Question: (a) A firm requires $10,000,000 for 2 years and can issue 1-year commercial paper at 12 percent. The firm wants to protect against higher interest rates that may prevail when it refinances 1 year hence. Assume that 1-year treasury bills currently yield 9 percent, and that the current futures price equals the current spot price. Calculate the dollar amount of 1-year treasury-bill futures needed to fully hedge against a possible 2-percentagepoint rise in interest rates 1 year hence.
(b) Let:
i0 = current interest rate on 1-year commercial paper
i1 = interest rate on 1-year commercial paper I year hence x = i1 - i0 = increase in interest rate during the year r = interest premium on commercial paper over treasury bills (c > 0)
r0 = i0 - r = current yield on 1-year treasury bills
r1 = i1 - c = yield on a 1-year treasury bill 1-year hence
P0 = current futures price, per $1, of 1-year treasury bills
P1 = spot price, per $1, of 1-year treasury bills in I year
L = dollar amount of commercial paper issued
D = total dollar amount of treasury bills sold in futures contract
(c) Plot the unanticipated interest loss or gain on the loan as a function of x. On the same graph, plot the capital gain or loss on the treasury-bill futures contract as a function of x. Interpret your graph.