Question

The risk-free rate is 3.00% and the market risk premium is 7.50%. A stock with a β of 1.69 just paid a dividend of $1.82. The dividend is expected to grow at 22.07% for three years and then grow at 3.32% forever. What is the value of the stock?

Answer format: Currency: Round to: 2 decimal places.

Answer 1

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

= 0.03 + 1.69 x 0.075

= 15.675% or 0.15675

So, the value will be computed as follows:

= ($ 1.82 x 1.2207) / 1.15675¹ + ($ 1.82 x 1.2207²) / 1.15675² + ($ 1.82 x 1.2207³) / 1.15675³ + 1 / 1.15675³ [ ($ 1.82 x 1.2207³ x 1.0332) / ( 0.15675 - 0.0332) ]

= $ 2.221674 / 1.15675 + $ 2.711997452 / 1.15675² + $ 3.310535289 / 1.15675³ + 1 / 1.15675³ [ ($ 27.68470304) ]

= $ 2.221674 / 1.15675 + $ 2.711997452 / 1.15675² + $ 30.99523833 / 1.15675³

= $ 23.97 Approximately

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