Question

Portman Industries just paid a dividend of $3.12 per share. The company expects the coming year to be very profitable, and its dividend is expected to grow by 16.00% over the next year. After the next year, though, Portman’s dividend is expected to grow at a constant rate of 3.20% per year. (Note: Do not round your intermediate calculations.)
The risk-free rate (r _RF) is 5.00%, the market risk Term Value premium (RP _M) is 6.00%, and Portman's beta is 1.90. Assuming that the market is in equilibrium, use the information just given to complete the table. What is the expected dividend yield for Portman's stock today?
a. 12.40%
b. 13.88%
c. 9.92%
d. 11.92%

Answer 1

Answer:

The correct option is (b), 13.88%

Explanation:

Given:

D0 = $3.12

Expected growth in dividend (D1) next year = 16% or 0.16

Dividend paid next year = 3.12 × (1+0.16)

                                      = $3.6192

Now calculate horizon value. For that cost of equity needs to be computed which can be calculated using CAPM:

Cost of equity (Re) = Rf + β(Rm)

                              = 0.05 + 1.9(0.06)

                              = 0.164 or 16.4%

Horizon value = $\frac{Dividend\ second\ year\ (D2)}{Re-g}$

Growth rate is 0.032 from second year onward

Horizon value = $\frac{3.6192 (1.032)}{0.164-0.032}$

                      = $28.3

Now we have to calculate intrinsic value of stock:

Intrinsic value = $\frac{D1}{1+Re} +\frac{Horizon\ value}{1+Re}$

                       = $\frac{3.6192}{1.164} +\frac{28.3}{1.164}$

                        = $27.42

Expected Dividend = D1÷Intrinsic value

                              = 3.6192 ÷ 27.42

                               = 13.2

Expected dividend yield is 13.2 approximately which is close to 13.88 (difference due to rounding off of intermediary calculations)