Takeda Development Corporation has issued a $100 million floating rate note (FRN) that will mature in three years. The FRN has quarterly coupons equal to three-month LIBOR, payable in arrears and due on the first business day of each quarter. Anne Yelland, Takeda Development's Treasurer, wants to hedge against an increase in three-month LIBOR during the remaining term to maturity of the FRN. To implement the hedge, she realizes she can use either of two alternatives: An interest rate cap or a package of over-the-counter (OTC) call options on interest rates.
a. State whether, to correctly implement the hedge using each of the two alternatives,Yelland should:
i. buy or sell an interest rate cap
ii. buy or sell a package of over-the-counter (OTC) call options on interest rates
Discuss one requirement that both alternatives must meet for Yelland's hedge to be effective. Yelland decides to implement the hedge using an interest rate cap with the following characteristics:
- The reference rate on the interest rate cap is three-month LIBOR.
- The cap rate (strike rate) is 5.50 percent.
*The length of the agreement is for the remaining three-year life of the FRN.
- The notional principal of the cap is $100 million.
- There is quarterly settlement of the cap, payable in arrears.
The following table shows the three-month annualized LIBOR observed on the first business day of each quarter during the first year of the cap.
THREE-MONTH ANNUALIZED LIBOR BEGINNING OF
EACH QUARTER
Quarter Three-month Annualized LIBOR
1 4.50%
2 6.50%
3 7.50%
4 7.00%
b. Compute the payoff (in dollars) to the interest rate cap at the beginning of each of the following two quarters:
(1) Quarter 2
(2) Quarter 3
6. 6. A Spanish pension fund is considering buying a five-year floating-rate note named "El Oso Grande." El Oso Grande would have a coupon reset formula of three times six-month (Spanish peseta) LIBOR minus 24 percent, subject to a minimum coupon rate of 0 percent if peseta LIBOR were to fall below 8 percent. Currently, six-month peseta LIBOR is 11.20 percent, so the initial coupon would be based on a rate of 9.60 percent. The five-year, semiannual payment, 100 million peseta floating-rate note can be bought at par value. The pension fund intends to use derivative instruments to convert El Oso Grande into a synthetic fixed-rate asset. Quotes for five-year, semiannual settlement interest rate swaps, caps, and floors on six-month Spanish peseta LIBOR are obtained from a Madrid commercial
bank specializing in derivative products. Interest Rate Swaps: The pension fund can pay a fixed rate of 13.50 percent and receive six-month peseta LIBOR, or the fund can receive a fixed rate of 13.35 percent and pay six-month peseta LIBOR.
Interest Rate Caps:
Strike Rate The Fund Buys the Cap The Fund Writes the Cap
24% 125 BP 90 BP
Interest Rate Floors:
Strike Rate The Fund Buys the Floor The Fund Writes the Floor
8% 175 BP 140 BP
(Recall that the premiums on the caps and floors are quoted as a percentage of the notional principal.)
a. Indicate the specific combination of transactions that provides a synthetic fixed-rate asset to the pension fund.
b. Calculate the "all-in," fixed rate of return. Assume that Spanish peseta LIBOR, the coupon rate on El Oso Grande, the swap fixed rate, and the strike rate on the caps and floors are all stated on a semiannual bond basis.
7. You are considering the purchase of a convertible bond issued by Bildon Enterprises, a noninvestment- grade medical service firm. The issue has seven years to maturity and pays a semiannual coupon rate of 7.625 percent (i.e., 3.8125 percent per period). The issue is callable by the company at par and can be converted into 48.852 shares of Bildon common stock. The bond currently sells
for $965 (relative to par value of $1,000), and Bildon stock trades at $12.125 a share.
a. Calculate the current conversion value for the bond. Is the conversion option embedded in this bond in the money or out of the money? Explain.
b. Calculate the conversion parity price for Bildon stock that would make conversion of the bond profitable.
c. Bildon does not currently pay its shareholders a dividend, having suspended these distributions six months ago. What is the payback (i.e., break-even time) for this convertible security and how should it be interpreted?
d. Calculate the convertible's current yield to maturity. If a "straight" Bildon fixed-income issue with the same cash flows would yield 9.25 percent, calculate the net value of the combined options (i.e., the issuer's call and the investor's conversion) embedded in the bond.