Question

Investors require an 8% rate of return on Levine Company's stock (i.e., r_s = 8%).

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) -5%, (2) 0%, (3) 4%, or (4) 7%? 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 does not make sense if the expected growth rate is equal to or less than the required rate of return.
   2. 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.
   3. 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.
   4. These results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate.
   5. These results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate.

Answer 1

a)
If growth rate is -5%:

P0 = D0 * (1+g) / (r - g)
= $2 * (1 - 5%) / (8% - (-5%))
= $1.90 / 13%
= $14.62

Current value = $14.62

If growth rate is 0%:

P0 = D0 * (1+g) / (r - g)
= $2 * (1 + 0%) / (8% - 0%)
= $2 / 8%
= $25

Current value = $25

If growth rate is 4%:

P0 = D0 * (1+g) / (r - g)
= $2 * (1 + 4%) / (8% - 4%)
= $2.08 / 4%
= $52

Current value = $52

If growth rate is 7%:

P0 = D0 * (1+g) / (r - g)
= $2 * (1 + 7%) / (8% - 7%)
= $2.14 / 1%
= $214

Current value = $214

b)
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 (II)