Question

# A company currently pays a dividend of \$3.2 per share (D0 = \$3.2). It is estimated...

A company currently pays a dividend of \$3.2 per share (D0 = \$3.2). It is estimated that the company's dividend will grow at a rate of 16% per year for the next 2 years, and then at a constant rate of 5% thereafter. The company's stock has a beta of 1.1, the risk-free rate is 7.5%, and the market risk premium is 4.5%. What is your estimate of the stock's current price?

Last dividend D0 = \$3.2

the company's dividend will grow at a rate of 16% per year for the next 2 years

=> D1 = D0*1.16 = 3.2*1.16 = \$3.712

and D2 = D1*1.16 = 3.712*1.16 = \$4.3059

and then at a constant rate g = 5%

beta of stock = 1.1

risk free rate Rf = 7.5%

Market risk premium MRP = 4.5%

using CAPM, expected return on stock = Rf + Beta*MRP

=> Ke = 7.5 + 1.1*4.5 = 12.45%

So, stocks price at year 2 using constant dividend growth model is

P2 = D2*(1+g)/(Ke - g) = 4.3059*1.05/(0.1245 - 0.05) = \$60.6875

So, current price of stock is sum of PV of future dividends and P2 discounted at Ke

=> P0 = D1/(1+Ke) + D2/(1+Ke)^2 + P2/(1+Ke)^2

=> P0 = 3.712/1.1245 + 4.3059/1.1245^2 + 60.6875/1.1245^2 = 54.70

So, current price of stock is \$54.70

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