# doubt in equity

this is from the cfa website practice question

The final and perpetual growth rate: 5% Estimated earnings per share (EPS) in 2019 \$5.04 Dividend payout ratio 40%

Still concerned with the estimate of growth after 2019, Stack asks Armishaw what the present value of growth opportunities (PVGO) will be in 2019 when the perpetual growth period begins.

Q. The most appropriate answer to Stack’s question about the PVGO is:

1. −\$14.11.
2. −\$12.43.
3. \$19.32.
Solution

A is correct.

Value of no-growth level perpetuity in 2019 V0 = (5.04 × 1.05)/0.15 = \$35.28 all EPS paid out as dividends Value as a perpetual growing stream (i.e., using the constant growth Gordon model) V0 = D1/r−g = 5.04×(1+0.05)×0.400/.15−0.05 = \$21.17

D1 = EPS1 × Payout ratio

Perpetual growth at 5% PVGO = \$21.17 − \$35.28 = −\$14.11 PVGrowth − PVNoGrowth

my doubt is why do we have to conisider ( 1 + g ) for the no growth case, isin’t it just E/r?

E1/r go and read the curriculum again

I agree that you should use E0 to compute the no-growth value of the stock (and have written CFA Institute about this), but they say to use E1 (= E0 × (1 + g)).

Sorry.

Could the reason behind that be that E1 is assumed to have no growth, since E0 has already grown to E1 ??

thanks for the info!!!

You’re welcome.