Question

Microsoft has just paid a dividend of $1 per share (this dividend is already paid sometimes called Dividend 0). It is estimated that the companys dividend will grow at a rate of 35% in year 1 and 20% in year 2. The dividend is then expected to grow at a constant rate of 1% thereafter. The companys opportunity cost of capital is 11% what is an estimate Microsofts stock using the nonconstant growth technique?

Answer 1

	Required rate=	11.00%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	1	35.00%	1.35		1.35	1.11	1.2162
2	1.35	20.00%	1.62	16.362	17.982	1.2321	14.59459
	Long term growth rate (given)=	1.00%			Value of Stock =	Sum of discounted value =	15.81

Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 2 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor

Value of stock = PV of future cash flows

=PV of non constant growth dividends + PV of terminal value

=Current dividend*(1+growth rate year 1)/(1+discount rate)+Current dividend*(1+growth rate year 1)*(1+growth rate year 2)/(1+discount rate)^2+Current dividend*(1+growth rate year 1)*(1+growth rate year 2)^2/(1+discount rate)^2*(1+ constant growth rate)/(discount rate-constant growth rate)

=1*(1+0.35)/(1+0.11)+1*(1+0.35)*(1+0.2)/(1+0.11)^2+1*(1+0.35)*(1+0.2)/(1+0.11)^2*(1+0.01)/(0.11-0.01)

=15.81