Chapter 24: problems 3(a-d), 6(a-c), 8(a-c), and 10(a-c)

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  • Chapter 24: Problems 3(a-d), 6(a-c), 8(a-c), and 10(a-c)




Problem 3(a-d)


3. The treasurer of a British brewery is planning to enter a plain vanilla, three-year, quarterly settlement interest rate swap to pay a fixed rate of 8 percent and to receive three-month sterling LIBOR. But first he decides to check various cap-floor combinations to see if any might be preferable. A market maker in British pound sterling OTC options presents the treasurer with the following price list for three-year, quarterly settlement caps and floors:







Strike Rate






582 GBP

597 GBP

320 GBP

335 GBP












The prices are in basis points, which when multiplied by the notional principal give the actual purchase or sale price in pounds sterling. These quotes are from the perspective of the market maker, not the firm. That is, the treasurer could buy a 9 percent cap from the market maker for 220 BP, or sell one for 205 BP. The strike rates are quoted on a 365-day basis, as is sterling LIBOR.


In financial analysis of this sort, the treasurer assumes that the three-year cost of funds on fully amortizing debt would be about 8.20 percent (for quarterly payments). Should another structure be considered in lieu of the plain vanilla swap?




Problem 6(a-c)


6. You are considering the purchase of a convertible bond issued by Bildon Enterprises, a non-investment-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., breakeven 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.


Problem 8(a-c)


8. On May 26, 1991, Svensk Exportkredit (SEK), the Swedish export credit corporation, is- sued a Bull Indexed Silver Opportunity Note (BISON). Consider an extended version of this BISON issue that has the following terms:




            Maturity                                                May 26, 1993


            Coupon                                                 6.50%


            Face Value                                            USD 30 million


            Purchase Price                                      100,123% of par value


Additionally, this BISON includes a redemption feature that, for each USD 1,000 of face value held at maturity, repays the investor’s principal according to the following formula:


USD 1,000 + [(Spot Silver Price per Ounce − USD 4.46) × (USD 224.21525)]


a. Demonstrate that, from SEK’s perspective, the BISON represents a combination of a straight debt issue priced at a small premium and a derivative contract. Be explicit as to the type of derivative contract and the underlying asset on which it is based. What implicit speculative position are the investors who buy these bonds taking?


b. Calculate the yield to maturity for an investor holding USD 10,000 in face value of these BISON if the May 1993 spot price for silver is (1) USD 4.96 per ounce, or (2) USD 3.96 per ounce.


c. In May 1991 (i.e., when the BISON were used), the prevailing delivery price on a two- year silver futures contract was USD 4.35 per ounce. If SEK wanted to hedge its BISON-related exposure to silver prices with an offsetting futures position at this price, what type of position would need to be entered? Ignoring margin accounts and underwriting fees, calculate SEK’s average annualized borrowing cost of funds for the resulting synthetic straight bond.




Problem 10(a-c)


10. A firm has 100,000 shares of stock outstanding priced at $35 per share. The firm has no debt and does not pay a dividend. To raise more capital, it plans to issue 10,000 warrants, each allowing for the purchase of one share of stock at a price of $50. The warrants are European-style and expire in five years. The standard deviation of the firm’s common stock is 34 percent, and the continuously compounded, five-year risk-free rate is 5.2 percent.


a. Estimate the fair value of the warrants, first using the relevant information to calculate the Black-Scholes value of an analogous call option.


b. Determine the stock price at expiration, assuming the warrants are exercised if the value of the firm is at least $5,200,000.


c. Using the information in Parts a and b about initial and terminal warrant and stock prices, discuss the relative merits of these two ways of making an equity investment in the firm.






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