Question

Investors require a 15% rate of return on Levine company’s stock (that is, ????= 15%).

(1) What is its value if the previous dividend (??0 ) was $2, and investors expect

dividends to grow at a constant rate of (ⅰ) -5%, (ⅱ) 0%, or (ⅲ) 5%?

(2) Using data from part (1) (??0=$2), what would the Gordon (constant growth) model

value be if the required rate of return was 15% and the expected growth rate was

20%? Is this a reasonable result? Explain.

Answer 1

1)

we can calculate the value of stock from the following formula:-

Po=div0*(1+g)/Re-g

Div0= divident in year 0

Re = required rate of return

G= constant growth rate

value if the previous dividend (??0 ) was $2, and investors expect dividends to grow at a constant rate of -5%

Po=div0*(1+g)/Re-g

= 2*(1-0.05)/0.15+0.05

= $9.5

value if the previous dividend (??0 ) was $2, and investors expect dividends to grow at a constant rate of -0%

= 2*(1+0)/0.15-0

= $13.33

value if the previous dividend (??0 ) was $2, and investors expect dividends to grow at a constant rate of 5%

= 2*(1+0.05)/0.15-0.05

= $21

2) value as per  Gordon (constant growth) model can be calculated using the following formula :-

P0=DIV1/Re-g

Div1= divident in year 1

Re = required rate of return

g= constant growth rate

= 2*(1+0.2)/0.15-0.2

= -$40.80

Here the value is -ve.But the results may not be reasonable when there is an assumption that internal rate of return (rs) and cost of capital (k) are constant, Because these are the 2 values which underlie the Gordon (constant growth) model.