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# what the hell - growing annuity

Fri 23 Jul, 2021 12:17 pm
Guys

I am doing an exercise (I don't know for how long now) that I just can't understand, worst, it's quite simple.

opportunity cost for equity holders = 10%

Stock C is expected to pay a dividend of \$5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i.e., years 2 through 6) and zero thereafter. PV?
The guy gave us the solution:

(1) PV growing annuity: PV = 5 [ (1/ 0.10 − 0.20) − (1.20^5 /(0.10 − 0.20) × 1.105^5) ] = 27.25

(2)PV perpetuity: 5 * (1.20^5/0.10/1.105=77.25

PC = 27.25 + 77.25 = \$104.50

How on earth does he find 27.25? In my calculations ( 0.10-0.20)= - 0.1
I'm always stuck with a negative number. I don't get it
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engineer

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Fri 23 Jul, 2021 12:53 pm
@anna005,
This is pretty straightforward, you can do it by hand.

Year one: 5 dividend / 1.1 opportunity cost = 4.54 PV
Year two: 6 dividend / 1.1^2 oc = 4.96 PV
Year three: 7.2 dividend / 1.1^3 oc = 5.41 PV
Year four: 8.64 dividend / 1.1^4 oc = 5.90 PV
Year four: 10.37 dividend / 1.1^5 oc = 6.44 PV

So 27.25 total.

Not sure what formula you are using but it is ok to have negative numbers if your growth rate is higher than your opportunity cost. You end up with a negative number minus a bigger negative number so you get a positive.

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