Can I use the residual income model when book value of equity is negative?

The residual income (RI) model can technically still work with negative book value, but it requires careful interpretation. The formula is:

V0 = B0 + Sum of [PV of future RI]

Where RI_t = NI_t - r_e x B_{t-1}

If B0 is negative, the starting anchor is below zero, but future residual income adds value on top of that negative base.

Example — Westbrook Pharmaceuticals (fictional):

Westbrook spent years on R&D with no revenue, resulting in accumulated deficits.

Item	Value
Book value (B0)	-$200M
Expected NI (Year 1)	$50M
Required return (r_e)	12%
RI_1 = NI - r_e x B0	$50M - 12$200M) = $50M +$24M = $74M

Notice something counterintuitive: when B0 is negative, the equity charge (r_e x B0) is also negative, which increases residual income. The model 'credits' the company for generating earnings despite having a negative equity base.

Projected RI Model (simplified 3-year explicit + terminal):

Year	Book Value (start)	NI	RI	PV of RI
1	-$200M	$50M	$74M	$66.1M
2	-$150M	$60M	$78M	$62.2M
3	-$90M	$70M	$80.8M	$57.5M
Terminal				$320M (est.)

V0 = -$200M +$66.1M + $62.2M +$57.5M + $320M =$305.8M

The value is positive because the present value of future residual incomes far exceeds the negative book value anchor.

Practical Concerns:

1. Model Instability: With negative BV, small changes in assumptions cause large percentage swings in value
2. Economic Meaning: Negative BV often signals high intangible value not reflected on the balance sheet (tech companies, pharma)
3. Alternative Approach: Many analysts prefer FCFE or EV/EBITDA for firms with negative book value, as these do not rely on a book value anchor
4. Clean Surplus Violation: If the firm has frequent other comprehensive income items, the clean surplus assumption may not hold, further weakening the RI approach

Exam Tip: The CFA exam may test whether you understand that RI still 'works' mechanically with negative BV, but acknowledge its limitations. Be prepared to suggest alternative valuation approaches when BV is negative.

Practice residual income problems in our CFA Level II bank.