Question

Titanic Corporation has 10 million share outstanding, selling currently at a price of $50 per share. The company expects earnings per share next year to be $7.50. The company retains one-third of each year's earnings and reinvests these funds in projects with an expected return of 15% (thus, ROE is 15%)

What Rate of return do the shareholders require?

Suppose that, unexpectedly, the company announces plans to retain an additional $3 per share for the next ten years. These additional funds will be invested in ten separate perpetual projects, each with an expected rate of return of 9%. The required rate of return on the new projects would be the same as the current required return. As a result of this announcement. Titans Stock price is?

Do you think Titanic is more of a growth company before or after this announcement?

Answer 1

(a) Expected EPS = E1 = $ 7.5, Retention Ratio = Firm Retains one-third of each year's earnings = 1/3 and ROE = 15 %

Expected Dividend = D1 = E1 x (1-Retention Ratio) = 7.5 x (2/3) = $ 5

Expected Growth Rate = g = ROE x Retention Ratio = 15 x (1/3) = 5 %

Let the required Rate of Return be r

Current Price = P0 = $ 50

Therefore, r = (D1/P0) + g = (5/50) + 0.05 = 0.15 or 15 %

(b) Additional Retained Earnings = $ 3 per share

Retention Ratio = 3/7.5 = 0.4 and ROE = 9%

Additional Growth generated by this Additional Retention = ROE x Retention Ratio = 9 x 0.4 = 3.6%

Total Growth = 5 + 3.6 = 8.6 %

Expected Dividend (Post Additional Retention) = (7.5 - 2.5 - 3) = $ 2

Therefore, New Stock Price = 2 / (0.15 - 0.086) = $ 31.25

Titanic was more of a growth company prior to the retention of additional earnings as the returns generated by this additional investment is lower than the minimum required rate of return. This results in the observable decline in stock price post declaration of this additional retention.