Question

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 .30. Its earnings this year will be $2 per share. Investors expect a 12% rate of return on the stock.

a. At what price and P/E ratio would you expect the firm to sell?

b. What is the present value of growth opportunities?

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?

Short answer

a.$23.33 &11.67

b. $6.67

c. $3.33

Step-by-step solution

Step by Step SolutionStep 1: Given information

EPS = $2

b= 0.3

ROE = 20%

k = 12%

g = ROE x b = 0.20 x 0.3 = 0.6

Calculation of price and P/E ratio ‘a’

P₀= D₁/ k – g

= EPS x (1 – b) / k – (ROE x b)

= $2 x (1 – 0.3) / 0.12 – 0.20 x 0.3

= $1.4 / 0.12 – 0.06

= $23.33

This can be calculated by dividing the current price by the projected earning

P₀/ E₁= 1 – b / k – (ROE x b)

= 1 – 0.3 / 0.12 – 0.20 x 0.3

= 11.67

Calculation of present value of growth opportunities ‘b’

PVGO = P₀– E₁/ k

= D₁/ (k – g) – (E₁/ k)

=$1.4 / 0.12 – 0.06 - $2 / 0.12

=$6.67

Calculation of impact of reducing plowback ratio

g = ROE x b = 0.20 x 0.2 = 0.04 = 4%

D₁= EPS x (1 - b) = $2 x (1 – 0.2) = $1.6

P₀= D₁/ k – g = $1.6 / 0.12 – 0.04 = $20

P/E = $20 / $2 = 10.0

PVGO = P₀– E₁/ k

= $20.00 - $2/ 0.12 = $3.33