From Schweser Practice Exams - Book 1 - Exam 3pm - Q 18.2: Data given in vignette: Smiler borrows short-term funds to meet expenses on a temporary basis and typically makes semiannual interest payments based on 180-day LIBOR plus 150bps. Smiler will need to borrow $25m in 90 days to invest in new equipment. To hedge the interest rate risk on the loan, Ng is considering the purchase of a call option on 180-day LIBOR with a term to expiration of 90 days, an exercise rate of 4.8% and a premium of 0.000943443 of the loan amount. Current 90-day LIBOR is 4.8%. 18.2 If Ng purchases the interest rate call, and 180-day LIBOR at option expiration is 5.73%, the annualized effective rate for the 180-day loan is closet to: A. 6.6982% B. 6.5346% C. 6.3785% ------------------------- Schweser solution: Initial layout is $25m - PV(option premium) option premium = 0.000943443*25m = 23586 PV(option premium) = 23586 * (1 + (0.048+0.015)*90/360) = 23957 Initial layout = $25m - 23957 = $24,976,043 Effective loan cost = $25m + (interest on loan) interest on loan = (0.048+0.015)*(180/360)*25m = 787,500 Effective loan cost = $25,787,500 EAR = (25,787,500/24,976,043)^(365/180)-1 = 6.6982% (choice A) ------------------------ My solution: I did everything like the above, except I included the option payoff which has been completely omitted from the solution and possible answers! Effective loan cost = $25m + (interest on loan) - (option payoff) interest on loan = (0.048+0.015)*(180/360)*25m = 787,500 option payoff = (0.0573 - 0.048)*(180/360)*25m = 116,250 Effective loan cost = $25,671,250 EAR = (25,671,250/24,976,043)^(365/180)-1 = 5.7250% Anyone have some thoughts on this one?? Am I missing something??
Your mistake is that you calculated the interest on the loan given the strike rate for LIBOR (4.8%) instead of 5.73%. Since the position is hedged with the option, the maximum interest cost is capped at LIBOR = 4.8%. So Schwesser ignores the fact that 5.73%>4.8% and correctly calculates the interest, ignoring the payoff on the option. You could use your approach as well but you would need to use 5.73% (plus spread) for the interest rate on the loan which would net with the payoff on the option to still get you to 4.8%.
That’s great! Thanks for the explanation…