# Corporate finance: Black-Scholes Option Pricing Model; Residual dividend distribution policy

1) 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

2) Chandler Communications' CFO has provided the following information:
? The company's capital budget is expected to be \$5,000,000.
? The company's target capital structure is 70 percent debt and 30 percent equity.
? The company's net income is \$4,500,000.

If the company follows a residual distribution policy (with all distributions in the form of dividends), what portion of its net income should it pay out as dividends this year?

#### Solution Preview

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Inputs

Stock Price= S= \$48.00
Exercise price = X= \$45.00
Time to expiration = T-t= 0.75 year
Risk free rate = r = 5.00% or 0.05

Calculations

N is the cumulative normal distribution function
N(d1) 0.718891
N(d2) 0.641713
X * e ^ -r(T-t) = 43.3437 =45x e ^ (-0.05x0.75)

Thus,
Value of call= S N(d1) - X * e -r(T-t) * N(d2)= \$6.6926 =48 x 0.718891 - ...