Question

Problem 9-12 Valuation of a constant growth stock Investors require a 18% rate of return on Levine Company's stock (that is, rs = 18%). a. What is its value if the previous dividend was Do = $1.00 and investors expect dividends to grow at a constant annual rate of (1) -4%, (2) 0%, (3) 4%, or (4) 12%? Round answers to the nearest hundredth. (1) $ (2) $ (3) $ (4) $ b. Using data from part a, what would the Gordon (constant growth) model value be if the required rate of return was 15% and the expected growth rate were (1) 15% or (2) 20%? Are these reasonable results? I. The results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate. II. The results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate. III. These results show that the formula does not make sense if the expected growth rate is equal to or less than the required rate of return. IV. The results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate. V. The results show that the formula does not make sense if the required rate of return is equal to or greater than the expected growth rate. -Select- » c. Is it reasonable to think that a constant growth stock could have g > rs? I. It is not reasonable for a firm to grow indefinitely at a rate equal to its required return. II. It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. III. It is reasonable for a firm to grow indefinitely at a rate higher than its required return. IV. It is not reasonable for a firm to grow even for a short period of time at a rate higher than its required return. V. It is not reasonable for a firm to grow indefinitely at a rate lower than its required return.

Answer 1

Because of multiple questions, only the first question is being answered here.

Given information:

r_s= 18%

D₀ = $1.00

We will use Gordon's constant growth model to calculate the stock value. Value of stock = D₁ / (r-g)

First we need to calculate D₁ using D₀ and g. Subsequently, substitute the value of D₁ in to the formula above to calculate the value of the stock.

Part 1 - Dividend growth rate g = -4%

D₁ = D₀ ( 1 + g) = 1.00 * (1 + (-0.04)) = 1.00 * 0.96 = $0.96

Now substitute the value of D₁ in the formula above:

Value of stock = 0.96 / (0.18 - (-0.04)) = 4.36

Part 2 - Dividend growth rate g = 0%

D₁ = D₀ ( 1 + g) = 1.00 * (1 + (0)) = 1.00 * 1 = $1.00

Now substitute the value of D₁ in the formula above:

Value of stock = 1.00 / (0.18 - (0)) = 5.56

Part 3 - Dividend growth rate g = 4%

D₁ = D₀ ( 1 + g) = 1.00 * (1 + (0.04)) = 1.00 * 1.04 = $1.04

Now substitute the value of D₁ in the formula above:

Value of stock = 1.04 / (0.18 - (0.04)) = 7.43

Part 4 - Dividend growth rate g = 12%

D₁ = D₀ ( 1 + g) = 1.00 * (1 + (0.12)) = 1.00 * 1.12 = $1.12

Now substitute the value of D₁ in the formula above:

Value of stock = 1.12 / (0.18 - (0.12)) = 18.67