Even Better Products has come out with a new and improved product. As a result, the firm projects an ROE of 20%, and it will maintain a plowback ratio of 0.30. Its projected earnings are $2 per share. Investors expect a 14% rate of return on the stock. a.
At what price and P/E ratio would you expect the firm to sell? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Price $
P/E ratio
b.
What is the present value of growth opportunities? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

PVGO $
c.
What would be the P/E ratio and the present value of growth opportunities if the firm planned to reinvest only 20% of its earnings? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

P/E ratio
PVGO $

Answer and Explanation:

The computation is shown below:

a. The price and P/E ratio is

Price = Current year dividend ÷ (Required rate of return - growth rate)

where,

Growth rate is

= ROE × plowback ratio

= 20% × 0.30

= 6%

And, the current year dividend is ×

= $2 × (1 - 0.30)

= $1.4

So, the price is

= $1.4 ÷ (0.14 - 0.06)

= $17.50

Now the P/E ratio is

= $17.50  ÷ 2

= 8.75

b)  For the present value of growth opportunities, the formula and the computation is

= Price of the stock - earnings ÷ required rate of return

= $17.50 - $2 ÷ 0.14

= 3.21

c)  The P/E ratio and the present value of growth opportunities is

But before that we need to find out the price which is

Price = Current year dividend ÷ (Required rate of return - growth rate)

where,

Growth rate is

= ROE × plowback ratio

= 20% × 0.20

= 4%

And, the current year dividend is

= $2 × (1 - 0.20)

= $1.6

So, the price is

= $1.6 ÷ (0.14 - 0.04)

= $16

Now the P/E ratio is

= $16  ÷ 2

= 8

And, the growth opportunities is

= Price of the stock - earnings ÷ required rate of return

= $16 - $2 ÷ 0.14

= 1.72