### Recent Question/Assignment

Assignment 4; due Tues April 26 (beginning of class)
The first three questions are about the Boston Chicken case.
1. Why are yields lower for convertibles than straight debt? All other things being equal, should a callable (or redeemable) convertible trade for a higher or lower yield than a noncallable convertible?
2. Determine the per-share price of each attached call option in the convertible bond using the Black-Scholes model. Use the approach of pricing them as an option on the stock. The case provides the underlying stock price and the implied exercise price (which is the ratio of the bond par value to the conversion ratio). You will need to make an assumption about the volatility of the stock returns. You can try a few if you wish. You can use the spreadsheet on D2L to compute Black Scholes prices.
3. Now compute the per-share value of the convertible issue as an option on the firm value. Follow the procedure I showed in class (the dilution adjustment approach in the case is incorrect). Recall the per-share formula from your PP slides:
E§ V F T• ¸ c ¨ , ,

The m in the notes represented the number of existing shares. But in the case, we need to add to m the number of new shares issued when all the employee stock options are exercised (these will be exercised before the bonds are converted).
A key part of the calculation is the firm value, V, which has three parts:
1) The total market value of existing equity,
2) The total value of the convertible bond issue, net of investment-banking fees
3) The current market value of employee stock options. We are told these are all deep in the money (check your notes for valuing price of a low-exercise-price call options). You will need to make an assumption about the average strike price.
Finally, as in problem 2, you should try a few reasonable firm-value volatilities.
Please show your calculations and pricing inputs in the assignment you submit.
4. Suppose the capital structure of Canton Corp. is comprised of equity and a single issue of zero coupon bonds with par value of \$100 million and maturing in one year. The value of the firm is currently \$150 million and will be worth either \$200 or \$75 in one year. The continuously compounded interest rate is 4.879% (or 5% APR with annual compounding). Assume that there will be no dividends paid on the stock before the end of the year.
a) What should the bonds be worth today?
b) What is the total value of Canton’s equity today?
c) Suppose equity holders have the ability to increase the volatility of the firm such that the yearend firm value will be either \$250 (in the up state) or \$60 (in the down state) instead of \$200 and \$75. Determine the impact of the volatility change on the value of the firm’s debt and equity.
The remaining two are practice problems for the exam. You do not need to hand them in.
5. You hold 10,000 call options on XYZ with a \$65 strike and expiration in May. The delta of each contract is 0.45. What position in \$70 strike May calls (when combined with the 10,000 May 65 calls) would make the portfolio delta neutral? The 70 strike calls have a delta of 0.40.
6. A firm has a capital structure composed of 9 million shares of stock, and a single issue of convertible debt with a face value of \$1 billion and maturing in 7 years. The debt can be converted into 1 million shares of stock just before maturity.
a) Carefully draw the payoff at maturity of the convertible bond as a function of the firm value. Be sure to indicate the dilution ration and the breakeven firm value above which conversion is optimal.
b) How will an increase in the volatility of the value of the firm affect the value of the convertible debt?
c) If the firm value is currently worth \$4 billion, and follows a lognormal process with volatility of 40%, how would you value the option to convert?