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# Option Pricing, Warrants, Lease or Buy, Duration of Bond

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1. GS, Inc. stock is selling for \$28 a share. A 3-month call on GS stock with a strike price of \$30 is priced at \$1.50. Risk-free assets are currently returning 0.3% per month. What is the price of a 3-month put on GS stock with a strike price of \$30?

2. A firm has 100 shares of stock and 40 warrants outstanding. The warrants are about to expire, and all of them will be exercised. The market value of the firm's assets is \$2,000, and the firm has no debt. Each warrant gives the owner the right to buy 2 shares at \$15 per share. What is the price per share of the stock?

3. What is the value of a 9-month call with a strike price of \$45 given the Black-Scholes Option Pricing Model and the following information?
Stock price \$48
Exercise price \$45
Time to expiration .75
Risk-free rate .05
N(d1) .718891
N(d2) .641713

4. Calculate the duration of a 4-year \$1,000 face value bond, which pays 8% coupons annually throughout maturity and has a yield to maturity of 9%.

5. Turner, Inc. has \$4.2 million in net working capital. The firm has fixed assets with a book value of \$48.6 million and a market value of \$53.4 million. Martin & Sons is buying Turner, Inc. for \$60 million in cash. The acquisition will be recorded using the purchase accounting method. What is the amount of goodwill that Martin & Sons will record on its balance sheet as a result of this acquisition?

6. The Parent CO. has decided to acquire a new electronic milling machine. Parent Co. can purchase the machine for \$87,000 which has an expected life of 8 years and will be depreciated using 7 class MACRS rates of .1428, .2449, .1749, .125, .0892, .0892, .0892 and any remainder in year 8. Miles Leasing has offered to lease the machine to Parent Co. for \$14,000 a year for 8 years. Parent Co. has an 18.64% cost of equity, 12% cost of debt, a 1:1 D/E ratio and faces a 34% marginal tax rate. Should they lease or buy?

7. A stock is currently priced at \$24 per share, the standard deviation of its return is 60% a year, and the risk free rate is 4 percent per year. The firm pays \$0.30 quarterly (\$1.20 a year) dividend per share. What is the price of a call option with a strike price of \$25 and a maturity of three months?

8. From the previous question, what is the price of a put option with the same exercise price and time to expiration as the call option?

#### Solution Preview

Please complete the following problems eight problems in an Excel File with step-by-step solution to the problems.
1. GS, Inc. stock is selling for \$28 a share. A 3-month call on GS stock with a strike price of \$30 is priced at \$1.50. Risk-free assets are currently returning 0.3% per month. What is the price of a 3-month put on GS stock with a strike price of \$30?

We will use Put- Call Parity to calculate the value of Put

c+ Xe^-(r(T-t)) = p+S

Put :To determine the value of Put given the value of Call

Inputs

Stock Price= S= \$28.00
Exercise price = X= \$30.00
Time to expiration = T-t= 3 months
Risk free rate = r = 0.30% per month
Call= \$1.5000

Calculations

X * e ^(-r(T-t)) = \$29.7312 =30x e ^ (-0.003x3)

p=c+Xe^(-r(T-t))-S)= \$3.2312 =1.5 + 29.7312 - 28

2.      A firm has 100 shares of stock and 40 warrants outstanding. The warrants are about to expire, and all of them will be exercised. The market value of the firm's assets is \$2,000, and the firm has no debt. Each warrant gives the owner the right to buy 2 shares at \$15 per share. What is the price per share of the stock?

Market Value of firm's assets= \$2,000

Number of warrants= 40
Each warrant gives the owner the right to buy 2 shares for \$ 15 each
Number of additional shares= 2 x 40= 80
Additional cash for the company when the warrants are exercised= \$1,200 =15x80

Value of the firm when the warrants are exercised= \$2000 + \$ 1200= \$3,200
Total number of outstanding shares when the warrants are exercised=100+80= 180

Therefore price per share= \$ 3,200 / 180= \$17.78

Answer: Price per share of the stock= \$17.78

3.      What is the value of a 9-month call with a strike price of \$45 given the Black-Scholes Option Pricing Model and the following information?
Stock price \$48
Exercise price \$45
Time to expiration 0.75
Risk-free rate 0.05
N(d1) 0.718891
N(d2) 0.641713

We will use Black Scholes Pricing Formula
Value of call= S N(d1) - X * e -r(T-t) * N(d2)

Inputs

Stock Price= S= \$48.00
Exercise price = X= \$45.00
Time ...

#### Solution Summary

This solution answers the Black-Scholes option pricing model, pricieng of put option, duration of a bond, goodwill, lease or buy decision etc. Calculations are provided in plain text and in the attached Excel file.

\$2.19