Question

Constant Growth Stock Valuation Investors require a 15% rate of return on Brooks Sisters' stock  .

1. What will be Brooks Sisters' stock value if the most recent dividend was $2 and if investors expect dividends to grow at a constant compound annual rate of (1) −5%, (2) 0%, (3) 5%, and (4) 10%?

2. Using data from part a, what is the Gordon (constant growth) model value for Brooks Sisters' stock if the required rate of return is 15% and the expected growth rate is (1) 15% or (2) 20%? Are these reasonable results? Explain.

3. Is it reasonable to expect that a constant growth stock would have g

   Constant Growth Stock Valuation Investors require a 15% rate of return on Brooks Sisters' stock  .

4. What will be Brooks Sisters' stock value if the most recent dividend was $2 and if investors expect dividends to grow at a constant compound annual rate of (1) −5%, (2) 0%, (3) 5%, and (4) 10%?

5. Using data from part a, what is the Gordon (constant growth) model value for Brooks Sisters' stock if the required rate of return is 15% and the expected growth rate is (1) 15% or (2) 20%? Are these reasonable results? Explain.

6. Is it reasonable to expect that a constant growth stock would have g>Rs?

7. ?

Answer 1

(a) Recent Dividend = Current Dividend = D0 = $ 2, Required Return on Stock = r = 15 %,

For a given growth rate g%, the constant growth model values stocks as per the equation below:

Current Stock Price = P0 = [D0 x (1+g)] /[(r-g)] where g is the growth rate, D0 is the current dividend and r is the required return on the stock

Hence, when g = -5 %

P0 = [2 x 0.95]/[0.15-(-0.05)] = $ 9.5

g = 0 %

P0 = 2/0.15 = $ 13.33

g = 5%

P0 = [(2 x 1.05)/(0.15-0.05)] = $ 21

g = 10%

P0 = [(2 x 1.1) / (0.15-0.1)] = $ 44

(b) When g =15%/20%, the r - g = 0 which seemingly would boost P0 to infinity. This is so because the constant growth formula is the result of the constant growth geometric series converging to a finite value. The constant growth geometric series converges to a finite value only when rs > g and not when rs < = g. Hence, the growth rates cannot be 15% or 20% indefinitely. However, the growth rate can be 15%/20% in the short run during which they are to be simply discounted by rs individually and cannot be clubbed together into a single formula (as done by the constant growth model).

(c) As already explained in part (b), a constant growth stock will never have g > rs. However, the same might be true in shorter time periods.