Question

A company has just paid a dividend of $ 2 per share, D0=$ 2 . It is estimated that the company's dividend will grow at a rate of 18 % percent per year for the next 2 years, then the dividend will grow at a constant rate of 7 % thereafter. The company's stock has a beta equal to 1.4, the risk-free rate is 4.5 percent, and the market risk premium is 4 percent. What is your estimate of the stock's current price? Round your answer to two decimal places.

Answer 1

Solution:
	The stock's current price is   $83.74
Working Notes:
	The stock's current price
	= D1/(1+r) + D2/(1+r)^2 + P2/(1+r)^2
	We calculate required rate of return using CAPM
	risk free rate rf = 4.5%
	Market risk premium (rm-rf) = 4%
	Beta B = 1.4
	r= required rate of return= ??
	r = rf + (rm-rf) x B
	r = 4.5% + 4% x 1.4
	r = 4.5% + 5.6%
	r = 10.1%
	D1 = dividend in year 1 = D0 x (1 + g) = $2 x (1 + 0.18) =2.36
	D2 = dividend in year 2 = D1 x (1 + g) = $2.36 x (1 + 0.18) =2.7848
	D3 = dividend in year 3 = D2 x (1 + g) = $2.7848x (1 + 0.07) =2.979736
	calculation of terminal value at the end of 2nd year the price at end of year 2 is P2
	Using Gordon constant growth model :
	P2 = D3 / (r - constant growth rate),
	P2= ??
	g= constant growth rate=7%
	D3=2.979736
	r= required rate of return= 10.1%
	P2 = D3 / (r - constant growth rate),
	P2 = 2.979736 / (10.1% - 7%),
	P2 = 96.12051613
Now	The stock's current price
	= D1/(1+r) + D2/(1+r)^2 + P2/(1+r)^2
	=2.36/(1+10.1%) + 2.7848/(1+10.1%)^2 + 96.12051613/(1+10.1%)^2
	=83.73502095
	=$83.74
Please feel free to ask if anything about above solution in comment section of the question.