Question

Grott and Perrin, Inc., has expected earnings of $3 per share for next year. The firm's ROE is 20%, and its earnings retention ratio is 70%. If the firm's market capitalization rate is 15%, what is the present value of its growth opportunities?

Answer 1

Answer:

The present value of its growth opportunities is $70

Explanation:

Data provided in the question;

Expected earning per share, E = $3

The firm's ROE = 20% = 0.2

Earnings retention ratio = 70% = 0.70

Firm's market capitalization rate = 15% = 0.15

Now,

The present value of its growth opportunities is calculated using the formula

= $\frac{E\times\textup{(1-retention rate)}}{\textup{(capitalization rate}-\textup{ROE}\times\textup{retention rate)}}-\frac{E}{\textup{capitalization rate}}$

on substituting the respective values, we get

= $\frac{\ 3\times\textup{(1-0.70)}}{\textup{(0.15}-\textup{0.2}\times\textup{0.70)}}-\frac{\ 3}{\textup{0.15}}$

or

= $90 - $20

or

= $70

Hence, The present value of its growth opportunities is $70