Lost Profits and Business Interruption: Method

Lost Profits, Business Interruption and the Alternatives

What the tool computes

Commercial damages for a breach of contract, a business tort or an infringement are usually measured as the profits the plaintiff would have earned but for the wrongful act, reduced to a single sum at the date of judgment. The same arithmetic, with the policy's own definitions, measures the business income an insurer owes after a covered suspension of operations. The tool takes a monthly revenue and cost history, projects the revenue the business would have earned through the loss period, sets the revenue actually earned against it, removes the costs avoided on the lost sales, adds the costs of mitigation and deducts the profits earned in mitigation, and brings every month to the valuation date with prejudgment interest or a discount factor. A second section applies the insurance forms to the period of restoration; a third capitalises the lost stream as the value of a lost asset and computes a reasonable royalty. Money is a plain number in one currency; the rates are entered in percent per year; dates and periods are text.

Standard of proof

Lost profits must be proved with reasonable certainty as to their existence; once the fact of damage is established the amount need only be shown as a matter of just and reasonable inference, "although the result be only approximate" (Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 563 (1931); Bigelow v. RKO Radio Pictures, 327 U.S. 251 (1946)). The wrongdoer whose act made the measurement uncertain cannot complain of the uncertainty. The projection must still rest on adequate data: a trend fitted to a history the event interrupted, a comparable business, or a budget the business was meeting.

But-for revenue

Two methods of proof are generally recognised (Lehrman v. Gulf Oil Corp., 500 F.2d 659, 667 (5th Cir. 1974)):

• Before-and-after. The plaintiff's own record before the event is projected through the loss period. The tool fits a trend to the pasted history by ordinary least squares: a growth trend, ln R = a + b t, whose extrapolation grows by a constant g_mo = e^b − 1 a month ((1 + g_mo)¹² − 1 a year), or a linear trend, R = a + b t. Seasonal businesses are handled by ratio-to-trend indices: for each calendar month the mean of actual / trend over the history, normalised so the twelve average 1; the but-for revenue of a loss month is its trend value times its index. R² of the raw fit is low for a seasonal history because the seasonal swing is not in the trend; the indices carry it. A history of at least two full years is needed for stable indices (the output prints the number of observations behind each).
• Yardstick. Where the business has no usable record (a startup, or a market in which the whole industry moved), a closely comparable business or an industry index is the standard. The benchmark series is scaled by k = ΣR / ΣB over the history months the two share, and the loss months' but-for revenue is k times the benchmark. The benchmark must cover every loss month; its own seasonality carries through.

An entered projection (a budget, a contract schedule, another expert's figures) is the third option. The loss period runs from the start date to the end date inclusive; a month partly inside it is prorated by days, both its but-for and its actual revenue. The history must end before the loss start month.

Avoided costs

Where the injury is lost sales volume, the plaintiff avoided the cost of producing those sales; damages are the lost revenue less the avoided cost (Reference Guide on Estimation of Economic Damages, Section VI.B). The tool offers an entered variable-cost ratio or a regression of total cost on revenue over the history, cost = a + b × revenue: the slope b is the cost avoided per unit of lost revenue and the intercept a the fixed cost per month that continues whatever the sales. The regression is the Guide's "statistical method to determine how costs vary with sales"; it treats the short-run cost structure as linear, so a history that spans a capacity change or a step in fixed costs should be split or the ratio entered. The output prints a, b and R².

Lost profits of the period are the lost contribution margin plus the reasonable extra costs incurred to mitigate (temporary premises, expediting, overtime) less the mitigation credits (profits earned with the released capacity or a substitute contract). The defendant bears the burden of proving a failure to mitigate (Reference Guide, Section VII.C). Both amounts are spread over the loss months in proportion to their length so that they carry the right interest.

Interest and discounting: ex post and ex ante

Each month's lost profit flows at the mid-point of its part of the month. Under the usual ex post rule the losses are valued at the date of judgment: a month before the valuation date is a past loss and earns prejudgment interest from its mid-point to the valuation date, simple (I = L i t) or compounded annually (I = L[(1 + i)^t − 1]) as the forum provides; a month after it is a future loss discounted to the valuation date, DF = (1 + r)^−t. The Reference Guide's Table 3 tabulates both forms of interest at 7 % over ten years (compound 1,579, simple 1,485 on 100 a year), and its Tables 1 and 2 show the discounting of future losses and the special case in which growth and discounting offset. The Federal Circuit holds that lost profits are reduced to present value as of the date of judgment, not the date of breach, and that a risky stream takes a risk-adjusted discount rate (Energy Capital Corp. v. United States, 302 F.3d 1314 (2002), 10.5 % rather than the Treasury yield). Interest after judgment follows 28 U.S.C. 1961 (the 1-year constant-maturity Treasury yield, compounded annually); on a federal contract claim interest runs from the contracting officer's receipt of the claim at the Treasury rate fixed for each six-month period, 41 U.S.C. 7109, which the Delay and Claims Analysis tool tabulates.

The ex ante valuation treats the stream as it looked when the event occurred: every month is discounted to the loss start date at the discount rate and the sum is carried forward to the valuation date at the prejudgment rate. The two agree when the discount rate equals a compound prejudgment rate; they differ when the forum's interest rate is below the risk-adjusted discount rate (the ex ante value is then lower, because the risk discount is applied to the past months too), and the ex ante form is the one that excludes information learnt after the event (Reference Guide, Section VIII.F, on subsequent unexpected events). The tool prints both and names the ex post value as the usual measure.

Sensitivity to growth

The projection is the most contested part of a lost-profits study. The chart recomputes the ex post value for a family of projections that start from the trend level of the last history month and grow at g a year with the same seasonal indices, for g from ten points below to ten points above the fitted rate; the value of the method actually used is drawn as a line. The spread shows how much of the figure rests on the growth assumption.

Business interruption (insurance)

Business income coverage pays the loss of business income during the period of restoration, the time needed to repair or replace the damaged property, after a suspension caused by a covered direct physical loss (CRS Insight IN11295). Two historical forms define the loss; the tool computes both from the same inputs and they agree by identity:

• Gross earnings. Gross earnings are sales less the cost of merchandise sold, materials and supplies consumed and services purchased from outsiders; the loss is the reduction in gross earnings less the charges and expenses that do not necessarily continue: L = ΔS (1 − c) − E_disc − P_excl.
• Net income plus continuing expenses (the form of the ISO Business Income coverage form CP 00 30, named only). Business income is the net income (net profit or loss before income taxes) that would have been earned plus the continuing normal operating expenses incurred, including payroll; the loss is that sum less the gross profit actually earned in the period, which is the but-for net income less the actual net income: L = NI_bf + E_cont + P_cov − GP_act.

The ordinary-payroll limitation covers the payroll of employees other than officers, executives, department managers and contract employees for a fixed number of days (90 or 180) from the start of the suspension; the tool covers the fraction N / days of the period's ordinary payroll and treats the rest as a cost the insured is expected to shed. Extra expense (temporary location, rented equipment, expediting) is added in full under a combined business income and extra expense form. Coinsurance: the amount of insurance required is the coinsurance percentage times the business income of the 12 months following the policy inception (net income plus all operating expenses, which equals sales less cost of sales); when the limit carried is below it the payment is reduced in the ratio carried / required, the same penalty formula the National Flood Insurance Program applies to condominium buildings insured below 80 % of replacement cost (FEMA IS-1104, Section VII). The deductible is taken off and the payment is limited to the amount of insurance; the uninsured part is reported. Monthly limits of indemnity, the extended period of indemnity, civil-authority and contingent coverage are not modelled; the policy's own wording governs every definition.

Diminution in value and reasonable royalty

Where the wrongful act destroyed an income-producing asset or the business itself, the measure may be the market value of what was lost rather than a stream of lost profits (Schonfeld v. Hilliard, 218 F.3d 164 (2d Cir. 2000): the fair market value of the lost asset, what a willing buyer would pay a willing seller, which may rest on the income the asset would produce). The tool capitalises the annual lost-profit stream, V = LP / (r − g) for a perpetuity growing at g (capitalisation factor 1 / (r − g), the Reference Guide's Section VI.I: a factor from comparable businesses times the annual loss) or V = LP [1 − ((1 + g)/(1 + r))ⁿ] / (r − g) for a stream of n years. The annual stream is entered or taken from the lost-profits section scaled to a year.

A patent owner recovers lost profits on the infringer's sales only on proof of demand for the patented product, the absence of acceptable non-infringing substitutes, the capacity to exploit the demand and the amount of the profit (Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152, 1156 (6th Cir. 1978)); otherwise the measure is a reasonable royalty, the amount a willing licensor and licensee would have agreed on at the time the infringement began, weighed with the fifteen factors of Georgia-Pacific Corp. v. United States Plywood Corp., 318 F. Supp. 1116, 1120 (S.D.N.Y. 1970), which the output lists. The tool's arithmetic is the royalty base (the infringer's sales of the accused product) times the rate; the factors set the rate.

Reading the results

The revenue table gives, for every loss month, the days inside the period, the trend and seasonal index, the but-for revenue of the full month and of the part in the period, the actual revenue and the lost revenue. The avoided-cost lines give the regression (or the entered ratio), the costs avoided and the lost margin; the interest table gives each month's lost profit, its mid-point, the years to the valuation date, the interest or discount factor and the value at the valuation date, with the ex post total, the ex ante total and the annualised stream below it. The business-interruption section prints both forms, the payroll limitation, the coinsurance test, the deductible and the loss payable with a bar chart from the lost gross profit to the payment; the last section prints the capitalised value and the royalty.

Limits

Not modelled: multiple regressions with explanatory variables beyond time (prices, advertising, the economy), ARIMA or exponential-smoothing projections (the Forecasting tool offers them), a recovery ramp after the loss period (enter the ramp months in the loss period with their actual revenue), taxes on the award, lost profits from increased costs rather than lost sales, startup businesses without a history (yardstick or an entered projection only), the monthly limit of indemnity and extended period of indemnity of the insurance forms, and the apportionment of a royalty base among patented and unpatented features. The default history, actual revenue, benchmark index and insurance figures are illustrative and are stated so on the page.

Default case

An illustrative retail business with a 36-month history (January 2021 to December 2023, revenue 3.88 million, strong December peaks) is interrupted from 1 January 2024 to 30 June 2024: closed for three months, then 41,000, 52,000 and 58,000 of revenue in April to June. The growth trend gives 9.60 % a year with seasonal indices from 0.78 (February) to 1.35 (December); the but-for revenue of the six months is 699,793.50 against 151,000 actual, lost revenue 548,793.50; the cost regression gives a variable-cost ratio of 0.5354 (fixed cost 41,924.06 a month, R² 0.975), lost profits 254,980.78; with 5 % simple prejudgment interest to 1 January 2025 the ex post value is 264,812.22 and the ex ante value at 6 % is 264,186.14. The business-interruption section on the same six months with 55 % cost of sales, 25,000 continuing and 5,000 discontinued expenses a month, 10,000 ordinary payroll a month limited to 90 days, 15,000 extra expense, a 400,000 limit at 80 % coinsurance and a 2,500 deductible gives a loss of 186,627.41 by both forms, a coinsurance penalty (required 485,144.28, ratio 0.8245) and a loss payable of 166,373.73, leaving 35,253.67 uninsured. An independent numpy script of the whole model (References/Lost-Profits/checks/) reproduces every figure.