Question

In year 2008, Janet’s firm is using a two-stage dividend discount model (DDM) to find the intrinsic value of SmileWhite Co.

The risk-free interest rate is 4.5% and expected return of market is 14.5% and beta of the SmileWhite Co. is 1.15.

In 2008, dividend per share is $1.72 for the company. Dividends are expected to grow at a rate of 12% per year for the next three years until 2011. After 2011 dividend growth rate will be at constant rate 9% per year indefinitely.  

B. What was the intrinsic value of SmileWhite Co. stock when the analyst was evaluating the stock (that is in year 2008)?       (15 points)

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) ]

required rate of return is computed as follows:

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

= 4.5% + 1.15 x (0.145 - 0.045)

= 16% or 0.16

So, the value will be as follows:

= ($ 1.72 x 1.12) / 1.16 + ($ 1.72 x 1.12²) / 1.16² + ($ 1.72 x 1.12³) / 1.16³ + 1 / 1.16³ x [ ($ 1.72 x 1.12³ x 1.09) / (0.16 - 0.09) ]

= $ 1.9264 / 1.16 + $ 2.157568 / 1.16² + $ 2.41647616 / 1.16³ + 1 / 1.16³ x [ ($ 37.62798592) ]

= $ 1.9264 / 1.16 + $ 2.157568 / 1.16² + $ 40.04446208 / 1.16³

= $ 28.92 Approximately

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