Question

A company currently pays a dividend of $1.6 per share (D₀ = $1.6). It is estimated that the company's dividend will grow at a rate of 24% per year for the next 2 years, and then at a constant rate of 8% thereafter. The company's stock has a beta of 1.7, the risk-free rate is 7%, and the market risk premium is 2.5%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Solution:
	The stock's current price is   $69.83
Working Notes:
Notes:	Stock's current price can be computed using DDM (Dividend Discount Model), for which we would need cost of equity which we will compute using CAPM.
	The stock's current price (ass per DDM)
	= D1/(1+r) + D2/(1+r)^2 + P2/(1+r)^2
	We calculate required rate of return using CAPM
	risk free rate rf = 7%
	Market risk premium (rm-rf) = 2.5%
	Beta B = 1.7
	r= required rate of return= cost of equity=??
	r = rf + (rm-rf) x B
	r = 7% + 2.5% x 1.7
	r = 7% + 4.25%
	r = 11.25%
Now	We compute dividends
	D1 = dividend in year 1 = D0 x (1 + g) = $1.60 x (1 + 24%) =1.984
	D2 = dividend in year 2 = D1 x (1 + g) = $1.984 x (1 + 24%) =2.46016
	D3 = dividend in year 3 = D2 x (1 + g) = $2.46016 x (1 + 8%) =2.6569728
	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=8%
	D3=2.6569728
	r= required rate of return= 11.25%
	P2 = D3 / (r - constant growth rate),
	P2 = 2.6569728/ (11.25% - 8%),
	P2 = 81.75300923
Now	The stock's current price
	= D1/(1+r) + D2/(1+r)^2 + P2/(1+r)^2
	=1.984/(1+11.25%)^1 + 2.46016/(1+11.25%)^2 +81.75300923/(1+11.25%)^2
	=69.82582541
	=$69.83
Please feel free to ask if anything about above solution in comment section of the question.