Question

Samford Corp. does not plan on making any dividend payments on its common stock for the next four years. The first annual dividend payment, which will be made 5 years from today, will be in the amount of $5 per share, and dividends are expected to grow at 10 percent per year thereafter. If you require a 15 percent annual return on Samford stock, what price will you pay for the stock today?

$115.00

$110.00

$64.75

$57.18

None of the Above

Answer 1

As per the Dividend Discount Model, the current price of a stock (today) is equal to the sum of the present values of all future dividend payments on the stock.

Price of stock : P₀ = D1 / (Ke - g)

(where, D1 is the expected dividend in the year after the one in which the first dividend payment is made, Ke is the cost of equity for the company or the required return of the investor = 15%, and g is the constant growth rate of dividends = 10%)

Here, the first dividend is paid after 5 years so it will be D5, and the next dividend will be D6

D6 = D5 x (1+g) (D5 is the first dividend payment)

= $5 x (1+0.10) = $5.50 (expected dividend for the 6th year)

The Price of the stock in year 5 : P5 will be D6 / (Ke - g)

= $5.50 / (0.15 - 0.10)

= $5.50 / 0.05

= $ 110

Since the first dividend payment will be made 5 years from today, we have to find its present value today by discounting it back.

Present Value of D5 = Future value / (1+r)ⁿ (here r is the required return, and n is number of years)

= $5 / (1+0.15)⁵

= $5 / 2.0114

= $2.49

Similarly, the present value of P5 = $ 110 / (1+0.15)⁵

= $ 110 / 2.0114

= $54.69

The price you will pay for the stock today : P₀ = Present Value of D5 + Present Value of P5

= $2.49 + 54.69

= $57.18 (option 4)