Question

Problem 9-12
Valuation of a constant growth stock

Investors require a 18% rate of return on Levine Company's stock (i.e., r_s = 18%).

1. What is its value if the previous dividend was D₀ = $3.00 and investors expect dividends to grow at a constant annual rate of (1) -5%, (2) 0%, (3) 3%, or (4) 11%? Round your answers to two decimal places.
   (1) $   
   (2) $   
   (3) $   
   (4) $   
   
2. 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?  
   
   1. The results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate.
   2. 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.
   3. 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.
   4. 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.
   5. The results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate.
   
   -Select-IIIIIIIVVItem 5
   
3. Is it reasonable to think that a constant growth stock could have g > r_s?
   
   1. It is not reasonable for a firm to grow even for a short period of time at a rate higher than its required return.
   2. It is not reasonable for a firm to grow indefinitely at a rate lower than its required return.
   3. It is not reasonable for a firm to grow indefinitely at a rate equal to its required return.
   4. It is not reasonable for a firm to grow indefinitely at a rate higher than its required return.
   5. It is reasonable for a firm to grow indefinitely at a rate higher than its required return.

Answer 1

(a) Given, Rate of return required = r = 18%

D0 = 3

Growth rate = g

Hence, D1 = D0(1+g)

1. when g = -5%,

Price of Stock P0 = D1/(r - g) = 3(1-0.05)/(0.18 + 0.05) = 12.39

2. when g = 0%,

Price of Stock P0 = D1/(r - g) = 3(1+0.0)/(0.18 - 0.0) = 16.67

3. when g = 3%,

Price of Stock P0 = D1/(r - g) = 3(1+0.03)/(0.18 - 0.03) = 20.6

4. when g = 11%,

Price of Stock P0 = D1/(r - g) = 3(1+0.11)/(0.18 - 0.11) = 47.57

(b)

when g = 15%,

Price of Stock P0 = D1/(r - g) = 3(1+0.15)/(0.18 - 0.15) = 117

when g = 20%,

Price of Stock P0 = D1/(r - g) = 3(1+0.20)/(0.18 - 0.20) = -180

The price of the stock when g>r is -ve

Hence, (III)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.

(c) It is not possible for the company to grow at rate greater than the rate of return indefinetely

(IV) It is not reasonable for a firm to grow indefinitely at a rate higher than its required return.