Modelling staged land payments in a development cash flow: the IRR, the profit, the implied vendor rate and the effect on peak equity.
A deferred land payment raises a developer's IRR whenever the premium the landowner charges implies a financing rate below the project's own IRR, and it always lowers profit. On an illustrative scheme, paying 4.0 million of a 10.0 million land price up front and 6.6 million at practical completion lifts the ungeared IRR from 15.33 to 18.00 per cent while cutting profit from 10.00 to 9.40 million. The deferral stops adding IRR at a premium of 1.98 million, where its implied rate reaches 15.33 per cent.
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 →
Landowners often accept staged payments: a deposit on exchange and the balance on planning, on start on site or on completion. In return they ask for a higher total price. The developer then has two numbers moving in opposite directions, a lower profit and a later outflow, and the appraisal has to say which one wins. The way to answer it in a model is to put each payment in its own period, run both cases off the same timeline, and convert the premium into an interest rate you can compare with something.
| Input | Value |
|---|---|
| Land price, paid in full at quarter 0 | 10.0 |
| Build cost, quarters 1 to 8, 3.75 a quarter | 30.0 |
| Gross development value, received 25.0 in each of quarters 9 and 10 | 50.0 |
| Deferred option: paid at quarter 0 | 4.0 |
| Deferred option: balance 6.0 plus premium 0.60, paid at quarter 8 | 6.60 |
The premium is 10.0 per cent of the deferred balance for two years of deferral. Purchase costs, finance and sales costs are left out so that only the land timing moves.
Cash flow per quarter = − land payments − build cost + sales receipts
Annualised IRR = (1 + quarterly IRR)4 − 1. In Excel: =(1+IRR(C10:M10))^4-1
Implied vendor rate = (deferred amount paid ÷ deferred amount)4 ÷ quarters deferred − 1 = (6.60 ÷ 6.0)4 ÷ 8 − 1
Peak equity = the most negative cumulative cash flow: =-MIN(C11:M11)
Step 1: pay up front. The cumulative cash flow runs from -10.00 at quarter 0 to -40.00 at quarter 8, then -15.00 after the first sales and +10.00 at the end. IRR 15.33 per cent, profit 10.00, a 25.0 per cent profit on cost.
Step 2: defer. Quarter 0 falls to -4.00 and quarter 8 carries 3.75 of build plus 6.60 of land. The cumulative position is 6.0 lighter from quarter 0 to quarter 7, 0.60 heavier at quarter 8 when the balance and premium fall due, and closes at 9.40. IRR 18.00 per cent, a gain of 2.67 points; profit on cost 23.2 per cent.
Step 3: price the deferral. (6.60 ÷ 6.0)0.5 − 1 = 4.88 per cent a year. The landowner is lending the developer 6.0 for two years at 4.88 per cent, far below the 15.33 per cent the project earns on its money, so the IRR rises.
| Structure | IRR | Profit | Peak equity |
|---|---|---|---|
| Land paid up front | 15.33% | 10.00 | 40.00 |
| Balance at completion, quarter 8 | 18.00% | 9.40 | 40.60 |
| Balance at first sales, quarter 9 | 18.53% | 9.40 | 34.00 |
Deferring to completion does not reduce peak funding at all: it increases it by the premium, to 40.60, because the balance falls due in the same quarter as the last build payment, which is exactly where the cumulative curve bottoms out. Only a payment out of the first sales receipts, quarter 9, cuts the peak, to 34.00, a saving of 6.00, because the 25.0 of receipts covers the 6.60 and leaves 18.40. If the reason for deferring is to reduce the equity cheque, the trigger date matters more than the premium.
| Premium | Total land price | Implied vendor rate | IRR | Profit |
|---|---|---|---|---|
| 0.00 | 10.00 | 0.00% | 19.16% | 10.00 |
| 0.30 | 10.30 | 2.47% | 18.58% | 9.70 |
| 0.60 | 10.60 | 4.88% | 18.00% | 9.40 |
| 1.20 | 11.20 | 9.54% | 16.84% | 8.80 |
| 2.00 | 12.00 | 15.47% | 15.30% | 8.00 |
| 3.00 | 13.00 | 22.47% | 13.37% | 7.00 |
The IRR advantage disappears at a premium of 1.98, a total land price of 11.98, where the implied rate equals the project IRR of 15.33 per cent. That is the general rule for conventional cash flows: deferral adds IRR when the vendor's implied rate is below the project's IRR. On a geared scheme compare the implied rate with the cost of the equity or mezzanine the deferral replaces instead, because that is the money it saves.
Convert the landowner's premium into an annual rate and compare it with the project's IRR: 4.88 per cent against 15.33 here, so the deferral adds 2.67 points of IRR for 0.60 of profit, and it pays only up to a premium of 1.98. Then check what it does to peak equity, which depends on the trigger, not the price. 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 timing flags place each payment in its period and how to calculate peak funding on a development.
Divide the deferred amount actually paid by the amount deferred, raise it to the power of one over the years of deferral and subtract one. Paying 6.60 in two years instead of 6.0 today implies (6.60 / 6.0) to the power 0.5, minus one: 4.88 per cent a year.
Only if the balance falls due after the cumulative cash flow has turned. In the illustrative scheme a balance paid at completion adds the 0.60 premium to the peak, taking it to 40.60, while the same balance paid out of the first sales receipts cuts the peak from 40.00 to 34.00.
Up to the point where the implied rate equals the return on the money it frees. On the ungeared illustrative scheme that is a premium of 1.98 on a 6.0 balance deferred two years, an implied 15.33 per cent, equal to the project IRR. On a geared scheme use the cost of the equity or mezzanine replaced.
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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