The Back Room just paid an annual dividend of $1.65 a share.The firm expects to pay dividends forever and to increase the dividend by 3 percent annually.What is the expected value of this stock five years from now if the discount rate is 14 percent?

Question

Quizplus · Accepted Answer

To calculate the expected value of the stock 5 years from now, we need to forecast the dividends for the next five years using the growth rate of 3%:
D1 = $1.65 x (1 + 3%) = $1.70
D2 = $1.70 x (1 + 3%) = $1.75
D3 = $1.75 x (1 + 3%) = $1.81
D4 = $1.81 x (1 + 3%) = $1.87
D5 = $1.87 x (1 + 3%) = $1.93

Next, we need to calculate the expected price of the stock five years from now using the dividend discount model:
P5 = D6 / (r - g)
where r is the discount rate and g is the growth rate.

Plugging in the numbers, we get:
P5 = $1.93 / (0.14 - 0.03) = $17.91

Therefore, the expected value of the stock five years from now is $17.91.
The best choice is B.

The Back Room Just Paid an Annual Dividend of $1