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