Genestek Inc. just paid a $5.00 dividend. Due to a new product about to be released, analysts expect the company to grow at a supernormal rate of 15% for three years. After that it is expected to grow at a normal rate of 4% indefinitely. Stocks similar to Genestek are currently earning shareholders a return of 12%. The estimated selling price of the stock is:

A) $76.56
B) $86.10
C) $83.43
D) $91.14

Question

Victoria Anderson · Accepted Answer

Final Answer : B, Explanation :   The estimated selling price of the stock can be calculated using the dividend discount model (DDM) for a stock with supernormal growth for a finite period followed by perpetual growth. First, calculate the dividends for the first three years using the supernormal growth rate of 15%, then calculate the price at the end of year 3 using the perpetual growth rate of 4%, and finally discount all future cash flows back to the present value using the required rate of return of 12%.1. Calculate future dividends:- Year 1: $5.00 * (1 + 0.15) = $5.75- Year 2: $5.75 * (1 + 0.15) = $6.61- Year 3: $6.61 * (1 + 0.15) = $7.602. Calculate the selling price at the end of year 3 using the Gordon Growth Model (also known as the Perpetual Growth Model):  P 3 = D 4 r − g = 7.60 ∗ ( 1 + 0.04 ) 0.12 − 0.04 = 7.90 0.08 = $ 98.75  P_3 = \frac{D_4}{r - g} = \frac{7.60 * (1 + 0.04)}{0.12 - 0.04} = \frac{7.90}{0.08} = \$98.75  P 3 ​ = r − g D 4 ​ ​ = 0.12 − 0.04 7.60 ∗ ( 1 + 0.04 ) ​ = 0.08 7.90 ​ = $98.75  3. Discount all future cash flows (dividends and selling price) back to the present value:  P V = 5.75 ( 1 + 0.12 ) + 6.61 ( 1 + 0.12 ) 2 + 7.60 + 98.75 ( 1 + 0.12 ) 3  PV = \frac{5.75}{(1 + 0.12)} + \frac{6.61}{(1 + 0.12)^2} + \frac{7.60 + 98.75}{(1 + 0.12)^3}  P V = ( 1 + 0.12 ) 5.75 ​ + ( 1 + 0.12 ) 2 6.61 ​ + ( 1 + 0.12 ) 3 7.60 + 98.75 ​ P V = 5.75 1.12 + 6.61 1.2544 + 106.35 1.404928  PV = \frac{5.75}{1.12} + \frac{6.61}{1.2544} + \frac{106.35}{1.404928}  P V = 1.12 5.75 ​ + 1.2544 6.61 ​ + 1.404928 106.35 ​ P V = 5.13 + 5.27 + 75.70 = 86.10  PV = 5.13 + 5.27 + 75.70 = 86.10  P V = 5.13 + 5.27 + 75.70 = 86.10  Therefore, the estimated selling price of the stock is $86.10.

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