Question

A company currently pays a dividend of $1.25 per share (D0 = $1.25). It is estimated that the company's dividend will grow at a rate of 20% per year for the next 2 years, and then at a constant rate of 6% thereafter. The company's stock has a beta of 1.1, the risk-free rate is 4%, and the market risk premium is 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

Beta of the stock = β = 1.1

Market risk premium = MRP = 5%

Risk-free rate = r_F = 4%

Cost of equity of the company can be calcuated usinf the CAPM Equation:

r = r_F + (β*MRP) = 4% + 1.1*5% = 9.5%

Dividend that was paid recently = D₀ = $1.25

Since the Divident grows by 20% per year for the next two years, we have, D₁ = 1.25*1.2 = $1.5 and D₂ = 1.5*1.2 = $1.8

Present value of D₁ and D₂ are:

PV of D₁ = D₁/(1+r) = 1.5/(1+9.5%) = 1.5/1.095 = 1.36986301369863

PV of D₂ = D₂/(1+r)² = 1.8/1.095² = 1.50121974103959

After that, the dividend grows at a constant rate of 6%. D₃ = 1.8*1.06 = $1.908

After year 2, the dividend paid becomes perpetuity. The value of this perpetuity in year 2 is given by the formula:

Value of the future dividends growing at g = 6% is given by the formula:

Value of future dividends at t = 2 is D₃/(r-g) = 1.908/(9.5% - 6%) = 54.5142857142857

Therefore, PV value of future dividends (starting from year 3) =  54.5142857142857/(1.095)² =  45.4655121571991

Stock's current price is the sum of he present values of expected future dividends.

Therefore, Stock Price = PV of D₁ + PV of D₂ + PV value of future dividends (starting from year 3) = 1.36986301369863 + 1.50121974103959 + 45.4655121571991 = 48.3365949119374

Answer -> 48.34