Question

Suppose a firm will receive 15,000,000 ¥ in 180 days.

a. [2 pts] If the forward rate is 0.143$/ ¥, what would be the value of receivables using the forward?

b. [4 pts] Suppose the dollar-renminbi exchange rate is uncertain. It could be:

0.13$/ ¥ with 12% probability

0.11$/ ¥ with 51% probability, or

0.17$/ ¥ with 37% probability.

What is the expected receivable with the expected exchange rate? Should the firm use the forward or take the risk?

c. [5 pts] If an option existed with a strike price of 0.16$/ ¥ and a premium of 0.02$/ ¥, should the firm use the option, the forward, or neither?

Answer 1

Here,

Amount Receivable = Yen 15,000,000

Forward Rate = 0.143$/ YEn

So Amount Receivable as per forward rate = .143 * 15000000 = $2145000

Now Expected Spot rate after 1 year ,

(.13*.12 + .11*.51 + .17*.37) = 0.1346$ / Yen

So AMount Receivable due to this =.1346 * 15000000 = $2019000

Since higher amount is received in Forward rate hence forward rate should be used,

If option is there of .16 and .02 is the premium

Now in 37% of case, receivable will be .17 - .02 = .15 (37% probability of reaching .17 i which case option need not be exercised)

63% of case receivable will be .16 - .02 as lower expectation will be there and hence option will vbe exercised

So Expected value with option

.63*.14 + .37*.15 = $.1437/ yen

Now value received due to this = .1437 * 15000000 = $21555000

Hence option should be used as it gives the best outcome