CFA Level IEquity InvestmentsHard
A stock currently pays a dividend of $2.00 (D0). Analysts project an unusually high near-term growth rate of 20% that will decline linearly over the next 8 years to a long-term sustainable growth rate of 5%, which will then continue indefinitely. Using the H-model with a required return of 12%, what is the estimated value of the stock?
- A$64.29
- B$12.86
- C$30.00
- D$47.14
Show answer & explanationAnswer & explanation
Correct answer: D. $47.14
H = 8/2 = 4 (half-life of the linear decline). H-model: V0 = [D0/(r−gL)] × [(1+gL) + H×(gS−gL)] = [2.00/(0.12−0.05)] × [(1.05) + 4×(0.20−0.05)] = 28.571 × [1.05+0.60] = 28.571 × 1.65 = $47.14.
Why the other options are wrong
- A. This results from mistakenly using H=8 (the full transition period) instead of half.
- B. This results from swapping gS and gL in the excess growth term, producing a negative adjustment.
- C. This is the simple Gordon growth result using only the long-term growth term, ignoring the excess growth adjustment.
H-model (declining growth DDM)
Values a stock when dividend growth declines linearly from a high initial rate to a stable long-term rate over a specified transition period, using a half-life adjustment (H).
- H = one-half of the transition period in years
- Formula: V0 = D0/(r-gL) × [(1+gL)+H(gS-gL)]
- Approximates a more complex multistage model with a single closed-form expression
Memory trick: Growth glides down like a ramp — take the midpoint (H) to capture the slope.