt liability of 500000 x (1.09) = $ 545000 after one year.

The three situations described above create liabilities different from $ 545000, thereby proving that Japanese borrowing would be beneficial in case (b) and (c), but not in case (a). This is because case(a) has effective financing rate greater than 9%, the US financing rate.