Q3. Suppose that BRW corporation is borrowing F = $300M at a floating rate equaling (6 months) LIBOR plus a spread s = 3.40% for T = 5 years. (Interest payments are made semi-annually.) To better manage its cashflows, BRW simultaneously enters a 5-year swap as fixed payer on N1 = $180M; the swap rate is c = 0.0260. Finally, BRW purchases an interest cap with strike rate K = 0.0280 on a notional N2 = $120M.

a) At date t1 = 2y, LIBOR is reported as r(2, 2.5) = 0.0305. What is the net payment made by BRW on the loan and derivative positions at date 2.5y?

b) At date t2 = 4y, LIBOR is reported as r(4, 4.5) = 0.0140. What is the net payment made by BRW on the loan and derivative positions at date 4.5y?

c) On the same axes, draw (i) a payoff diagram of the interest paid by BRW on its loan at payment date t given the LIBOR rate 6 months earlier, r(t0.5, t), and (ii) a payoff diagram showing the net payment (interest plus derivative payoffs) made by BRW at the same payment date.