Question

Lincoln Motors does not pay dividends currently but plans to pay its first dividend of $1.00 three years from today (D3). The dividend will grow at 10% in years 4 and 5 and after year 5 will grow at 3% forever. Find the price per share of Lincoln Motors if the required rate of return is 8%.

Answer 1

Solution:
	Price per share of stock Lincoln Motors today is $19.39
Working Notes:
	Value per share we get by getting present value of all the dividend during the life share , which we get using dividend discount model. In our case Dividend growth is 10% in 4th & 5 year there after there will be constant growth dividend at 3% per year. So after 5th year we get present value of dividends after 5th year as price of the stock at end of 5th year which is also known as terminal value , the all the dividend till 5th year and the price at end of 5th year will be discounted at required rate of return to get its price per share today.
Now
	Using Dividend discount method.
	P0= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3+ D4/(1+r)^4 + D5/(1+r)^5 + P5/(1+r)^5
	Here
	g=10% growth rate in 4th year & 5th year
	P5 = Price at end of 5th year =?? Which we get using Gordon formula
	G= 3% = Constant growth rate after 5th year
	Required rate of return of the stock r =8%
	D1 = $0
	D2 = $0
First	D3 = $1.00
	D4 = D3 x (1+g) = $1 x (1+ 0.10) = $1.10
	D5 = D4 x (1+g) = $1.10 x (1+.10) = $1.21
	D6 = D5 x (1+G) = $1.21 x (1+.03) = $1.2463
	Calculating Price at end off 5th year P5
	Using Gordon growth model : P5 = D6 / (r - G )
	P5 = D6 / (r - G )
	= $1.2463/( 0.08 - 0.03)
	= $24.926
At Last	We calculate price per share of stock Lincoln Motors today
	P0= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3+ D4/(1+r)^4 + D5/(1+r)^5 + P5/(1+r)^5
	P0= 0/(1+0.08)^1 + 0/(1+0.08)^2 + 1/(1+0.08)^3+ 1.1/(1+0.08)^4 + 1.21/(1+0.08)^5 + 24.926/(1+0.08)^5
	P0= 19.39008752
	P0= $19.39
Please feel free to ask if anything about above solution in comment section of the question.