A Phase I flags a historic industrial use and the buyer has three weeks to exchange. The decision is an expected-value calculation, and the probability is the input nobody writes down.
A Phase II investigation is worth commissioning when the expected loss it lets you avoid exceeds its cost: probability of contamination, times the chance the investigation finds it, times the exposure. On an illustrative 24,000,000 acquisition with a 1,350,000 exposure, a 30,000 investigation plus 15,000 of delay pays only if the probability of contamination is above 3.92 per cent. The Phase I report says "low", which is not a number.
Worked in full in Real Estate Transaction Due Diligence by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The Phase I desktop study has come back with a light industrial use on the site forty years ago. No evidence of contamination, no evidence of its absence. A Phase II, with boreholes and laboratory analysis, would take three weeks and push exchange back. The usual outcome is a judgement call recorded as "risk accepted" or "investigation commissioned", without the arithmetic that should decide it.
| Input | Value |
|---|---|
| Purchase price | 24,000,000 |
| Phase II fee | 30,000 |
| Cost of three weeks' delay (commitment fees, extended exclusivity) | 15,000 |
| Remediation cost if contamination is found | 1,200,000 |
| Income lost during remediation | 150,000 |
| Exposure if contaminated | 1,350,000 |
| Probability the investigation finds contamination that exists | 85% |
| Probability of contamination, central case | 5% |
The exposure is 5.62 per cent of the price. The fee is 0.125 per cent. Neither number alone tells you anything: what matters is the exposure weighted by how likely it is and how likely the investigation is to reveal it. The model assumes that contamination found before exchange is priced off, or the buyer walks away; contamination not found is the buyer's after completion.
Expected loss without investigation = p × E
Expected loss with investigation = p × (1 − d) × E + cost
Value of the investigation = p × d × E − cost
Break-even probability p* = cost ÷ (d × E)
p is the probability of contamination, d the detection rate, E the exposure. In Excel, with cost in B1, detection in B2 and exposure in B3: =B1/(B2*B3).
At 5 per cent, buying without the investigation carries an expected loss of 67,500. With it, the residual expected loss, contamination that exists but is missed, is 10,125, and the fee brings the total to 40,125. The investigation is worth 27,375 on its fee alone: it avoids 57,375 of expected loss for 30,000. Add the 15,000 of delay and the value falls to 12,375.
| Cost counted | Cost | Break-even probability |
|---|---|---|
| Fee only, perfect detection | 30,000 | 2.22% |
| Fee only, 85% detection | 30,000 | 2.61% |
| Fee plus delay, 85% detection | 45,000 | 3.92% |
A break-even of 3.92 per cent sits uncomfortably inside the range a consultant usually means by "low", which in practice covers a few per cent either side of it. The decision is genuinely marginal, and it is marginal on a number that nobody in the transaction has written down. That is the point of doing the arithmetic: it turns an argument about whether the risk is acceptable into a question the environmental consultant can answer, namely whether the probability is nearer 2 per cent or 5.
| Exposure | p 1% | p 2% | p 5% | p 10% | Break-even |
|---|---|---|---|---|---|
| 500,000 | −40,750 | −36,500 | −23,750 | −2,500 | 10.59% |
| 1,350,000 | −33,525 | −22,050 | 12,375 | 69,750 | 3.92% |
| 3,000,000 | −19,500 | 6,000 | 82,500 | 210,000 | 1.76% |
The exposure matters as much as the probability, because the value of the investigation depends on their product. On a site where contamination would mean a 3,000,000 dig-out and a long void, the investigation pays at 1.76 per cent and is clearly worth doing. Where the worst case is a 500,000 cap-and-contain solution, it needs a probability above 10 per cent, which a light industrial history rarely supports. Before debating the probability, ask the consultant for a credible remediation range: it is usually easier to evidence than the probability, and it often settles the question.
The two common mistakes run in opposite directions. The first compares the fee with the worst case: 1,350,000 against 30,000, forty-five times the cost, so the investigation always looks cheap. That ignores the probability and would justify every test on every site. The second compares the fee with the full expected loss, 67,500 against 30,000, and forgets both that the investigation misses some contamination and that three weeks of delay has a cost. Done properly, the margin shrinks from 37,500 to 12,375, and at 2 per cent it reverses.
Two cases where the arithmetic does not decide. If the lender's conditions precedent require a Phase II, it is a cost of the financing, not a choice. And if the seller will give an environmental indemnity from a creditworthy entity, or a policy can be placed for less than the investigation, the expected loss falls to the uncovered part and the break-even moves up. Price each instrument against the same exposure before choosing between them.
Write the decision as a break-even: cost divided by detection rate times exposure, 3.92 per cent here. Then ask the consultant whether the probability is above or below it, and for the remediation range that sets the exposure. The free workbook for the book prices the one finding the book's case leaves unpriced in the same way, on its own figures, and a related article shows what the whole diligence exercise returned.
Compare its cost with the expected loss it lets you avoid: probability of contamination times the chance the investigation finds it times the exposure. With an 85 per cent detection rate and a 1,350,000 exposure, a 30,000 fee breaks even at a 2.61 per cent probability, and at 3.92 per cent once 15,000 of delay cost is added.
Consultants rarely say. Treat it as a range rather than zero, and test the decision at both ends. In the illustrative case, a 2 per cent probability makes a Phase II a loss of 22,050 in expected terms, while 5 per cent makes it worth 12,375, so the answer turns on a number the report does not give.
When the exposure is small relative to its cost, or when another instrument covers the risk more cheaply. With a 500,000 exposure the same 45,000 investigation needs a 10.59 per cent probability of contamination to pay, which is rarely justified on a light industrial history. An indemnity or a policy may then be the better use of the money.
This article is one calculation from Real Estate Transaction Due Diligence. 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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