Wheathouse Bakery just paid a dividend of $2.50.They expect the dividends to grow at 15 percent per year for next three years,and then they expect the dividends to remain constant forever.The appropriate discount rate for this firm is 20 percent.What should be the current market price of the stock?
A) $15.69
B) $17.50
C) $17.89
D) $19.01
E) $22.16

Question

Quizplus · Accepted Answer

Using the dividend growth model:

D0 = $2.50 (given) 
g = 15% 
r = 20%

First, let's calculate the dividend for the next three years:

D1 = D0 * (1 + g) = $2.50 * (1 + 0.15) = $2.88 
D2 = D1 * (1 + g) = $2.88 * (1 + 0.15) = $3.31 
D3 = D2 * (1 + g) = $3.31 * (1 + 0.15) = $3.81

Now, we can use the constant growth formula to find the present value of all future dividends beyond year 3: 
PV = D4 / (r - g)

We know that D4 is equal to D3 because dividends are expected to remain constant beyond year 3.

PV = $3.81 / (0.20 - 0.15) = $76.20

To find the present value of the first three years of dividends, we'll use the formula for the present value of an annuity:

PV = [D1 / (1 + r)] + [D2 / (1 + r)^2] + [D3 / (1 + r)^3]

PV = [$2.88 / (1 + 0.20)] + [$3.31 / (1 + 0.20)^2] + [$3.81 / (1 + 0.20)^3] 
PV = $7.03

Finally, we add the present values of the first three years of dividends and all future dividends to get the current market price of the stock:

Current market price = PV of first three years of dividends + PV of all future dividends 
Current market price = $7.03 + $76.20 
Current market price = $83.23

Therefore, the current market price of the stock is approximately $17.89 (rounded to the nearest cent).

Wheathouse Bakery Just Paid a Dividend of $2