Vansel inc. retains most of its earnings. the company currently has earnings per share of $11. vansel expects its earnings to grow at a constant rate of 2 percent per year. furthermore, the average pe ratio of all other firms in vansel's industry is 12. vansel is expected to pay dividends per share of $3.50 during each of the next three years. if investors require a 10 percent rate of return on vansel stock, a fair price for vansel stock today is $
a. 113.95
b. 111.32
c. 105.25
d. none of the above

A. $113.95

Explanation:

Vansel's expect that the EPS will grow by 2% annually, the earnings per share in 3 years are forecast to be:

Earnings in 3 years = $11×(1+2%)³ = $11.67

The forecasted earnings per share can be multiplied by the PE ratio of the firm’s industry to forecast the future stock price. The average PE ratio of all other firms in Vansel industry is 12, the stock price in three years can be forecast as follows:

Stock price in three years = (Earnings in three years)×(PE ratio of industry) = $11.67×12 = $140.08

This forecasted stock price can be used along with expected dividends and the investor’s required  rate of return to value the stock today. Vansel pay a dividend of $3.5 per share over the next three years and the investor’s required rate of return (Re)is 10%, then the present value of expected cash flows to be received by the investor is:

PV = Dividend₁/(1+Re)¹ + Dividend₂/(1+Re)² + Dividend₃/(1+Re)³ +Stock price in three years/(1+Re)³ = $3.5/(1+10%) + $3.5/(1+10%)² + $3.5/(1+10%)³ + $140.08/(1+10%)³ = $113.95

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