Question

VALUATION OF A CONSTANT GROWTH STOCK

Investors require a 16% rate of return on Levine Company's stock (i.e., rs = 16%).

What is its value if the previous dividend was D0 = $3.25 and investors expect dividends to grow at a constant annual rate of (1) -5%, (2) 0%, (3) 4%, or (4) 11%? Do not round intermediate calculations. Round your answers to two decimal places.

(1) $

(2) $

(3) $

(4) $

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?

These results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate.

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.

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.

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.

These results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate.

Is it reasonable to think that a constant growth stock could have g > rs?

It is not reasonable for a firm to grow even for a short period of time at a rate higher than its required return.

It is not reasonable for a firm to grow indefinitely at a rate lower than its required return.

It is not reasonable for a firm to grow indefinitely at a rate equal to its required return.

It is not reasonable for a firm to grow indefinitely at a rate higher than its required return.

It is reasonable for a firm to grow indefinitely at a rate higher than its required return.

Answer 1

Ans (1) Rs = 16% , Do = $3.25

VAlue of share Po =

1. When g = -5% = Po = Do(1+g)/ (ke-g) = 3.25( 1-0.05)/ (0.16+0.05) = 14.70$

2. When g = 0% = Po = Do(1+g)/ (ke-g) = 3.25( 1-0.00)/ (0.16-0.00) = 20.3125$

3. When g = 4% = Po = Do(1+g)/ (ke-g) = 3.25( 1-0.04)/ (0.16-0.04) = 28.17$

4.  When g = 4% = Po = Do(1+g)/ (ke-g) = 3.25( 1-0.04)/ (0.16-0.04) = 72.15$

5. When g = 11% = Po = Do(1+g)/ (ke-g) = 3.25( 1-0.11)/ (0.16-0.11) = 72.15$

Answer (2) ke = 15%

(i) g = 15% Therefore D1 = Do(1+g) = 3.25(1+0.15) = 3.7375$

with Gordan constant growth model value is

Po = D1/(ke-g) = 3.7375 / ( 15%-15%) = infinity

(ii) g = 20% Therefore D1 = Do(1+g) = 3.25(1+0.20) = 3.90$

with Gordan constant growth model value is

Po = D1/(ke-g) = 3.90 / ( 15%-20%) = - 78 which is also unreasonable

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.

Yes it is reasonable to think that a constant growth stock could have g > Rs