Question

Assume a major investment service has just given Big Lake Realty its highest investment rating, along with a strong buy recommendation. As a result, you decide to take a look for yourself and to place a value on the company's stock. Here's what you find. This year, Big Lake paid its stockholders an annual dividend of $4.66 a share, but because of its high rate of growth in earnings, its dividends are expected to grow at the rate of 9% a year for the next five years and then to level out at 5% a year. So far, you've learned that the stock has a beta of 124, the risk-free rate of return is 3.9%, and the expected return on the market is 10.1%. Using the CAPM to find the required rate of return, put a value on this stock Using the CAPM, the required rate of return on the investment is % (Round to two decimal places.) The value of the company's stock is $ (Round to the nearest cent)

Answer 1

The required rate of return is computed as shown below:

= risk free rate + beta x (return on market - risk free rate)

= 3.9% + 1.24 x (10.1% - 3.9%)

= 11.588% or 11.59% Approximately

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 + Dividend in year 4 / (1 + required rate of return)⁴ + Dividend in year 5 / (1 + required rate of return)⁵ + 1 / (1 + required rate of return)⁵ [ ( Dividend in year 5 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 4.66 x 1.09¹) / 1.11588¹ + ($ 4.66 x 1.09²) / 1.11588² + ($ 4.66 x 1.09³) / 1.11588³ + ($ 4.66 x 1.09⁴) / 1.11588⁴ + ($ 4.66 x 1.09⁵) / 1.11588⁵ + 1 / 1.11588⁵ x [ ($ 4.66 x 1.09⁵ x 1.05) / (0.11588 - 0.05) ]

= $ 5.0794 / 1.11588 + $ 5.536546 / 1.11588² + $ 6.03483514 / 1.11588³ + $ 6.577970303 / 1.11588⁴ + $ 7.16998763 / 1.11588⁵ + $ 114.2757591 / 1.11588⁵  

= $ 5.0794 / 1.11588 + $ 5.536546 / 1.11588² + $ 6.03483514 / 1.11588³ + $ 6.577970303 / 1.11588⁴ + $ 121.4457468 / 1.11588⁵

= $ 87.78 Approximately

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