# (Duration) What is the duration of a bond with three years to maturity and a coupon of 7 percent paid annually if the bond sells at par? (Do not round intermediate calculations and round your final answer to 5 decimal places. (e.g., 32.16161))

**1.**(WACC) If Wild Widgets, Inc., were an all-equity company, it would have a beta of .85. The company has a target debt–equity ratio of .40. The expected return on the market portfolio is 11 percent, and Treasury bills currently yield 4 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 7 percent. The bond currently sells for $1,080. The corporate tax rate is 34 percent.

a) What is the company’s cost of debt? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

b) What is the company’s cost of equity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

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c) What is the company’s weighted average cost of capital? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

**2. **(IPO Underpricing) The Woods Co. and the Garcia Co. have both announced IPOs at $40 per share. One of these is undervalued by $9, and the other is overvalued by $4, but you have no way of knowing which is which. You plan on buying 1,000 shares of each issue. If an issue is underpriced, it will be rationed, and only half your order will be filled.

a) If you could get 1,000 shares in Woods and 1,000 shares in Garcia, what would your profit be? (Do not round intermediate calculations.)

b) What profit do you actually expect? (Do not round intermediate calculations.)

**3. **(Lease or Buy) Wolfson Corporation has decided to purchase a new machine that costs $3.2 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for $3.2 million. The repayment schedule is four yearly principal repayments of $800,000 and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of $950,000 per year are due at the beginning of each of the four years of the lease.

a) What is the NAL of leasing for Wolfson? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

b) What is the maximum annual lease Wolfson would be willing to pay? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole dollar amount. (e.g., 32))

**4. **(Black-Scholes) A stock is currently priced at $35. A call option with an expiration of one year has an exercise price of $50. The risk-free rate is 7 percent per year, compounded continuously, and the standard deviation of the stock’s return is infinitely large. What is the price of the call option?

**5. **(Put-Call Purity) A put option and a call option with an exercise price of $85 and three months to expiration sell for $2.40 and $5.09, respectively.

If the risk-free rate is 4.8 percent per year, compounded continuously, what is the current stock price? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

**6. **(Marking to Market) You are long 10 gold futures contracts, established at an initial settle price of $1,580 per ounce, where each contract represents 100 ounces. Over the subsequent four trading days, gold settles at $1,587, $1,582, $1,573, and $1,584, respectively.

a) Calculate the profit or loss for each trading day. (A negative amount should be indicated by a minus sign. Do not round intermediate calculations.)

b) Compute your total profit or loss at the end of the trading period. (Input amount as a positive value. Do not round intermediate calculations.)

**7. ** (Duration) What is the duration of a bond with three years to maturity and a coupon of 7 percent paid annually if the bond sells at par? (Do not round intermediate calculations and round your final answer to 5 decimal places. (e.g., 32.16161))

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**8. **You enter into a forward contract to buy a 10-year, zero coupon bond that will be issued in one year. The face value of the bond is $1,000, and the 1-year and 11-year spot interest rates are 5 percent and 7 percent, respectively.

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a) What is the forward price of your contract? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

b) Suppose both the 1-year and 11-year spot rates unexpectedly shift downward by 2 percent. What is the new price of the forward contract? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))