Question

8. If D1 = $1.25, g (dividend growth rate) = 4.7%, and P0 = $26.00, what is the stock’s expected dividend yield for the coming year?

a. 4.12% b. 4.34% c. 4.57% d. 4.81% e. 5.05%

Answer 1

Given :

Divident for the coming year (D1) = 1.25

Divident growth rate (g) = 4.7%

Current stock price (P0) = $26

Cost of equity (k) = ?

Stock price for coming year (P1) = ?

The question asks to compute expected divident yield for the coming year ie, year 1. The formula is:

Divident yield = Annual divident / Stock price

Here we have annual divident = 1.25. Stock price to be used in this formula is the stock price for the coming year (P1). For calculating P1, cost of equity (k) is to be calculated.

Computation of cost of equity (k)

According to divident growth model, stock price for current year is computed using the following formula,

P0 = D1 / (k-g)

Using this formula find k.

k-g = D1 / P0

k = (D1 / P0 ) + g

k =(1.25 / 26) + 0.047

k = 0.0481 + 0.047

k = 0.095 ie, k = 9.5%

Computation of stock price for the coming year (P1)

P1 = (D1(1+g)) / (k-g)

= (1.25(1+0.047)) / (0.095-0.047)

= (1.25 x 1.047) / 0.048

= 1.308 / 0.048

= 27.26    P1 = 27.26

Computation of expected Divident yield for the coming year

Divident yield = Annual divident / Current stock price

Divident yield for the coming year = Divident for the coming year / Stock price for the coming year

= 1.25 / 27.26

= 0.0458

Therefore stock's expected divident yield for the coming year is 4.58%

Answer is c. 4.57%