Charge equity capital before calling earnings residual

Learning goals

• Calculate residual-income model equity value.
• Explain why 4 applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 45 minutes, excluding further revision.

Shared case and decision context

A company begins with book equity 100 and earns 14 in year one. Equity required return is 10%. Assume clean surplus, no other comprehensive income and zero residual income after year one. The analyst discounts the year-one residual at 10%.

Economic or professional mechanism

Residual income deducts a charge for equity capital from accounting earnings. Positive net income does not necessarily mean economic value creation if it fails to cover the equity charge. The valuation adds the present value of future residual income to current book value, provided accounting and clean-surplus adjustments are handled consistently.

Apply, challenge and communicate

Residual income is 4 and value 103.6364. Persistence assumptions strongly affect continuing residual income in realistic cases. Review asset impairments, dirty-surplus items and overly optimistic ROE forecasts. Do not add book equity a second time after valuing the residual-income stream.

Book value, continuing residuals and accounting reliability

Residual income is earnings less the required charge on beginning equity. With clean surplus, equity value equals current book value plus discounted future residual income; value is recognized in the initial book base as well as later abnormal earnings. A company with dependable book values but irregular distributions can be a useful candidate, while distorted assets, dirty-surplus OCI or aggressive revenue can undermine both base and forecast. DDM, FCFE and residual-income models converge when accounting, cash flows and terminal assumptions are consistent.

For constant ROE 14%, r 10%, g 4%, book 100 and stable clean-surplus conditions, justified P/B=1+(.14−.10)/(.10−.04)=1.6667, giving value 166.6667. Given P/B 1.5 instead, implied residual-income growth from this stable model isg=.10−(.14−.10)/(.5)=2%. This is a market-implied assumption, not an observed growth fact.

A multistage model forecasts earnings and beginning book equity separately, then justifies whether excess returns fade, persist or end at the horizon. If the first future residual is 4 and subsequent residuals persist at a decay factor 0.6 under a constant 10% discount rate, the perpetual residual PV is 4/(1.10−.6)=8, so value 108. Immediate competition could imply faster decay; barriers may support slower decay. Explicitly test book-value adjustments and terminal persistence rather than selecting whichever terminal creates the desired price.

Make the clean-surplus identity an actual reconciliation

Clean surplus links beginning book equity, comprehensive owner-adjusted earnings and distributions: B1=B0+E1−D1 when there are no contributions, repurchases or other direct-to-equity items. With B0=100, earnings 14 and dividends 4, B1=110. The residual-income charge for year one is r×B0, not r×B1; at r=10%, RI1=4. If year-two earnings are 15.4, the year-two charge is 11 and RI2=4.4.

For this separate two-year example assume zero residual income after year two. Value is 100+4/1.10+4.4/1.10²=107.2727. This is not the one-year value 103.6364 from the initial case: extending excess earnings changes the forecast. If an OCI loss, foreign-currency translation change or share transaction bypasses net income, reconcile book equity and adjust the earnings measure/valuation consistently rather than force the unadjusted net-income series into a clean-surplus formula. A falling book value is not automatically negative residual income.

Formula and assumptions

RI_t=NI_t−ke*B_(t−1); V0=B0+sum(RI_t/(1+ke)^t)

Case analysis with explicit assumptions

1. A company begins with book equity 100 and earns 14 in year one. Equity required return is 10%. Assume clean surplus, no other comprehensive income and zero residual income after year one. The analyst discounts the year-one residual at 10%.
2. Method: RI_t=NI_t−ke*B_(t−1); V0=B0+sum(RI_t/(1+ke)^t)
3. Case result: 103.64. Residual income is 4 and value 103.6364. Persistence assumptions strongly affect continuing residual income in realistic cases. Review asset impairments, dirty-surplus items and overly optimistic ROE forecasts. Do not add book equity a second time after valuing the residual-income stream.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• The need to add book equity infinitely often is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov
• Reference · www.cfainstitute.org