Question

Laurel Enterprises expects earnings next year of $4 per share. The company will pay out all of its earnings to investors. Its expected return on new investment (i.e., ROE) is 12%.

The required rate of return is 10%. What is the intrinsic value of the stock today?

Laurel Enterprises expects earnings next year of $4 per share. The company will retain $2.4 of its earnings to reinvest in new projects that have an expected return of 12% per year (i.e., ROE is 12%). The rest of the earnings will be paid out to its investors.

Suppose the company will keep the retention rate constant in future. What is the growth rate of earnings for its share? ______%

Following question 16

If the dividends grow at the same rate as the earnings, and the required return of the stock is 10%, what is the intrinsic value of the stock?

Following question 17

Use the same setup as 17 except that the ROE for the new projects is 9% now, what is the intrinsic value of the stock?

Hint: since the ROE is now lower, the dividend growth rate will be slower than the growth in #17. You'll first need to find the dividend growth rate and then calculate the intrinsic value.

Answer 1

a) Since retention ratio =0 , growth =ROE*Retention ratio =0
Intrinsic value of the stock =Dividend Per share/Required Rate =4/10% =40

b) Retention ratio =Retained Earnings/Income =2.4/4 =60%
growth =ROE*Retention ratio =12%*60% =7.2%
Dividend =4-2.4 =1.6
Intrinsic Value of the stock =Dividend next year/(Required Rate-Growth) =1.6/(10%-7.2%) =57.14

c)If ROE =9%
growth =ROE*Retention ratio =9%*60% =5.4%
Dividend =4-2.4 =1.6
Intrinsic Value of the stock =Dividend next year/(Required Rate-Growth) =1.6/(10%-5.4%) =34.78