Question

Stewart Industries expects to pay a $3.00 per share dividend on its common stock at the end of the year (i.e. D₁ = $3.00). The dividend is expected to grow 25 percent a year until t = 3,

after which time the dividend is expected to grow at a constant rate of 5 percent a year (i.e. D₃ = $4.6875 and D₄ = $4.9219). The stock’s beta is 1.2, the risk-free rate of interest is 6 percent, and the market risk premium (i.e., r_m –r_rf) is 5 percent. What is the company’s current stock price?

Answer 1

The company's stock price is computed as shown below:

The value of the stock is computed as shown below:

= Dividend in year 1 / (1 + required rate of return)¹ + Dividend in year 2 / (1 + required rate of return)² + Dividend in year 3 / (1 + required rate of return)³ + 1 / ( 1 + required rate of return)³ [ ( Dividend in year 3 (1 + growth rate) / ( required rate of return - growth rate ) ]

The required rate of return is computed as follows:

= Risk free rate + Beta x Market risk premium

= 0.06 + 1.2 x 0.05

= 12% or 0.12

So, the value of the stock will be as follows:

= $ 3 / 1.12 + ( $ 3 x 1.25 ) / 1.12² + ( $ 3 x 1.25² ) / 1.12³ + 1 / 1.12³ [ ( $ 3 x 1.25² x 1.05 ) / ( 0.12 - 0.05) ]

= $ 3 / 1.12 + $ 3.75 / 1.12² + $ 4.6875 / 1.12³ + 70.3125 / 1.12³

= $ 59.05 Approximately

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