Question

20. Company Q’s ROE (return on equity) is 14%. It pays out one-half of its earnings as cash dividends (payout ratio = 50%). Current book value per share is $50. Book value per share will grow as Q reinvests earnings. Assume that the ROE and payout ratio stay constant for the next 4 years. After that, competition forces ROE down to 11.5% and the payout increases to 0.8. The cost of capital is 11.5%. a. What are Q’s EPS and dividends next year? How will dividends grow in years 2, 3, 4, 5 and subsequent years? b. What is Q’s stock worth per share? How does that value depend on the payout ratio and growth rate after year 4?

Answer 1

Company Q
Given :
Dividend Payout Ratio=	50%
So Retention Ratio=1-50%=	50%
ROE =	14%
We know EPS Growth Rate =Retention Rate *ROE
So For Year 1-4 , EPS growth Rate g	=50%*14% =	7.00%
Current EPS =Book Value per share*ROE	=$50*14%=	$7
Current Dividend =EPS*50% =$7*50%=	$                   5.00
So EPS Next Year =$7
Dividend next year =$3.5*1.07=	$                   3.75
From Year 5 on wards , ROE =11.5%
Dividend Payout =80%
So Retention Rate =20%
So EPS Growth rate from Year 5	=11.5%*20%=	2.30%

Yearly EPS , Dividend , Terminal Value of Dividends at Year 5 and their PV are given belwo;
Year	EPS	Dividend Pauout ratio	Dividned	PV factor @11.5%=1/1.115^n	PV of Dividends
1	7*1.07=7.49	50%	3.75	0.8969	3.36
2	7*1.07^2=8.01	50%	4.01	0.8044	3.22
3	7*1.07^3=8.58	50%	4.29	0.7214	3.09
4	7*1.07^4=9.18	50%	4.59	0.647	2.97
5	9.18*1.023=9.39	80%	7.51	0.5803	4.36
				Total	17.00
Terminal Value of Future dividends at Year 5 with 2.3% growth rate and 11.5% cost of equity =
	Yr5 dividend*1.023/(11.5%*2.3%)
	=7.51/1.023/(11.5%-2.3%)=83.51
PV of Terminal Value =83.51*0.5803=48.46
So PV of future dividend and terminal value =$17+$48.46=$65.46
So PV of future dividend and terminal value =$17+$48.46=$65.46
So Q's Stock is worth $65.46
The value depends on the growth rate and payout ratio after yr 4 as the Dividend in Year
dividend from year 5 depends on the EPS growth rate and retention rate as given in formula.
Also the termianl value of dividends year 5 onwards depends on the growth rate
and dividend amounts recivable which is a major part of the current value of the stock.