Question

Investors require a 7% rate of return on Levine Company's stock (i.e., r_s = 7%).

1. What is its value if the previous dividend was D₀ = $2.00 and investors expect dividends to grow at a constant annual rate of (1) -7%, (2) 0%, (3) 4%, or (4) 6%? Do not round intermediate calculations. Round your answers to the nearest cent.

   (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 was (1) 15% or (2) 20%? Are these reasonable results?
   
   1. These results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate.
   2. These results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate.
   3. 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.
   4. These 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.
   5. These 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-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.
   
   -Select-IIIIIIIVVItem 6

Answer 1

a.

P₀ = D₀ ( 1 + g) / (K_e -g)

P₀ = Price of stock at year 0

D₀ = Dividend at year 0 = $2

g = growth rate

K_e = Required rate of return = 7%

1. $2 ( 1- 0.07) /( 0.07 + 0.07) = $13.29

2. $2 /( 0.07) = $28.57

3. $2 ( 1+ 0.04) /( 0.07 - 0.04) = $69.33

4. $2 ( 1+ 0.06) /( 0.07 - 0.06) = $212

b. 1. P₀ = 2(1.15) / (0.15 - 0.15) = Undefined

2. P₀ = 2(1.20) / (0.15 - 0.20) = -$48 , which is a nonsense

IV . These 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. No,

IV It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. Such a stock, in theory, would become so large that it would eventually overtake the whole economy.