Question

Eastern Electric currently pays a dividend of about $1.71 per share and sells for $25 a share.

a.	If investors believe the growth rate of dividends is 4% per year, what is the opportunity cost of capital? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Cost of Capital

%

b.	If investors' opportunity cost of capital is 10%, what must be the growth rate they expect of the firm? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Growth rate

%

c.	If the sustainable growth rate is 5% and the plowback ratio is .5, what must be the return on equity ROE? (Round your answer to 2 decimal places.)

ROE

%

Answer 1

a

As per dividend discount model formula,

Stock price = Expected dividend/ (Cost of capital – Dividend growth rate)

$ 25 = $ 1.71 x 1.04/ (Cost of capital – 0.04)

$ 25 = $ 1.7784/ (Cost of capital – 0.04)

(Cost of capital – 0.04) = $ 1.7784/$ 25

                                          = 0.071136

Cost of capital = 0.071136 + 0.04 = 0.111136 or 11.11%

Opportunity cost of capital is 11.11%

b.

Let the growth rate be g,

$ 25 = $ 1.71 x (1+g)/ (0.1 – g)

$ 1.71 x (1+g) = $ 25 x (0.1 – g)

$ 1.71 x (1+g) = $ 2.5 - $ 25 x g

$ 1.71 x (1+g) + $ 25 x g = $ 2.5

$ 1.71 + $ 1.71 g + $ 25 g = $ 2.5

$ 1.71 + $ 1.71 g + $ 25 g = $ 2.5

$ 1.71 + $ 26.71 g = $ 2.5

$ 26.71 g = $ 2.5 - $ 1.71 = $ 0.79

g = $ 0.79/$ 26.71 = 0.0295769374766 or 2.96 %

Expected growth rate of the firm is 2.96 %

c.

Sustainable growth rate = Return on equity x (1 – Dividend payout ratio)

                                         = Return on equity x Plow-back ratio

0.05 = Return on equity x 0.5

Return on equity = 0.05/0.5 = 0.1 or 10 %

ROE is 10 %