How do you handle a multi-stage DDM when one phase has negative earnings growth?

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:

1. 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.
2. Forgetting to compound negative growth: D1 = D0 x (1 + g) still works with g = -0.08.
3. 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.

Practice multi-stage DDM problems in our CFA Level II bank.