Question

A company has just paid a dividend of $ 3 per share, D₀=$ 3 . 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 5 % 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

Step-1, Calculation of the Required Rate of Return (Ke)

As per CAPM Approach, the Required Rate of Return is calculated as follows

Required Rate of Return = Risk-free Rate + (Beta x Market Risk Premium)

= 4.50% + (4% x 1.4)

= 4.50% + 5.60%

= 10.10%

Step-2, Dividend for the next 2 years

Dividend per share Year 1 (D1) = $3.54 per share ($3.00 x 118%)

Dividend per share Year 2 (D2) = $4.18 per share ($3.54 x 118%)

Step-3, Share Price in Year 2

Share Price in Year 2 (P2) = D2(1 + g) / (Ke – g)

= $4.18(1 + 0.05) / (0.1010 – 0.05)

= $4.39 / 0.0510

= $86.00 per share

Step-4, The Current Stock Price

The Current Stock Price is the Present Value of the Future Dividend plus the present value of the share price in year 5

= D1/(1 + r)¹ + D2/(1 + r)² + P2/(1 + r)²

= [$3.54 / (1 + 0.1010)¹] + [$4.18 / (1 + 0.1010)²] + [$86.00 / (1 + 0.1010)²]

= $3.21 + $3.45 + $70.95

= $77.61 per share

“Hence, the estimate of the stock's current price would be $77.61”