Question

An analyst feels that Ruth Inc.’s earnings and dividends will grow at 16% for three years, after which growth will fall to a constant rate of 7%. If cost of equity is 11%, and Ruth’s most recently paid dividend was $3.5. What is the value of Ruth’s stock using the multistage growth model?

	A.	$108
	B.	$104
	C.	$118
	D.	$95

Answer 1

C. $ 118

As per dividend discount model, current stock price is the present value of future dividends which is calculated as follows:
Step-1:Present value of non-constant growt period
Year	Dividend	Discount factor	Present Value
a	b	c=1.11^-a	d=b*c
1	$       4.06	0.9009	$             4
2	$       4.71	0.8116	$             4
3	$       5.46	0.7312	$             4
Total			$          11
Working:
Dividend of Year:
1	=	$       3.50	*	1.16	=	$       4.06
2	=	$       4.06	*	1.16	=	$       4.71
3	=	$       4.71	*	1.16	=	$       5.46
Step-2:Present value of constant growth period
Present Value	=	D3*(1+g)/(Ke-g)*DF3
	=	$        107
Where,
D3	=	Year 3 dividend	=	$       5.46
g	=	Growth rate	=	7.00%
Ke	=	Requirde return	=	11.00%
DF3	=	Year 3 discount factor	=	0.7312
Step-3:Present Value of dividends
Present Value of Dividends	=	$          11	+	$        107
	=	$        118