Question

Constant Growth Stock Valuation

Investors require a 14% rate of return on Brooks Sisters' stock (r_s = 14%).

1. What would the estimated value of Brooks' stock be if the previous dividend was D₀ = $1.75 and if investors expect dividends to grow at a constant annual rate of (1) - 6%, (2) 0%, (3) 5%, or (4) 10%? Do not round intermediate calculations. 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 14% and the expected growth rate is (1) 14% or (2) 15%? Are these reasonable results? Round your answers to the nearest cent. Use a minus sign to enter negative values, if any. If your answer is zero, enter "0".
   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 6
      
   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 8
3. Is it reasonable to expect that a constant growth stock would have g_L > r_s?
   -Select-YesNoItem 9

Answer 1

Answer : Calculation of Estimated Value of Brook's Stock :

Value of Stock = [D0 * (1 + growth rate)] / [Required Return - Growth rate]

When g = -6%

Value of Stock = [1.75 * (1 + (-0.06))] / [0.14 - (-0.06)]

= 1.645 / 0.20

= 8.225 or 8.23

When g = 0%

Value of Stock = [1.75 * (1 + 0] / [0.14 - 0]

= 1.75 / 0.14

= 12.5

When g = 5%

Value of Stock = [1.75 * (1 + 0.05)] / [0.14 - 0.05]

= 1.8375 / 0.09

= 20.42

When g = 10%

Value of Stock = [1.75 * (1 + (0.10)] / [0.14 - 0.10]

= 1.925 / 0.04

= 48.125 or 48.13

(b.) If Growth rate is 14% then Stock Price will be undefined.Therefore No, it is not a reasonable result, because in this case the value of stock is undefined.

If Growth rate is 15% the stock price will become negative .Therefore .No, it is not a reasonable result, because in this case the value of stock is negative, which is nonsense.

(c.) No ,it is not reasonable to expect that a constant growth stock would have g_L > r_s