CFA Level IEquity InvestmentsHard
A stock just paid a dividend of $1.00 (D0). Dividends are expected to grow at 20% annually for the next three years, after which growth is expected to stabilize at a constant 5% per year indefinitely. The required rate of return is 10%. Using a two-stage dividend discount model, what is the estimated intrinsic value of the stock today?
- A$30.84
- B$25.97
- C$33.02
- D$27.26
Show answer & explanationAnswer & explanation
Correct answer: A. $30.84
D1=1.20, D2=1.44, D3=1.728. Terminal value at t=3: D4/(r-g)=1.728×1.05/0.05=36.288. Discount each cash flow: PV(D1)=1.0909, PV(D2)=1.1901, PV(D3)=1.2984, PV(TV)=36.288/1.331=27.264. Sum = 1.0909+1.1901+1.2984+27.264 = $30.84.
Why the other options are wrong
- B. This results from using D3 instead of D4 in the terminal value calculation.
- C. This results from failing to discount the terminal value back to present.
- D. This is only the discounted terminal value, omitting the explicit dividend PVs.
Two-stage dividend discount model
Values a stock by discounting an initial high-growth phase of dividends explicitly, then adding a discounted terminal value based on stable long-term growth.
- Terminal value uses next-period dividend: D(n+1)/(r-g)
- Terminal value must be discounted back to present at r
- Explicit-period dividends grow at the high initial rate
Memory trick: Sprint fast for three years, then settle into a steady long-term jog.