How long a completed scheme can sit unsold before finance on its costs consumes the developer's profit, with the formula, the Excel and the mistakes.
Profit erosion is the delay after which finance on the total development cost has grown the cost up to the gross development value: n = ln(1 + profit on cost) ÷ ln(1 + finance rate). On an illustrative scheme with a 30,000,000 GDV and 25,000,000 of cost, a 20.0 per cent profit on cost at a 7 per cent finance rate is eroded in 2.69 years, or 32.3 months.
Worked in full in Real Estate Financial Modeling by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A development appraisal reports profit as a margin, on cost or on GDV. Neither says how robust that margin is to the most common thing that goes wrong, which is time: a slow sales market, a buyer who pulls out, a delayed practical completion. Profit erosion converts the margin into months. Development appraisal software commonly prints it under the residual, and committees use it as a quick read of how much programme risk a scheme can absorb before the developer is working for nothing. It belongs in your own model beside the margin, and it takes one formula.
| Input | Value |
|---|---|
| Gross development value, net of sales costs | 30,000,000 |
| Total development cost, including finance to date | 25,000,000 |
| Profit | 5,000,000 |
| Profit on cost / profit on GDV | 20.0% / 16.7% |
| Finance rate applied to the whole cost | 7.0% a year |
The finance rate is applied to all of the cost, not just the loan. That is deliberate: the developer's own equity has a cost too, and the measure asks when the scheme as a whole stops covering its money.
Profit is gone when cost × (1 + r)n = GDV
So (1 + r)n = GDV ÷ cost = 1 + profit on cost
n = ln(1 + profit on cost) ÷ ln(1 + r)
In Excel: =LN(1+B4)/LN(1+B5) for years, times 12 for months; or =NPER(B5,0,-B2,B1) with cost in B2 and GDV in B1
Step 1: profit on cost. 5,000,000 ÷ 25,000,000 = 20.0 per cent, so GDV is 1.20 times cost.
Step 2: logs. ln(1.20) = 0.1823 and ln(1.07) = 0.0677.
Step 3: divide. 0.1823 ÷ 0.0677 = 2.69 years, or 32.3 months: about two years and eight months. Check: 25,000,000 × 1.072.69 = 30,000,000.
If the loan compounds monthly at 7 per cent a year nominal, 0.5833 per cent a month, the period is 2.61 years, or 31.3 months. Use the compounding basis of the facility.
The scheme can sit complete and unsold for just under 33 months before the profit is gone. The first year alone rolls up 1,750,000. A six-month delay costs 860,201, 17.2 per cent of the profit, and leaves a 16.0 per cent profit on cost. The relation is not linear: each month costs more than the last because the cost base it accrues on keeps growing.
| Profit on cost | 6% finance | 7% finance | 8% finance | 10% finance |
|---|---|---|---|---|
| 10% | 19.6 | 16.9 | 14.9 | 12.0 |
| 15% | 28.8 | 24.8 | 21.8 | 17.6 |
| 20% | 37.5 | 32.3 | 28.4 | 23.0 |
| 25% | 46.0 | 39.6 | 34.8 | 28.1 |
Moving from 7 to 10 per cent finance takes 9.4 months off the buffer at a 20 per cent margin, more than cutting the margin from 20 to 15 per cent, which takes 7.5. The standard formula holds values still. Let them move and add the costs of holding unsold stock, and the answer changes faster than either input suggests.
| Values a year | No holding costs | With holding costs |
|---|---|---|
| Rising 3.0% | 58 | 44 |
| Flat | 33 | 28 |
| Falling 5.0% | 19 | 17 |
The flat case gives 33 whole months, the first month in which cost overtakes value, against 32.3 from the formula. A market that falls 5 per cent a year while the stock sits unsold cuts the buffer from 33 months to 19, because the gap closes from both ends. That combination, slow sales in a falling market, is exactly when delays happen, so the flat-value figure is the optimistic one.
Profit erosion turns a margin into a time buffer: ln(1 + 20.0%) ÷ ln(1.07) = 2.69 years on this scheme. Report it next to the margin, and run it with falling values and holding costs, where it drops to 17 months. The book builds development models line by line, and the free workbooks for the book include a timed development residual case to try it on. See also how to convert profit on cost and profit on GDV and the IRR a 20 per cent profit on cost gives.
It is the length of delay, usually measured from completion, after which interest on the total development cost has grown the cost up to the gross development value, leaving no profit. It is a measure of how much time risk a scheme can absorb. A 20.0 per cent profit on cost at a 7 per cent finance rate erodes in 32.3 months.
Because finance accrues on cost, so the formula needs the ratio of value to cost: 1 + profit on cost. Using profit on GDV, 16.7 per cent in the worked case, gives 2.28 years instead of 2.69 and understates the buffer. Divide profit on GDV by one minus itself to convert it before using the formula.
Yes, sharply, because the gap closes from both sides. In the worked case a 5 per cent annual fall in values brings the erosion period from 33 whole months to 19, and adding 30,000 a month of holding costs brings it to 17. Rising values of 3 per cent a year extend it to 58 months.
This article is one calculation from Real Estate Financial Modeling. 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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