Security Value - Different Growth Rates

GBiron · November 2, 2016, 1:12am

Assume the current dividend of a security is $9.50. The dividend is expected to grow by 12% each year for two years and then 3% afterwards. The required rate of return is 15%. The security’s value is closest to:

A. $120.51

B. $95.58

C. $85.49

The answer is B, $95.58.

D₁ = $9.50 × (1+0.12) = $10.64

D₂ = $9.50 × (1+0.12)^² = $11.92

D₃= $9.50 × (1+0.12)^² × (1+0.03) = $12.27

V₂ = $12.27 / (.15 - .03) = $102.25

V = $10.64 / (1+0.15) + $11.92 / (1+0.15)^²+ $102.25 / (1+0.15)^²= $95.58

Confused as to why we take the third period dividend in perpetuity value and divide by (1+0.15)^² and not (1+0.15)^³. I assume it has to do with the fact that the final growth period were measuring is in perpetuity so we discount back for 2 periods, but I’m not entirely sure. If I am right and there is an easier way to think about this that would be great to hear as well.

cpk123 · November 2, 2016, 1:58am

draw a timeline

year 1- 12%

yr 2 - 12%

from yr 3 onwards 3%

Now if you discount that perpetuity back - you will get the total amount at year 2 - so you need to discount that back 2 years to get to year 0.

chadsandstedt · November 2, 2016, 2:11am

The sale or terminal value is actually taking place at the end of year 2 which is why it’s only being discounted by 2 years. In order to calculate the terminal value you need to project the year 3 dividend. You will never receive this year 3 dividend because you are selling the stock at the end of year 2.