Question

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Eki, Inc., a producer of table lamps, has a total of 1,500,000 shares outstanding. The current...

Eki, Inc., a producer of table lamps, has a total of 1,500,000 shares outstanding. The current value of the firm is $15 million (no debt). It issues a total of 50,000 2-year warrants to its two top executives with an exercise price of $30. If the risk-free rate is 10% and if the standard deviation of the Eki stock is 50%, compute the value (price) of each warrant if it can only be exercised on the expiration date.

Expert Solution

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

Eki, Inc., has number of shares of common stock = 1,500,000

Number of warrants =50,000

Exercise price of warrants X = $30.

Time period of expire t = 2 year

The market value of the company's assets = $15 million

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

= $15 million /1,500,000

= $15,000,000/1,500,000

= $ 10 per share

The standard deviation of stock σ = 50%

Risk free rate r = 10%

Assume that 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)	50.00%	d1	-0.91728
Time until Expiration (in Years) (t)	2.00	d2	-1.62438
Risk free rates (Annual) (r)	10.00%	N(d1)	0.17950
Stock Price (S0)	$10.00	N(d2)	0.05215
Strike price (X)	$30.00	B/S call value (C )	0.51416
Dividend yield	0.00%	B/S Put Value (P)	15.07608

Therefore the value of each warrant is the value of call option which is $0.51416

Formulas used in excel calculations –

jeff jeffy answered 7 months ago

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