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:
- −$14.11.
- −$12.43.
- $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?