Garcia Inc. has a current dividend of $3.00 per share (D0 = $3.00). Analysts expect that the dividend will grow at a rate of 25 percent a year for the next three years, and thereafter it will grow at a constant rate of 10 percent a year. The company's cost of equity capital is estimated to be 15 percent. What is the current stock price of Garcia Inc.?

Question

Quizplus · Accepted Answer

Using the dividend discount model and the given information:
D0 = $3.00
g1 = 25%
g2 = 10%
k = 15%

First, calculate the dividends for the next three years:
D1 = D0(1 + g1) = $3.00(1 + 0.25) = $3.75
D2 = D1(1 + g1) = $3.75(1 + 0.25) = $4.69
D3 = D2(1 + g1) = $4.69(1 + 0.25) = $5.86

Next, calculate the price of the stock at the end of year 3:
P3 = D4/(k - g2) = D3(1 + g2)/(k - g2) = $5.86(1 + 0.1)/(0.15 - 0.1) = $147.15

Finally, calculate the present value of the stock price at the end of year 3:
P0 = P3/(1 + k)^3 = $147.15/(1 + 0.15)^3 = $77.92

Add the present value of the dividends over the next three years:
PV = D1/(1 + k) + D2/(1 + k)^2 + D3/(1 + k)^3 = $3.75/1.15 + $4.69/1.15^2 + $5.86/1.15^3 = $17.50

Add the present value of the stock price at the end of year 3:
PV = PV + P0 = $77.92 + $17.50 = $95.42

Therefore, the current stock price of Garcia Inc. is $95.42, which is Choice C.