The following information is given about options on the stock of a certain company.
S 0 = 23 X = 20
r c = 0.09 T = 0.5
$\sigma$ 2 = 0.15
No dividends are expected.
Use this information to answer questions 1 through 8.
-If we now assume that the stock pays a dividend at a known constant rate of 3.5 percent,what stock price should we use in the model? (Due to differences in rounding your calculations may be slightly different."none of the above" should be selected only if your answer is different by more than 10 cents. )
A)22.60
B)19.65
C)23.00
D)21.99
E)none of the above

Question

Quizplus · Accepted Answer

The correct answer is A. The stock price should be adjusted to reflect the present value of the dividends that will be paid over the life of the option. The present value of the dividends is calculated as follows:PV = D * (1 - e^(-r * T)) / rwhere:D = dividend rater = risk-free rateT = time to expirationIn this case, the dividend rate is 3.5%, the risk-free rate is 9%, and the time to expiration is 0.5 years. Plugging these values into the formula, we get:PV = 0.035 * (1 - e^(-0.09 * 0.5)) / 0.09 = 0.0163This means that the present value of the dividends is $0.0163 per share. To adjust the stock price, we subtract the present value of the dividends from the current stock price. In this case, the current stock price is $23.00. Subtracting the present value of the dividends, we get:Adjusted stock price = $23.00 - $0.0163 = $22.984Rounding to the nearest cent, the adjusted stock price is $22.98.

The Following Information Is Given About Options on the Stock σ\sigmaσ

The Following Information Is Given About Options on the Stock $\sigma$