Question

The FI Corporation’s dividends per share are expected to grow indefinitely by 5% per year. a. If this year’s year-end dividend is $8 and the required rate of return is 10% per year, what must the current stock price be according to the DDM? b. If the expected earnings per share are $12, what is the value of the ROE on the firm’s investment opportunities? c. How much is the market paying per share for growth opportunities?

Answer 1

Answer and Explanation:

The computation is shown below:

a. The current stock price is

As we know that

Current stock price = (Dividend) ÷ (Required rate of return - growth rate)

= ($8) ÷ ( 10% - 5%)

= $160

b. Now the value of the ROE on the firm’s investment opportunities is

Given that

Dividend  = $8

And,  

The payout ratio = Dividend ÷ Earning per share

                            = $8 ÷ $12

                            = 0.666666666666667

And, retention  ratio (b) is

= 1- 0.666666666666667

= 0.333333333333333

In addition to it

indefinite growth rate (g) = 5%

So, the ROE is

= Growth rate ÷ retention ratio

= 0.15 ÷ 0.3333

= 15%

c. And, the market paying per share is

PVGO = Price - Earning per share ÷ required rate of return

where,

PVGO = Present Value of Growth Opportunity

So, the market paying per share is

= $160 - $12 ÷ 10%

= $160 - $120

= $40