A cap rate and a DCF are the same calculation under strict conditions; every gap between them in a real model can be named and priced.
Direct capitalisation and a DCF give the same value only when the income is stable, grows at a constant rate, and the cap rate equals the discount rate less that growth. On an illustrative office with 1,000,000 of NOI, a 5.50 per cent cap rate and a 7.5 per cent discount rate with 2 per cent growth, both give 18,181,818. Add a softer exit yield, selling costs and one lease expiry, and the DCF falls to 16,792,845, 7.6 per cent lower; the cap rate sees none of it.
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 →
Direct capitalisation divides one year's NOI by a market cap rate. A DCF discounts every year's cash flow and a sale price at a target return. The bridge between them is the growing perpetuity: value = NOI / (r − g). If the discount rate is 7.5 per cent and NOI grows 2 per cent a year for ever, the implied cap rate is 5.5 per cent, and the two methods are the same calculation written two ways. Every difference between them in a real model comes from something that breaks that identity, and a model reviewer should be able to name each one and price it.
| Input | Value |
|---|---|
| Year 1 NOI | 1,000,000 |
| NOI growth a year | 2.0% |
| Going-in cap rate (market evidence) | 5.50% |
| Discount rate | 7.5% |
| Hold period, years | 10 |
| Exit cap rate, on year 11 NOI | 5.75% |
| Selling costs | 1.5% |
| Year 4: tenant paying 40% of NOI leaves; one year void | 40% |
| Year 4: re-letting costs (incentives, fees, works) | 600,000 |
All figures are illustrative, not market data.
1. Direct capitalisation: 1,000,000 / 5.50% = 18,181,818. In Excel, =NOI1/CapRate.
2. DCF with stable income and an exit cap of 5.50%: NOI grows to 1,218,994 in year 11, the exit is 1,218,994 / 5.50%, and discounting everything at 7.5% gives 18,181,818. Identical, because 7.5% − 2.0% = 5.5%.
3. Now the realistic DCF. Year 4 cash flow is NOI of 1,061,208 less 424,483 of lost rent and 600,000 of re-letting cost: 36,725. Year 10 adds the net sale, 1,218,994 / 5.75% × (1 − 1.5%) = 20,881,904, to NOI of 1,195,093, for 22,076,997.
4. Discount years 1 to 10 at 7.5%: =NPV(7.5%,C2:L2) = 16,792,845.
| Step | DCF value | Change | Implied going-in cap |
|---|---|---|---|
| Stable income, exit cap 5.50%, no costs | 18,181,818 | 5.50% | |
| Exit cap 5.75% | 17,714,270 | −467,548 | 5.65% |
| Plus 1.5% selling costs | 17,559,979 | −154,291 | 5.69% |
| Plus the year 4 lease event | 16,792,845 | −767,134 | 5.95% |
The lease event is the largest item, and it reconciles exactly: 1,024,483 of lost rent and costs in year 4, discounted four years at 7.5 per cent, is 767,134. That is the adjustment a valuer makes below the line when using direct capitalisation on a building with a known void: capitalise the stable income, then deduct the present value of the event. 18,181,818 less 767,134 is 17,414,685, and the remaining gap to the DCF is the exit yield and the selling costs, which a cap rate on today's income cannot see.
Paying the direct cap value of 18,181,818 for the realistic cash flows earns 6.46 per cent, not 7.5. The cap rate is not wrong; it just carries the market's assumptions for a typical building, and this one is not typical.
| Discount rate | Exit 5.50% | Exit 5.75% | Exit 6.00% |
|---|---|---|---|
| 7.0% | 17,922,743 | 17,440,229 | 16,997,925 |
| 7.5% | 17,253,380 | 16,792,845 | 16,370,688 |
| 8.0% | 16,615,151 | 16,175,498 | 15,772,483 |
Even at a 7.0 per cent discount rate and no exit yield softening, the DCF stays below the direct cap value, because the void is real cash lost. To make the two agree on this building you would need a discount rate below 7 per cent, which is just the 6.46 per cent IRR read the other way.
A complete property model with rent roll, cash flow and returns sheets, built to the same conventions, is in the free workbook for this case. For the relation between yield, growth and return, see whether a property IRR equals cap rate plus growth, and for the NOI that belongs in the exit, forward or trailing NOI for the exit cap rate.
When NOI grows at a constant rate for ever, the exit cap rate equals the going-in cap rate, there are no selling costs, and the cap rate equals the discount rate minus growth. With 1,000,000 of NOI, 2 per cent growth and a 7.5 per cent discount rate, both methods give 18,181,818 at a 5.5 per cent cap rate.
Capitalise the stabilised income, then deduct the present value of the lost rent and re-letting costs below the line. In the illustration the year 4 event costs 1,024,483, worth 767,134 today at 7.5 per cent, so 18,181,818 becomes 17,414,685. Capitalising the reduced year 4 income instead would give 11,576,815, far too low.
Whatever discount rate makes the DCF equal to that price. Paying 18,181,818 for the illustrative office, with its 5.75 per cent exit cap, selling costs and year 4 void, earns 6.46 per cent unlevered, against the 7.5 per cent target, because the cap rate ignores the building's specific events.
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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