Stock Valuation Exam Training
Exam questions on stock valuation rarely stop at one formula. A common twist is nonconstant growth: dividends grow fast for a few years, then settle into steady growth. You discount the early dividends one by one, use the Gordon model for the rest, and add it all up.
Nonconstant growth stock valuation, explained simply
For a stock with nonconstant growth, discount each fast-growth dividend separately, use the Gordon model to price the stock at the point where growth becomes steady, then discount that price back too. In the example, the stock is worth about $19.44.
What this stock valuation exam lesson covers
- How to spot which stock valuation model a question needs
- How to value a stock with nonconstant (supernormal) growth
- Where to place the Gordon growth price on the timeline
- Common exam traps: D₀ versus D₁, and discounting the wrong year
Nonconstant growth formulas, explained
- D₁ to D_N
- Dividends during the high-growth years
- P_N
- Price at year N, when constant growth begins
- r
- Required return
- D_(N+1)
- First dividend of the constant-growth phase
- g
- Long-run constant growth rate
How to solve a nonconstant growth problem step by step (worked example)
A firm just paid a $1.00 dividend. Dividends will grow 20% a year for two years, then 5% a year forever. The required return is 12%. What is the stock worth today?
- D₁ = 1.00 × 1.20 = 1.20; D₂ = 1.20 × 1.20 = 1.44
- D₃ = 1.44 × 1.05 = 1.512
- P₂ = 1.512 ÷ (0.12 − 0.05) = 21.60
- P₀ = 1.20 ÷ 1.12 + (1.44 + 21.60) ÷ 1.12² ≈ 1.0714 + 18.3673
- P₀ ≈ 19.44
Answer: The stock is worth about $19.44 (rounded to the nearest cent).
Common stock valuation exam traps
| Trap | What goes wrong | Fix |
|---|---|---|
| D₀ vs D₁ | Using the dividend just paid in the Gordon formula | Grow it one year first: D₁ = D₀ × (1 + g) |
| Wrong year for P_N | Discounting the Gordon price from year N + 1 | P_N sits at year N; discount it N years |
| Growth at or above r | The Gordon formula gives nonsense | Only use it once growth is below the required return |
| Forgetting the last dividend | Leaving out D_N in year N | Add D_N and P_N together in year N |
Harder nonconstant growth questions
What if the 20% growth lasted three years instead of two?
D₁ = 1.20, D₂ = 1.44, D₃ = 1.728, then P₃ = 1.728 × 1.05 ÷ 0.07 = 25.92. Discounting it all at 12% gives about $21.90.
How much of the $19.44 comes from the price at Year 2?
P₂ of $21.60 is worth 21.60 ÷ 1.12² ≈ $17.22 today, about 88.6% of the total. Most of a growth stock's value sits in the years after the forecast.
Common stock valuation exam questions
How do you value a stock with nonconstant growth?
Write out each dividend during the fast-growth years. At the year when steady growth starts, use the Gordon model to find the price at that point. Then discount every early dividend and that future price back to today and add them up.
Why is the Gordon growth price discounted from year N and not year N + 1?
The Gordon formula P_N = D_(N+1) ÷ (r − g) gives a price one year before the dividend it uses. So a price built from D₃ is a Year 2 value and you discount it for two years. This is the single most common error on these problems.
How do I find the required return on a stock for an exam?
If the question gives price, next dividend and growth, use r = D₁ ÷ P₀ + g. If it gives a beta, a risk-free rate and a market return, use CAPM instead. Read the question for which pieces of data you actually have.
What is the best way to practice stock valuation problems?
Draw a timeline for every question, mark each dividend in the year it is paid, and label where any terminal price sits. Then solve problems of each type: zero growth, constant growth, nonconstant growth and solving for r, until the setup becomes automatic.