Question

Investors require a 15% rate of return on Brooks Sisters' stock (r_s = 15%).

1. What would the estimated value of Brooks' stock be if the previous dividend was D₀ = $4 and if investors expect dividends to grow at a constant annual rate of (1) - 6%, (2) 0%, (3) 7%, or (4) 10%? Round your answers to the nearest cent.
   1. $
      
   2. $
      
   3. $
      
   4. $
2. Using data from Part a, what is the constant growth model's estimated value for Brooks Sisters' stock if the required rate of return is 15% and the expected growth rate is (1) 15% or (2) 21%? Are these reasonable results? Explain.
   1. -Select-Yes, it is a reasonable result.No, it is not a reasonable result, because in this case the value of stock is undefined.No, it is not a reasonable result, because in this case the value of stock is negative, which is nonsense.Item 5
      
   2. -Select-Yes, it is a reasonable result.No, it is not a reasonable result, because in this case the value of stock is undefined.No, it is not a reasonable result, because in this case the value of stock is negative, which is nonsense.Item 6
3. Is it reasonable to expect that a constant growth stock would have g_L > r_s?
   -Select-YesNoItem 7

Answer 1

Value of stock = Next expected dividend/(required rate of return – growth rate)

(1)Value = 4(1-6%)/(15%+6%) = $17.90

(2)Value = 4(1+0%)/(15%-0%) = $26.67

(3)Value = 4(1+7%)/(15%-7%) = $53.50

(4)Value = 4(1+10%)/(15%-10%) = $88

b.Value = 4(1+15%)/(15%-815%) = not defined

No, it is not a reasonable result, because in this case the value of stock is undefined

At 21%, value = -80.67

Will provide negative value when g>required rate of return

No, it is not a reasonable result, because in this case the value of stock is negative, which is nonsense

c.No, growth rate cannot be higher than the required return till perpetuity