Wilbert's Clothing Stores just paid a $1.25 annual dividend.The company has a policy whereby the dividend increases by 2% annually.You would like to purchase 100 shares of stock in this firm but realize that you will not have the funds to do so for another three years.If you desire a 12% rate of return,how much should you expect to pay for 100 shares when you can afford to buy this stock? Ignore trading costs.

Question

Quizplus · Accepted Answer

Using the dividend discount model:
D1 = D0(1+g) where D1 is the dividend in the next year
D0 is the current dividend
g is the growth rate in dividends

In one year, Wilbert's Clothing Stores will pay a dividend of:
D1 = $1.25(1+.02) = $1.275

In two years, Wilbert's Clothing Stores will pay a dividend of:
D2 = $1.275(1+.02) = $1.3015

In three years, Wilbert's Clothing Stores will pay a dividend of:
D3 = $1.3015(1+.02) = $1.32853

Using the dividend discount model and assuming the stock is purchased in three years, the price of the stock should be:

P = D3/(r-g) where P is the price of the stock
r is the required rate of return
g is the growth rate in dividends

P = $1.32853/(.12-.02) = $1,353. Therefore, the best choice is C

Wilbert's Clothing Stores Just Paid a $1