Question

1. Suppose the company just paid dividend of $1. The dividends are expected to grow at 20% in Year 1 and 15% in Year 2. After that, the dividends will grow at a constant rate of 5% forever. If the required rate of return is 10%, compute today's price of the stock.
2. Suppose the company just paid dividend of $1. The dividends are expected to grow at 25% in Year 1 and 20% in Year 2, and 15% in Year 3. After that, the dividends will grow at a constant rate of 5% forever. If the required rate of return is 10%, compute today's price of the stock.
3. Suppose the company will not pay any dividends in Years 1 and 2. Suppose that the company pays dividend of $1 in Year 3 and after that the dividends will grow at 20% for the next two years. After that the dividends will grow at a constant rate of 5% forever. If the required rate of return is 10%, compute today's price of the stock.

Answer 1

1)	As per dividend discount model, current price of stock is the present value of future dividends.
	Step-1:Calculation of present value of future dividends of next 2 years
	Year	Dividend	Discount factor	Present value
	a	b	c=1.10^-a	d=b*c
	1	$       1.20	0.9091	$       1.09
	2	$       1.38	0.8264	$       1.14
	Total			$       2.23
	Working:
	Dividend of year :
	1	=	$       1.00	*	$       1.20	=	$       1.20
	2	=	$       1.20	*	$       1.15	=	$       1.38
	Step-2:Calculation of present value of dividends after year 2
	Present value	=	D2*(1+g)/(K-g)*DF2		Where.
		=	1.38*(1+0.05)/(0.10-0.05)*0.8264		D2	=	$       1.38
		=	$    23.95		g	=	5%
					K	=	10%
					DF2	=	0.8264
	Step-3:Calculation of price of stock
	Price of stock		=	Sum of present value of dividends
			=	$       2.23	+	$    23.95
			=	$    26.18