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 earnings this year will be $2 per share. Investors expect a 12% rate of return on the stock. Required: (a) At what price and P/E ratio would you expect the firm to sell

The correct answer is 23.33 and 11.67.

Explanation:

According to the scenario, the given data are as follows:

ROE = 20%

Plowback ratio = 0.30

Earning per share = $2

Rate of return = 12%

So, we can calculate the price and P/E ratio by using following formula:

First we calculate the growth rate of the company.

So, Growth rate (g) = Plowback ratio × ROE

By putting the value we get,

Growth rate = 0.30 × 0.20 = 6%

Now we calculate the price,

So, Price = Earning × ( 1 - Plowback ratio) ÷ ( Return rate - Growth rate)

= $2 × ( 1 - 0.30) ÷ ( 0.12 - 0.06)

= 1.4 ÷ 0.06

= 23.33

And P/E ratio = Price ÷ earning per share

= 23.33 ÷ 2

= 11.67