Question

Solarpower Systems expects to earn $2020 per share this year and intends to pay out $99 in dividends to shareholders​ (so,Upper D 0 equals $ 9D0=$9​) and retain $1111 to invest in new projects with an expected return on equity of 1919​%. In the​ future, Solarpower expects to retain the same dividend payout​ ratio, expects to earn a return of 1919​% on its equity invested in new​ projects, and will not be changing the number of shares of ordinary shares outstanding.

a.  Calculate the future growth rate for​ Solarpower's earnings.

b.  If the​ investor's required rate of return for​ Solarpower's share is

14​%​, what would be the price of​ Solarpower's ordinary​ shares?

c.  What would happen to the price of​ Solarpower's ordinary shares if it raised its dividends to $13 (d0=13) this year and then continued with that same dividend payout ratio​ permanently? Should Solarpower make this​ change? ​ (Assume that the​ investor's required rate of return remains at 14​%.)

d.  What would happened to the price of​ Solarpower's ordinary shares if it lowered its dividends to $3 and then continued with that same dividend payout ratio​ permanently? Does the constant dividend growth rate model work in this​ case? Why or why​ not? ​ (Assume that the​ investor's required rate of return remains at 14​% and that all future new projects will earn 19​%.)

Answer 1

Solution a	Earning per share	$           20.00
	Dividend payment	$             9.00
	Retention ratio=	(Earning - Dividend)/Earning
	Retention ratio=	(20-9)/20
	Retention ratio=	55%
	Return available	19%
	Growth rate=	Retention * Return
	Growth rate=	55%*19%
	Growth rate=	10.45%
Solution b	Current Dividend	$             9.00
	Rate of return	14.00%
	Growth Rate	10.45%
	Share Price	=Current Dividend*(1+Growth rate)/(Rate of return-Growth Rate)
	Share Price	=9*(1+0.1045)/(0.14-0.1045)
	Share Price	$         280.01
Solution c	Earning per share	$           20.00
	Dividend payment	$           13.00
	Retention ratio=	(Earning - Dividend)/Earning
	Retention ratio=	(20-13)/20
	Retention ratio=	35%
	Return available	19%
	Growth rate=	Retention * Return
	Growth rate=	35%*19%
	Growth rate=	6.65%
	Current Dividend	$           13.00
	Rate of return	14.00%
	Growth Rate	6.65%
	Share Price	=Current Dividend*(1+Growth rate)/(Rate of return-Growth Rate)
	Share Price	=13*(1+0.0665)/(0.14-0.0665)
	Share Price	$         188.63
Solution d	Earning per share	$           20.00
	Dividend payment	$             3.00
	Retention ratio=	(Earning - Dividend)/Earning
	Retention ratio=	(20-3)/20
	Retention ratio=	85%
	Return available	19%
	Growth rate=	Retention * Return
	Growth rate=	85%*19%
	Growth rate=	16.15%
	Current Dividend	$             3.00
	Rate of return	14.00%
	Growth Rate	16.15%
	Since growth rate here exceeds the required rate of return which will make the denominator
	negative so the dividend growth model will not work.