Question

A U.S. based firm has a receivable of Norwegian krone (NKr) of NKr 22,356,322, which will be received 110 days from today.
(a) The firm-specific interest rate for borrowing NKr is 4%, and the firm can invest dollars internally at a rate of return of 12%. The spot exchange rate is 7.5 NKr/$. Calculate the amount of dollars received with a money market hedge.
(b) Suppose the firm is also considering using a forward contract. The market rate of interest for NKr is 3.6%, and the market rate of interest in dollars is 9%. Calculate the amount of dollars received with a forward contract hedge. Is the money market hedge or the forward contract hedge preferred by the firm? Explain.
(c) Finally, suppose the firm did not have the possibilities in (a), but rather had to borrow and invest at the market rates given in (b). Show that the money market hedge would now be identical to a forward contract hedge.

Answer 1

a). Money market hedge:

The firm has a receivable of NKr so let it borrow USD.

PV of NKr receivable = receivable/(1+interest rate)^n = 22,356,322/(1 + 4%/(365/110))^1 = 22,090,031.21

Amount of dollar to be borrowed = PV of NKr receivable/spot rate = 22,090,031.21/7.5 = $2,945,337.50

Invest this at 12% p.a. to get = 2,945,337.50*(1+12%/(365/110) = $3,051,853.81 after 110 days

b). Forward market hedge:

NKr receivable = 22,356,322

Forward exchange rate (NKr/$) = spot rate*(1 + Interest rate NKr)/(1 + interest rate USD)

Interest rate NKr = 3.6%/(365/110) and Interest rate USD = 9%/(365/110)

= 7.5*(1+3.6%/(365/110))/(1+9%/(365/110)) = NKr 7.381/$

Sell NKr forward for 110 days at the forward rate to get 22,356,322/7.381 = $3,028,832.44

c). Supposing dollar investment rate is 9% p.a. and NKr borrowing rate is 3.6% p.a.

PV of NKR receivable = 22,356,322/(1 + 3.6%/(365/110)) = NKr 22,116,374.49

Dollar amount to be borrowed = PV of NKr receivable/spot exchange rate

= 22,116,374.49/7.5 = $2,948,849.93

Dollar amount to be received after investing at 9% p.a. for 110 days =

2,948,849.93*(1+9%/(365/110)) = $3,028,832.44

This is the same amount which the firm would get if they carried out a forward market hedge as shown in part (b).