How do you handle a multi-stage DDM when one phase has negative earnings growth?
I'm studying a CFA Level II case where a company faces declining earnings for 3 years before stabilizing. My DDM gives a weird result because the dividends shrink. How do I set up a multi-stage DDM with a negative growth phase without getting nonsensical values?
A negative growth phase in a multi-stage DDM simply means dividends decline during that period. The math is the same as positive growth — you just use a negative rate. The key is ensuring dividends remain positive throughout.
Setup — Thornbury Mining (fictional):
Thornbury faces commodity headwinds and is expected to cut dividends for 3 years, then stabilize and grow modestly.
| Phase | Years | Growth Rate | Description |
|---|---|---|---|
| Decline | 1-3 | -8% per year | Commodity downturn |
| Transition | 4-5 | +3% per year | Recovery begins |
| Stable | 6+ | +2% per year | Long-run terminal |
Given: D0 = $3.00, r = 11%
Step 1 — Project Dividends:
| Year | Growth | Dividend |
|---|---|---|
| 0 | — | $3.00 |
| 1 | -8% | $2.76 |
| 2 | -8% | $2.54 |
| 3 | -8% | $2.34 |
| 4 | +3% | $2.41 |
| 5 | +3% | $2.48 |
| 6 | +2% | $2.53 (terminal) |
Step 2 — Terminal Value at End of Year 5:
TV5 = D6 / (r - gL) = $2.53 / (0.11 - 0.02) = $28.11
Step 3 — Discount All Cash Flows:
| Year | Cash Flow | PV Factor | PV |
|---|---|---|---|
| 1 | $2.76 | 0.9009 | $2.49 |
| 2 | $2.54 | 0.8116 | $2.06 |
| 3 | $2.34 | 0.7312 | $1.71 |
| 4 | $2.41 | 0.6587 | $1.59 |
| 5 | $2.48 + $28.11 | 0.5935 | $18.15 |
| Total | $26.00 |
Common Pitfalls:
- Dividends going to zero: If the decline phase is too long or the rate too severe, dividends might turn negative — which is economically meaningless. Always check that dividends stay positive.
- Forgetting to compound negative growth: D1 = D0 x (1 + g) still works with g = -0.08.
- Terminal value dominance: Notice that ~70% of value comes from the terminal value. This is typical for declining-growth scenarios.
Exam Tip: The CFA exam may present a declining industry scenario. Be systematic: project each dividend, compute the terminal value, and discount everything. Do not panic when growth rates are negative.
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