Calibration worked on a two-year-old buyout: the discount at entry, the day-one test, the roll-forward, and what happens when the discount is changed.
Compute the discount the price paid implied against the peer set at entry, then apply the same relationship to today's peer multiple. A company bought at 7.8 times EBITDA when peers traded at 9.6 times was priced at an 18.75 per cent calibration discount. Two years later, with peers at 8.4 times and EBITDA of 24.0 million, the calibrated multiple is 6.83 times and enterprise value 163.8 million. Holding the entry multiple would have marked it at 187.2, and the uncalibrated peer median at 201.6.
Worked in full in The Private Markets Valuation Specialist by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Calibration is the step that ties a fair value model to the only observable transaction in a private company's life: the price the fund paid for it. IFRS 13 and the IPEV Guidelines both expect it. The idea is simple. Whatever the market saw in the company at entry, its size, its customer concentration, its growth, is assumed to persist unless something has changed and the change is documented. The arithmetic below shows why the choice of method moves equity value by up to 40 per cent.
| Input | At entry | Two years later |
|---|---|---|
| Enterprise value paid | 156.0 | |
| LTM EBITDA | 20.0 | 24.0 |
| Peer median EV/EBITDA | 9.6x | 8.4x |
| Net debt | 86.0 | 70.0 |
| Equity | 70.0 | ? |
Entry multiple = price paid ÷ entry EBITDA; calibration discount = 1 − entry multiple ÷ peer multiple
156.0 ÷ 20.0 = 7.8x. 1 − 7.8 ÷ 9.6 = 18.75%.
Day-one test: 9.6 × (1 − 18.75%) × 20.0 = 156.0. If the model, run at the acquisition date with acquisition-date inputs, does not return the price paid, it is not calibrated.
The day-one test is not a formality. A model that cannot reproduce the transaction price on the day it happened will produce a gain or loss at the first quarter end that has nothing to do with the company, and an auditor will ask for it to be explained.
Calibrated multiple = today's peer multiple × (1 − calibration discount)
8.4 × (1 − 18.75%) = 6.825x. EV = 6.825 × 24.0 = 163.8. Equity = 163.8 − 70.0 = 93.8.
In Excel, with the entry price in B2, entry EBITDA in B3, entry peers in B4, current peers in C4 and current EBITDA in C3: =C4*(B2/B3)/B4*C3.
The movement in enterprise value since entry, 7.8 million, splits cleanly. Peer multiples fell 12.5 per cent, which on the entry EBITDA costs 19.5 million. EBITDA grew 20.0 per cent, which at the calibrated multiple adds 27.3 million. The residual is zero. That decomposition is what goes in the valuation memo: one line the market caused, one line the company caused.
| Method | Multiple | EV | Equity | Against calibrated |
|---|---|---|---|---|
| Calibrated, ratio held | 6.83x | 163.8 | 93.8 | |
| Calibrated, turns held | 6.60x | 158.4 | 88.4 | −5.8% |
| Entry multiple held | 7.80x | 187.2 | 117.2 | +24.9% |
| Peer median, uncalibrated | 8.40x | 201.6 | 131.6 | +40.3% |
Holding the entry multiple is the most common shortcut, and it ignores the 12.5 per cent fall in peer multiples entirely: equity of 117.2, a 1.67x gross multiple on the 70.0 invested, against 1.34x calibrated. Holding the gap in turns, 1.8 turns below peers, is defensible but gives a different answer whenever peer multiples move, because a fixed number of turns is a larger proportion of a smaller multiple. Pick one convention, write it into the valuation policy, and apply it every quarter.
| Peer median | Calibrated multiple | Calibrated equity | Entry multiple held | Overstatement |
|---|---|---|---|---|
| 7.6x | 6.17x | 78.2 | 117.2 | 39.0 |
| 8.0x | 6.50x | 86.0 | 117.2 | 31.2 |
| 8.4x | 6.83x | 93.8 | 117.2 | 23.4 |
| 8.8x | 7.15x | 101.6 | 117.2 | 15.6 |
| 9.6x | 7.80x | 117.2 | 117.2 | 0.0 |
The entry-multiple shortcut is only right when the market has not moved. Equity sits on 70.0 of net debt, so every turn of peer multiple is amplified: a fall from 9.6 to 7.6 times, about a fifth, takes calibrated equity down by a third.
Calibration does not freeze the discount forever. If the company has fixed what the entry price penalised, say it has halved its largest customer's share of revenue, the discount can narrow. Narrowing it by a third, to 12.50 per cent, gives a multiple of 7.35x and EV of 176.4, adding 12.6 million. That 12.6 must appear as its own line in the roll-forward, labelled as a deliberate change in the calibrated relationship, with the evidence attached. A change you can isolate is a change you can defend; one buried in the peer line is not.
The double count. The calibration discount already prices size, concentration and illiquidity as the entry market saw them. Applying a further 15 per cent size discount on top takes the multiple to 5.80x, a 30.9 per cent total discount, and removes 24.6 million, 26.2 per cent of equity, for a risk already in the price.
Measure the relationship at entry, prove it with the day-one test, carry it forward, and change it only on evidence. Here that is 6.83 times and 163.8 million, not the 187.2 the entry multiple gives. The free market approach and calibration workbook builds the same chain with a roll-forward whose residual is zero, and a related article tests how large a marketability discount can be evidenced.
Running the valuation model at the acquisition date with acquisition-date inputs and checking it returns the price paid. Here peers at 9.6x, a calibration discount of 18.75 per cent and EBITDA of 20.0 give 156.0, the entry enterprise value. A model that fails the test will report a first-quarter gain or loss unrelated to the company.
Either can be defended, but they diverge when peer multiples move. With peers falling from 9.6x to 8.4x, a percentage discount gives 6.83x and equity of 93.8; holding 1.8 turns gives 6.60x and 88.4, 5.8 per cent lower. The convention belongs in the valuation policy and should not change between quarters.
Not for a risk the entry price already reflected. The calibrated discount embeds size and concentration as the market saw them. Adding a further 15 per cent takes the multiple from 6.83x to 5.80x and removes 24.6 million, 26.2 per cent of equity value, for the same risk counted twice.
This article is one calculation from The Private Markets Valuation Specialist. 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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