A stock will pay an annual dividend next year of $5 per share. Dividends will grow...

A stock will pay an annual dividend next year of $5 per share. Dividends will grow at 30% for the following 2 years and then at 5% thereafter. What is V₀ if K=0.1?

Expert Solution

V0 is $149.59

Working:

As per dividend discount method, current share price is the present value of future dividends.

Step-1:Present value of dividend of next 3 years

Year	Dividend	Discount factor	Present value
a	b	c=1.1^-a	d=b*c
1	$ 5.00	0.909091	$ 4.55
2	$ 6.50	0.826446	$ 5.37
3	$ 8.45	0.751315	$ 6.35

Total			$ 16.27

Working;

Dividend of Year :

1					=	$ 5.00
2	=	$ 5.00	*	1.3	=	$ 6.50
3	=	$ 6.50	*	1.3	=	$ 8.45

Step-2:Calculation of terminal value of dividend at the end of year 3

Terminal value	=	D3(1+g)/(Ke-g)DF3		Where,
	=	$ 133.32		D3(Dividend of year 3)	=	$ 8.45
				g (Growth rate in dividend)	=	5%
				Ke (Required return)	=	10%
				DF3 (Discount factor of year 3)	=	0.751315


Step-3:Sum of present value of future dividends

Sum of present value of future dividends	=	$ 16.27	+	$ 133.32
	=	$ 149.59

jeff jeffy answered 1 year ago

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