# Security Value - Different Growth Rates

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

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.

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.

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.