Question

Rump Electric Power Ltd expects to earn $20 per share this year and intends to pay out $8 per share in dividends to shareholders and retain $12 per share to invest in new projects with an expected return on equity of 20%. In the future, Rump Electric Power Ltd expects to retain the same dividend payout ratio, expects to earn 20% return on its equity invested in new projects, and will not be changing the number of ordinary shares outstanding.

Required:

(a) Calculate the future growth rate for Rump Electric Power Ltd’s earnings.

(b) If the investor’s required rate of return for Rump Electric Power Ltd’s shares is 15%, what would be the price of its ordinary shares?

(c) What would happen to the price of Rump Electric Power Ltd’s ordinary shares if it raised its dividends to $12 per share this year and then continued with that same dividend payout ratio permanently? Should Rump Electric Power Ltd make this change? (Assume that the investor’s required rate of return remains at 15%.)

(d) What would happen to the price of Rump Electric Power Ltd’s ordinary shares if it lowered its dividends to $4 this year and then continued with that same dividend payout ratio permanently?

(e) Does the constant dividend growth rate model work in this case? Explain why or why not? (Assume the investor’s required rate of return remains at 15% and that all future new projects will earn 20%.)

Answer 1

(a) future growth rate of earnings = return on equity*(1-dividend payout ratio)

dividend payout ratio = dividend per share/earnings per share = $8/$20 = 0.4 or 40%

future growth rate of earnings = 0.20*(1-0.40) = 0.20*0.60 = 0.12 or 12%

the future growth rate for Rump Electric Power Ltd’s earnings is 12%.

(b) price of ordinary shares = expected dividend/(required rate of return - dividend growth rate)

dividend growth rate will also be equal to future growth rate of earnings.

price of ordinary shares = $8/(0.15 - 0.12) = $8/0.03 = $266.67

the price of its ordinary shares would be $266.67.

(c)  the price of Rump Electric Power Ltd’s ordinary shares will go down.

new dividend payout ratio = $12/$20 = 0.60 or 60%

new future growth rate of earnings = 0.20*(1-0.60) = 0.20*0.40 = 0.08 or 8%

new price of ordinary shares = $12/(0.15 - 0.08) = $12/0.07 = $171.43

Rump Electric Power Ltd should not make this change because it will lead to lower share price. with higher dividend, discount rate also increases from 0.03 to 0.07 which reduced the share price. keeping the same investment rate in new projects will create value for the firm and shareholders because return on equity of 20% is higher than required return of 15%.

(d) the price of Rump Electric Power Ltd’s ordinary shares will be negative which is not possible.

new dividend payout ratio = $4/$20 = 0.20 or 20%

new future growth rate of earnings = 0.20*(1-0.20) = 0.20*0.80 = 0.16 or 16%

new price of ordinary shares = $4/(0.15 - 0.16) = $4/-0.01 =-$400

price of ordinary share can never be negative. also dividend growth rate is higher than required return which is not sustainable in the long run.