Tax losses save tax only as the business earns enough to use them, so their value is a discounted schedule, and an acquisition can stretch that schedule by years.
A net operating loss is worth the present value of the tax it saves, year by year, as the business earns enough to use it, not the balance times the tax rate. On an illustrative $20.0 million NOL at a 25 per cent tax rate, the face value is $5.00 million but the losses take six years to use under the 80 per cent limit, and at a 12 per cent discount rate they are worth $3.31 million. After a change of ownership that triggers a Section 382 limit of $1.40 million a year, the same losses are worth $2.34 million.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Tax loss carryforwards show up in a valuation in three places: in a target's tax notes, in a seller's argument for a higher price, and in a buyer's model as a line that nobody wants to own. The shortcut, NOL × tax rate, answers a question nobody asked: what the losses would be worth if the company could use them all today. It cannot. A loss saves tax only in a year when there is taxable income to shelter, under US federal rules a loss arising in a tax year beginning after 2017 can be carried forward indefinitely but can shelter at most 80 per cent of a year's taxable income, and after an ownership change Section 382 caps the annual use again. Each of those turns the face value into a schedule, and a schedule has to be discounted.
| Item | Value |
|---|---|
| NOL carryforward, post-2017, no expiry | $20.0m |
| Tax rate, illustrative combined | 25% |
| Taxable income before NOL, year one | $3.0m |
| Annual increase in taxable income | $0.5m |
| Annual limit on NOL use, share of taxable income | 80% |
| Discount rate for the tax savings | 12% |
The discount rate deserves a word. The savings depend on the business generating taxable income, so they carry operating risk; discounting them at the cost of debt, as if they were certain, overstates them. Using the cost of equity or the unlevered cost of capital, here 12 per cent, puts them on the same footing as the cash flows that make them usable. The build of that rate is in how to calculate WACC step by step.
NOL used in year t = MIN(80% × taxable incomet, NOL remaining)
Tax savedt = NOL usedt × 25%
Value = Σ tax savedt / (1.12)t = $3.31 million
Excel, one column per year: =MIN(Limit*TaxableIncome,OpeningNOL) for the use, =OpeningNOL-Use for the closing balance that opens the next column, then =NPV(Rate,SavingsRow)
| Year | Taxable income | NOL used | Tax saved | Discount factor | Present value | NOL left |
|---|---|---|---|---|---|---|
| 1 | 3.0 | 2.4 | 0.60 | 0.8929 | 0.536 | 17.6 |
| 2 | 3.5 | 2.8 | 0.70 | 0.7972 | 0.558 | 14.8 |
| 3 | 4.0 | 3.2 | 0.80 | 0.7118 | 0.569 | 11.6 |
| 4 | 4.5 | 3.6 | 0.90 | 0.6355 | 0.572 | 8.0 |
| 5 | 5.0 | 4.0 | 1.00 | 0.5674 | 0.567 | 4.0 |
| 6 | 5.5 | 4.0 | 1.00 | 0.5066 | 0.507 | 0.0 |
| Total | 20.0 | 5.00 | 3.31 |
The undiscounted savings add up to the face value, $5.00 million, but they arrive over six years, so the present value is 66.2 per cent of it. Without the 80 per cent rule the company would use the whole balance in five years and the losses would be worth $3.50 million; the limit costs $0.19 million, small here because income grows quickly and the last year's use is capped by the balance, not the rule.
When an acquisition causes an ownership change, broadly an increase of more than 50 percentage points in the stake held by 5 per cent shareholders over a three-year testing period, which buying the whole company does, Section 382 limits the annual use of the pre-change losses to the value of the company's equity immediately before the change multiplied by the long-term tax-exempt rate published monthly by the IRS (the highest rate in the three months ending with the month of the change). Adjustments to that equity value, such as for capital contributions before the change, are left aside here. With an illustrative equity value of $40.0 million and a rate of 3.5 per cent, the annual limit is $1.40 million, a saving of $0.35 million a year.
Annual limit = 40.0 × 3.5% = 1.40; years to use 20.0 = 15, the last year using 0.4
Value at 12% = $2.34 million, 46.8 per cent of the face value and $0.97 million less than the same losses in the seller's hands
This is the number a buyer should pay for, and it is why a seller's valuation of its own losses and a buyer's valuation of the same losses can be a million dollars apart without either side being wrong. The seller can use $2.4 million to $4.0 million a year; the buyer can use $1.40 million.
| Discount rate | No limit | 80% limit | Section 382 limit |
|---|---|---|---|
| 10% | 3.70 | 3.53 | 2.60 |
| 12% | 3.50 | 3.31 | 2.34 |
| 15% | 3.24 | 3.02 | 2.02 |
| 20% | 2.86 | 2.62 | 1.62 |
Lower profits stretch the schedule in the same way the 382 limit does. At 70 per cent of the forecast taxable income the losses take eight years to use and are worth $2.97 million; at half the forecast, ten years and $2.63 million. A company whose forecast is in doubt has NOLs whose value is in doubt for the same reason, which is the argument for discounting them at an equity-like rate.
Counting the losses twice. If the free cash flow forecast already uses the NOL to reduce cash taxes, the DCF has captured the benefit, and adding a separate NOL value on top double counts it. The cleaner method is to tax the operating cash flows at the full rate, as in how to calculate unlevered free cash flow, and value the NOL as its own line in the bridge to equity, with its own schedule and its own limit. That keeps the terminal value free of a tax shield that runs out in year six, and it makes the 382 question visible to whoever reads the valuation. The second mistake is valuing the losses at face, $5.00 million here, which overstates them by $1.69 million before any ownership change and by $2.66 million after one.
The book treats a valuation as a set of separately defended lines that must reconcile, and its DCF workbook is in the free workbooks for the book's case.
Schedule the losses year by year against forecast taxable income, apply the 80 per cent rule and, after a change of control, the Section 382 cap, multiply each year's use by the tax rate and discount at an equity-like rate. On these figures that turns a $5.00 million face value into $3.31 million for the current owner and $2.34 million for a buyer.
A rate that reflects the risk that the business will not earn enough to use them, typically the cost of equity or the unlevered cost of capital rather than the cost of debt. On the illustrative $20.0 million NOL under the 80 per cent limit, the value is $3.53 million at 10 per cent, $3.31 million at 12 per cent and $2.62 million at 20 per cent.
After an ownership change, broadly a rise of more than 50 percentage points in 5 per cent shareholders' stakes over three years, the annual use of pre-change losses is capped at the equity value before the change times the IRS long-term tax-exempt rate. On illustrative figures of $40.0 million and 3.5 per cent, the cap is $1.40 million a year, so $20.0 million of losses takes 15 years to use and is worth $2.34 million at 12 per cent.
One or the other, never both. The cleaner method taxes operating cash flows at the full rate and adds the NOL as a separate present value in the bridge to equity, so the terminal value carries no shield that has run out. On the illustrative case that separate line is $3.31 million, against a face value of $5.00 million.
This article is one calculation from Business Valuation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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