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6. Company X is going to issue 2,000 stock option (200,000 shares) on its common stock...

6. Company X is going to issue 2,000 stock option (200,000 shares) on its common stock to the top executives today.  The exercise price on the stock options is $30 per share.    If past experience dictates that the executives will exercise their option by the 11th year on average and that the variance of stock returns is .15 (annual), calculate the value of these stock options assuming a dividend yield of 1% and a risk free rate of 4%.  The stock is trading at $27 per share. The company finds that 90% of options are exercised.

b.  What is the minimum value of the options that must be amortized on the company's financial statements according to FASB 123R?

Solutions

Expert Solution

6. (a)

Annualized Volatility(σ) = SQRT(Variance of stock returns)

Spot Price (So) 27
Strike Price (X) 30
Interest Rate ( r ) 4%
Time to maturity (T) 11
Variance of stock returns 15%
Annualized Implied Volatility (σ) 38.73%
Dividend Yield (q) 1%
d1 0.82
d2 -0.47
exp(-rt) 0.6440
exp(-qt) 0.8958
Call Premium (C) 13

Therefore, the value of these stock options is $13 per option.

(b) An option's minimum value is the intrinsic value of that option, which reflects the effective financial advantage resulting from the immediate exercise of that option.

The company X's 30 call option would have an intrinsic value of zero ($27 - $30 = -$3) because the intrinsic value cannot be negative.

jeff jeffy answered 1 year ago
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