Financial Management

1) Which of the following options will have a higher price and why?
a) A call option with an exercise price of $50 and 3 months to expiration, or a call option on
the same underlying stock with the same time to expiration but with an exercise price of
$53.
b) A put option with an exercise price of $70 and 3 months to expiration, or a put option on
the same underlying stock with the same time to expiration but with an exercise price of
$78.
c) A put option with an exercise price of $70 and 6 months to expiration, or a put option on
the same underlying stock with the same exercise price but with 9 months to expiration.
2) Suppose you own a call option with an exercise price of $50, and you also own a put option
on the same stock with the same time to expiration with an exercise price of $45.
a) Draw the payoff diagram for the call option on the expiration date. (Hint: Consider the
payoffs from the option in the following three stock price ranges: (i) stock price greater
than $50, (ii) stock price less than $50, and (iii) stock price equal to $50.)
b) Draw the payoff diagram for the put option on the expiration date. (Hint: Consider the
payoffs from the option in the following three stock price ranges: (i) stock price greater
than $45, (ii) stock price less than $45, and (iii) stock price equal to $45.)
c) Draw the payoff diagram for the payoff on the expiration date on a portfolio made up of
one call and one put option. (Hint: Consider the payoffs from the portfolio in the
following three stock price ranges: (i) stock price greater than $50, (ii) stock price less than
$45, and (iii) stock price between $45 and $50.)
3) Consider the following portfolio:
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Write a call option on 100 shares of Intel stock with an exercise price of $65, and hold a put
option on 100 shares of the same stock with the same time to expiration and the same
exercise price. Both options are European options. Assume you do NOT own the stock
and that you are an institution exempt from having to write only covered calls.
Draw the payoff diagram for this portfolio on the expiration date. {Hint: Compute the
total payoff from the portfolio on the expiration date assuming different stock prices. You
may want to consider the following stock price ranges: (i) stock price greater than $65, (ii)
stock price at $65, and (iii) stock price lower than $65. This will help you draw the payoff
diagram.}
4) Consider the options of a company where the stock price is $23.36. Suppose that the call
and put options of this company with an exercise price of $22.50 are trading in the options
market for a price of $2.61 (call) and $1.81 (put), respectively. Both options have 21 weeks
left for expiration.
If the call option is correctly priced, find the correct price of the corresponding put option
using the put-call parity relation. Assume that the annual risk-free rate is 0.4%. Is the put
option overvalued, correctly valued, or undervalued? Explain.
5) General Eclectics, Inc., has both European call and put options traded on the Chicago Board
of Exchange. Both options have the same exercise price of $40 and both expire in one
year. General Eclectic’s stock does not pay dividends. The call and the put are currently
selling for $8 and $2, respectively. The risk-free interest rate is 10% per annum. What
should the stock price of General Eclectics, Inc., be in order to prevent arbitrage?
6) Why is the price of a call option higher when the volatility of the underlying stock is
higher? Explain.
7a) Use the Black-Scholes model to price a call with the following characteristics.
Stock Price = $40
Exercise Price = $38
Time to expiration = 39 weeks
Stock price variance = 0.16
Riskfree interest rate = 6%
b) Compute the price of the corresponding put option using the put-call parity.
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8) What is the price of a Put option with the following characteristics?
Stock Price = $25
Exercise Price = $28
Time to expiration = 13 weeks
Stock price variance = 0.09 (i.e., volatility of 30%)
Riskfree interest rate = 6%
9) Abacus Associates, a new and highly innovative money managing firm run by two ExTulanians
(who took our course, but dropped out of school soon after to start this firm)
decides to offer the following “Portfolio Insurance” to the endowment fund of the Freeman
School of Business. The Freeman School fund is currently worth $60 million and it is
invested in a Portfolio of assets that have a variance of 0.0225 (volatility of 15%). Abacus
offers to guarantee a return of 5% on the portfolio over the next 39 weeks i.e., if the fund
value is below $63 million at the end of 39 weeks then Abacus Associates will make-up the
difference. (Of course, if the fund does better than 5% then the School gets to keep the
proceeds). For your computations assume that the riskfree rate is 6%.
a) Compare this Portfolio Insurance to a Put Option. In particular, specify the following
characteristics of the Put.
(i)What is the underlying asset of the put? (ii) Who writes the put? (iii) Who owns the
put? (iv) What is the expiration date of the put? (v) What is the exercise price of the
put? (vi) For what values of the Portfolio is the put in-the-money?
b) Using the Black-Scholes formula compute the fair price that our Dean should expect to pay
for this insurance.
10) Omniscient Inc., a producer of Telescopes and Binoculars, has a total of 400,000 shares
outstanding. The current market value of Omniscient is $12 million and it has zero debt in
its capital structure. It issues a total of 40,000 warrants (exercise price of $40) to its CEO
as incentive compensation.
a) What is the price per share of Omniscient’s stock before the warrants were issued?
b) To how much should the value of Omniscient rise so the warrants can be exercised?
c) Suppose that the market value of Omniscient rises to $20 million. Also suppose that the
CEO now pays the exercise price and exercises all the warrants. (Note: The $20 mil.
market value is before the exercise of warrants).
(i) What is the new price per share of Omniscient Stock?
(ii) What is the total gain for the CEO?
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(iii) Instead of warrants, assume that the CEO holds 40,000 call options (that someone
gave as a gift) with all the other characteristics held the same. What would be the
share price after the exercise of the options? What is the total gain for the CEO?
11) Pace Western Crystal, Inc., has outstanding 10 million common shares, and 200,000
warrants. Each warrant can purchase 5 shares of common stock at $15 per share. Warrant
holders exercised all their warrants today. Pace Western’s stock price before the exercise
was $17. What should the new stock price be after the exercise? Assume there is no other
information content on the exercise of the warrants.
12) Ryan Home Products, Inc., issued $430,000 of 8-percent convertible debentures. Each
bond is convertible into 28 shares of common stock anytime before maturity.
a) Suppose the current price of the bonds is $1000 and the current price of Ryan common
stock is $31.25.
(i) What is the conversion ratio?
(ii) What is the conversion price?
(iii) What is the conversion premium?
b) What is the conversion value of the debentures?
13) Acme Medical Supplies, Inc., issued zero coupon convertible bonds due 10 years from
today. The bond has a face value of $1,000 at maturity. Each bond can be converted into
25 shares of Acme’s common stock. The appropriate discount rate is 10%. The company’s
stock is selling for $12 per share. Each convertible bond is traded at $400 in the market
today.
a) What is the straight bond value?
b) What is the conversion value?
c) What is the value of the warrant component of the convertible bonds?
14) Please answer the Flowers questions indicated on the next page.
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Flowers Industries, Inc. (due on Thursday, April 26)
The following are some questions that are intended to help with the case analysis. The questions
will provide the structure necessary to discuss the case in class. Please answer the questions
written in bold (i.e., the first two questions) as part of your mini-report.
1) Why is Flowers seeking new capital? Is $50 million sufficient?
2) What are the relative merits of convertible debt compared to straight debt or
straight equity? Consider the effect on shareholders’ income, the risk that each
form of financing entails, whether the financing increases or reduces financial
flexibility, the effects on voting control, and the timing of the financing.
3) When are the investors likely to convert? When could the firm force conversion? (see
case exhibits 5 and 6).
4) What is the effect of each financing alternative on the reported earnings, ROE, and capital
structure of the firm? What would be the EPS under the three alternatives if the EBIT
were $40 million? $50 million?
5) Under the terms outlined in Exhibit 7, is the convertible fairly priced? (i.e., is the sum of
the bond portion and the option part equal to the par value?)
6) Should Marty Wood go forward with the convertible issue?