Question

Abel, Inc., has expected earnings of $3 per share for next year. The firm's ROE is 20%, and its earnings retention ratio is 50%. If the firm's market required rate on the stock is 15%, what is the present value of its growth opportunities?

A. Less than $12

B. Higher than $12 but less than $15

C. Higher than $18 but less than $20

D. Higher than $22

Answer 1

PV of growth Opportunities = PV of Share with growth in dividends - PV of share with no growth in dividends

In order to calculate the value of share, we will apply constant growth dividend discount model, according to which current value of share is present value of all dividends expected in future. Mathematically,

where V0 is value of share today, D1 is dividend expected next year, r is the required rate of return and g is growth rate.

We also need to calculate the growth rate, which can calculate using the mathematical expression for sustainable growth rate:

Sustainable growth rate, g = ROE * Retention Ratio = 20% * 50% = 10%

Now, value of share assuming no growth (g = 0%)

V0 = $20/share

Now, value of share assuming growth (g = 10%)

V0 = $60/share

Therefore, PV of Growth opportunities = $60 - $20 = $40 --> higher than $22 --> Answer is Option D