A stock is expected to pay the following dividends: $1.1 in 1 year, $1.6 in 2...

A stock is expected to pay the following dividends: $1.1 in 1 year, $1.6 in 2 years, and $1.9 in 3 years, followed by growth in the dividend of 6% per year forever after that point. The stock's required return is 14%. The stock's current price (Price at year 0) should be $____________.

Expert Solution

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

Step-1:Present value of next 3 year's dividend

	Year	Dividend	Present value of 1	Present value of dividend
	a	b	c=1.14^-a	d=b*c
	1	$ 1.10	0.8772	$ 0.96
	2	$ 1.60	0.7695	$ 1.23
	3	$ 1.90	0.6750	$ 1.28

	Total			$ 3.48

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

	Terminal Value		=	D3*(1+g)/(Ke-g)		Where,
			=	1.90*(1+0.06)/(0.14-0.06)		D3	Year 3 dividend	$ 1.90
			=	$ 25.18		g	Growth rate	6%
						Ke	Required Return	14%

Step-3:Present value of terminal value

	Present value		=	Terminal value at the end of Year 3*Present value of 1
			=	$ 25.18	*	0.6750
			=	$ 16.99
	Working:

	Present value of 1		=	(1+i)^-n		Where,
			=	(1+0.14)^-3		i	14%
			=	0.6750		n	3


Step-4:Present value of all dividends

	Present value of all dividends			=	$ 3.48	+	$ 16.99
				=	$ 20.47

Thus,
	The stock's current price (Price at year 0) should be				$ 20.47

jeff jeffy answered 1 year ago

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