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Superior Clamps, Inc., has a capital structure consisting of 8.6 million shares of common stock and...

Superior Clamps, Inc., has a capital structure consisting of 8.6 million shares of common stock and 916,000 warrants. Each warrant gives its owner the right to purchase one share of newly issued common stock for an exercise price of $22.50. The warrants are European and will expire one year from today. The market value of the company's assets is $171.5 million and the annual variance of the returns on the firm's assets is .30. Treasury bills that mature in one year yield a continuously compounded interest rate of 8.6 percent. The company does not pay a dividend. Use the Black-Scholes model to determine the value of a single warrant.

Solutions

Expert Solution

The real option analysis is used to take capital budgeting decisions by the management when they are investing in risky assets. It is generally used for projects investing in tangible assets instead of financial instruments. We can use the Black-Scholes model to determine the value of a single warrant as the price of call option.

We have following information

Superior Clamps, Inc., has number of shares of common stock = 8.6 million

Number of warrants =916,000

Exercise price of warrants X = $22.50.

Time period of expire t = 1 year

The market value of the company's assets = $171.5 million

Therefore share price S0 = the market value of the company's assets/ number of shares of common stock

= $171.5 million /8.6 million

= $ 19.94 per share

The annual variance of the returns on the firm's assets = 0.30

Therefore standard deviation σ = √variance = √ (0.30) = 0.5477

Treasury bills that mature in one year yield a continuously compounded interest rate (risk free rate) r = 8.6 percent.

The company does not pay a dividend.

Therefore value of the call option (C) can be calculated in following manner –

INPUTS

Outputs

Value

Standard deviation (Annual) (σ)

54.77%

d1

0.21052

Time until Expiration (in Years) (t)

1.00

d2

-0.33720

Risk free rates (Annual) (r)

8.60%

N(d1)

0.58337

Stock Price (S0)

$19.94

N(d2)

0.36798

Strike price (X)

$22.50

B/S call value (C )

4.03615

Dividend yield

0.00%

B/S Put Value (P)

4.74016

Therefore the value of a single warrant is the value of call option which is $4.03615

Formulas used in excel calculations –

jeff jeffy answered 11 months ago
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