# Real Estate Finance Concept Card: [Your name, elective or property, and date] > An elective-level concept card for commercial real estate finance as it is taught in an MBA real estate or > alternative investments elective: net operating income (NOI), the capitalisation rate and what it implies about > return and growth, the lender's three tests (loan to value, debt service coverage and debt yield), unlevered and > levered internal rates of return (IRR), the development pro forma (yield on cost and development spread) and the > equity waterfall between an investor and a sponsor. It builds on mba/mba-npv-irr-card and > mba/mba-capital-structure-card, and it uses the waterfall logic of mba/mba-pe-fund-economics-card at the level of one > property. It is for second-year MBA students in a real estate, private equity or corporate finance elective and for > candidates preparing for a real estate acquisitions or lending interview. Worked example A follows a fictional fund > that buys the Northfield Outdoor Co. distribution centre on a sale-leaseback, Worked example B is a half-solved > build-to-suit development for Corvane Robotics, and Exercise C asks for the maximum loan and the effect of a higher > interest rate. Source basis: Gordon (1959), Modigliani and Miller (1958), DiPasquale and Wheaton (1992) and the > textbook framework of Geltner, Miller, Clayton and Eichholtz, written up in original words with fictional numbers. > Replace every [bracketed] value and every row marked *Example*. This is a learning aid, not investment, credit, > legal, tax or valuation advice. ## Document control | Field | Value | |---|---| | Learner | [Your name] | | Elective, case or property | [Real estate elective, case name, property name] | | Rent roll or operating statement date | YYYY-MM-DD | | Model file and version | [File name, v0.1] | | Market evidence used | [Cap rate and rent sources, with dates] | | Reviewed by | [Learning team member, teaching assistant or mentor] | | Version | [0.1] | | Last updated | YYYY-MM-DD | ## Contents - [When to use it](#when-to-use-it) - [The idea in plain language](#the-idea-in-plain-language) - [Formulas and notation](#formulas-and-notation) - [Assumptions and limits](#assumptions-and-limits) - [How investors and lenders use the numbers](#how-investors-and-lenders-use-the-numbers) - [The model build step by step](#the-model-build-step-by-step) - [Worked example A (fully solved): a sale-leaseback of the Northfield distribution centre](#worked-example-a-fully-solved-a-sale-leaseback-of-the-northfield-distribution-centre) - [Worked example B (half solved): a build-to-suit for Corvane Robotics](#worked-example-b-half-solved-a-build-to-suit-for-corvane-robotics) - [Exercise C (unsolved): maximum loan and a higher rate](#exercise-c-unsolved-maximum-loan-and-a-higher-rate) - [Connections to other cards](#connections-to-other-cards) - [Common mistakes and misconceptions](#common-mistakes-and-misconceptions) - [Self-test questions](#self-test-questions) - [My notes and next steps](#my-notes-and-next-steps) - [Sources and further reading](#sources-and-further-reading) - [Answer key](#answer-key) ## When to use it Use the tools on this card when: - you must price an income-producing property, test a seller's asking price or explain a cap rate in an interview; - you are asked how much a lender will lend against a property, and which of the lender's tests binds; - you must compare an unlevered and a levered return and say whether debt helps or hurts at today's interest rates; - a company considers selling its buildings and leasing them back (a sale-leaseback), or a developer proposes a build-to-suit, and you must decide whether the numbers work for each side; - you read a joint venture agreement and must work out how the profits are split between the capital partner and the sponsor who finds, manages and sells the property. Do not use a single cap rate to value a property whose income will change sharply (a building with a major lease expiring next year, a development, a hotel in a cyclical market). For those, project the cash flows year by year and discount them, as in Worked example A, and treat the cap rate only as the way the market prices the exit. ## The idea in plain language A commercial property is valued for the cash it produces. The starting point is net operating income: rents and other income, less vacancy, less the operating expenses the owner pays. NOI is measured before debt service, before income tax and before capital expenditure on the building, so it describes the property and not the way it is financed. The capitalisation rate (cap rate) is NOI divided by value. Buyers and appraisers read market cap rates from recent sales of similar properties and divide a property's NOI by that rate to estimate its value. A low cap rate means investors pay a lot for each unit of income, because they expect income to grow or because they see the income as safe. The cap rate is not a return. Gordon (1959) showed that the price of a growing perpetuity is its next cash flow divided by the difference between the required return and the growth rate. Applied to property, the cap rate is roughly the required return minus the expected long-run growth of NOI (after the capital spending needed to keep the building competitive). A 6.5% cap rate with 3% expected growth implies a total return of about 9.5%. When interest rates rise, required returns rise, and cap rates usually follow, which lowers values even when rents do not change. DiPasquale and Wheaton (1992) give the framework most courses use: real estate links a market for space (where tenants pay rent), a market for assets (where investors set cap rates), and a construction sector that adds new space when values exceed replacement cost. Rents, values and new supply move together through that loop. Most properties are bought with a mortgage. The lender looks at the property, not at the buyer's other assets, so it sets limits: the loan cannot exceed a share of value (loan to value), NOI must cover the annual debt payment with a margin (debt service coverage), and NOI must be a minimum share of the loan (debt yield). Leverage raises the expected equity return when the property earns more than the debt costs, and lowers it when it earns less. Modigliani and Miller (1958) remind you that the higher expected return is compensation for higher risk, not free value. Many deals are joint ventures. A capital partner puts up most of the equity and a sponsor puts up a small share and does the work. The waterfall says who gets each distribution: first the partners get their capital back with a preferred return, then the sponsor receives a larger share of profits (the promote) as a reward for performance. ## Formulas and notation Net operating income and value from the cap rate: $$ NOI = EGI - OpEx = (PGI - V\&C + OI) - OpEx \qquad V_0 = \frac{NOI_1}{c_0} $$ Cap rate as a growing perpetuity (Gordon), with required unlevered return $r$ and long-run NOI growth $g$: $$ c \approx r - g $$ Lender tests, with loan $L$, annual debt service $DS$ and mortgage constant $k$: $$ LTV = \frac{L}{V} \qquad DSCR = \frac{NOI}{DS} \qquad DY = \frac{NOI}{L} \qquad k = \frac{DS}{L} $$ Annual debt service on a fully amortising loan at rate $i$ over $n$ years: $$ DS = L \cdot \frac{i}{1 - (1+i)^{-n}} $$ Unlevered and levered cash flows, with capital reserve $R_t$, sale at the exit cap rate $c_N$ and selling costs $s$: $$ PBTCF_t = NOI_t - R_t \qquad BTCF_t = PBTCF_t - DS_t \qquad V_N = \frac{NOI_{N+1}}{c_N} $$ $$ \text{Reversion to equity} = V_N (1 - s) - L_N $$ Returns: the IRR solves $\sum_{t=0}^{N} CF_t / (1+IRR)^t = 0$; the equity multiple is total distributions over equity invested. Development pro forma, with total development cost $TDC$ and stabilised NOI: $$ YoC = \frac{NOI_{stab}}{TDC} \qquad \text{Spread} = YoC - c_{market} \qquad \text{Profit on cost} = \frac{NOI_{stab}/c_{market} - TDC}{TDC} $$ | Symbol | Meaning | Note | |---|---|---| | $PGI$, $V\&C$, $OI$, $EGI$ | Potential gross income, vacancy and credit loss, other income, effective gross income | Rent roll first, then vacancy | | $OpEx$ | Operating expenses paid by the owner | Excludes debt service, income tax, depreciation and capital spending | | $NOI$ | Net operating income | Before debt service and capital spending | | $c_0$, $c_N$ | Going-in and exit cap rates | Exit cap is usually set at or above going-in for an ageing building | | $L$, $L_N$ | Loan amount and balance at exit | | | $DS$, $k$ | Annual debt service and mortgage constant | $k$ includes principal, so it exceeds the interest rate | | $R_t$ | Capital reserve | Roof, structure, tenant improvements and leasing commissions in multi-tenant property | | $PBTCF_t$, $BTCF_t$ | Property and equity before-tax cash flow | Unlevered and levered | | $YoC$ | Yield on cost (development yield) | Stabilised NOI over all-in cost | Excel: debt service `=PMT(5.5%,25,-36000)`; loan balance after 5 years `=-FV(5.5%,5,-PMT(5.5%,25,-36000),36000)`; returns `=IRR(B10:G10)`; value at exit `=NOI_6/Exit_cap`. For a loan with monthly payments use `=PMT(rate/12,n*12,-L)*12` and expect a slightly lower annual payment. ## Assumptions and limits - **Annual periods.** Rents and debt service are annual and paid at year end. Real leases pay monthly or quarterly in advance, which raises value slightly; real loans usually pay monthly. - **Single-tenant triple-net lease.** The tenant pays operating costs, insurance and property taxes, so the owner's NOI is the rent less a small non-recoverable amount. Multi-tenant buildings need a rent roll, a vacancy and re-leasing assumption for each lease, and reserves for tenant improvements and leasing commissions. - **Fixed-rate, fully amortising loan.** Commercial loans are often interest-only for some years, have a balloon payment at maturity, a floating rate with a hedge, prepayment penalties and covenants. Each changes the equity cash flows. - **No income tax.** Returns are before tax. Depreciation, interest deductibility, transfer taxes and special regimes (real estate investment trusts and their equivalents) change after-tax returns and differ by jurisdiction. - **Exit at a cap rate.** The sale price is NOI of the year after exit divided by the exit cap rate. That single assumption often drives more of the return than all the years of rent. - **Sale-leaseback accounting is not modelled.** Whether the seller can recognise a sale, and how the leaseback appears on its balance sheet, depends on the lease and revenue accounting standards it applies (see finance/lease-accounting-memo). - **No fees to the sponsor** other than the promote. Real joint ventures add acquisition, asset management and disposition fees. ## How investors and lenders use the numbers | Reader | Question | Outputs they look at | |---|---|---| | Acquisitions team | What can we pay and still meet our target return? | Going-in cap rate, unlevered IRR, levered IRR and equity multiple, exit cap sensitivity | | Investment committee | What drives the return, and what breaks it? | Share of return from the sale, exit cap and rent growth sensitivities, tenant credit | | Lender | Will NOI cover the loan with a margin, and is the loan safe if values fall? | LTV, DSCR by year, debt yield, tenant lease term against loan term | | Capital partner in a joint venture | How much of the profit goes to the sponsor, and when? | Waterfall by tier, partner IRR and multiple, promote | | Tenant in a sale-leaseback | What does the rent cost us compared with owning? | Rent against the cost of capital on the sale proceeds, lease terms and options | Property types are priced differently. Logistics buildings with long leases to strong tenants trade at low cap rates and need little capital spending; offices with short leases need more capital for re-leasing; hotels behave more like operating businesses. A model should say which risks the cap rate is pricing. ## The model build step by step ```mermaid flowchart TD A["Rent roll and operating statement"] --> B["NOI by year: income, vacancy, operating expenses"] B --> C["Price: going-in cap rate, closing costs"] C --> D["Loan sizing: LTV, DSCR and debt yield, take the lowest"] D --> E["Debt schedule: payment, interest, principal, balance"] B --> F["Unlevered cash flows and exit value at the exit cap rate"] E --> G["Levered cash flows: unlevered less debt service and loan repayment"] F --> G F --> H["Unlevered IRR and multiple"] G --> I["Levered IRR, equity multiple, cash-on-cash"] G --> J["Waterfall: return of capital and preferred return, then promote split"] I --> K["Sensitivities: exit cap, growth, rate, leverage"] ``` 1. **Income.** Build NOI from the rent roll: contract rent, expected vacancy, recoveries and owner costs. 2. **Price.** Apply the going-in cap rate and add closing costs (transfer taxes, legal, due diligence). 3. **Loan.** Compute the maximum loan under each lender test and take the smallest; add the financing fee. 4. **Debt schedule.** Payment, interest, principal and balance for each year. 5. **Unlevered cash flows.** NOI less reserves, plus the net sale proceeds at exit. 6. **Levered cash flows.** Unlevered cash flows less debt service, less the loan balance repaid at sale. 7. **Returns and waterfall.** IRRs, multiples, cash-on-cash and the split between partners. 8. **Sensitivities.** Exit cap, rent growth, interest rate and leverage. ## Worked example A (fully solved): a sale-leaseback of the Northfield distribution centre *Example* situation (all fictional): Northfield Outdoor Co. sells its distribution centre to a core-plus real estate fund (the Fund) and leases it back for 15 years on a triple-net lease. The year 1 rent is USD 4,100 thousand, rising 3% a year; the Fund bears 200 of non-recoverable costs, also rising 3% a year, so NOI is 3,900 in year 1 and grows 3%. The Fund pays a 6.50% going-in cap rate, closing costs of 1.5% of price, and a capital reserve of 100 a year. It plans to sell after 5 years at a 6.75% exit cap rate on year 6 NOI, with selling costs of 1.5%. The loan is 60% of price at a fixed 5.50%, amortising over 25 years with annual payments, with a 1% financing fee paid from equity. ### Step 1: price, loan and equity (USD thousand) | Item | Computation | Result | Excel | |---|---|---|---| | Price | 3,900 / 6.50% | 60,000.00 | `=3900/6.5%` | | Closing costs | 1.5% x 60,000 | 900.00 | `=1.5%*60000` | | Loan (60% LTV) | 60% x 60,000 | 36,000.00 | `=60%*60000` | | Financing fee | 1% x 36,000 | 360.00 | `=1%*36000` | | Equity | 60,000 + 900 + 360 - 36,000 | 25,260.00 | `=60000+900+360-36000` | | Annual debt service | 25-year annuity at 5.50% | 2,683.78 | `=PMT(5.5%,25,-36000)` | | Mortgage constant | 2,683.78 / 36,000 | 7.45% | `=2683.78/36000` | | Going-in debt yield | 3,900 / 36,000 | 10.83% | `=3900/36000` | ### Step 2: operating and debt schedule (USD thousand) | Year | NOI | Reserve | Unlevered cash flow | Interest | Principal | Closing loan | DSCR | Equity cash flow | Cash-on-cash | |---|---|---|---|---|---|---|---|---|---| | 1 | 3,900.00 | 100.00 | 3,800.00 | 1,980.00 | 703.78 | 35,296.22 | 1.45x | 1,116.22 | 4.42% | | 2 | 4,017.00 | 100.00 | 3,917.00 | 1,941.29 | 742.48 | 34,553.74 | 1.50x | 1,233.22 | 4.88% | | 3 | 4,137.51 | 100.00 | 4,037.51 | 1,900.46 | 783.32 | 33,770.42 | 1.54x | 1,353.73 | 5.36% | | 4 | 4,261.64 | 100.00 | 4,161.64 | 1,857.37 | 826.40 | 32,944.01 | 1.59x | 1,477.86 | 5.85% | | 5 | 4,389.48 | 100.00 | 4,289.48 | 1,811.92 | 871.86 | 32,072.16 | 1.64x | 1,605.71 | 6.36% | Year 1 in Excel: interest `=5.5%*36000` = 1,980.00; principal `=2683.78-1980` = 703.78; DSCR `=3900/2683.78` = 1.45x; equity cash flow `=3900-100-2683.78` = 1,116.22; cash-on-cash `=1116.22/25260` = 4.42%. ### Step 3: exit (USD thousand) | Item | Computation | Result | Excel | |---|---|---|---| | Year 6 NOI | 3,900 x 1.03^5 | 4,521.17 | `=3900*1.03^5` | | Gross sale price | 4,521.17 / 6.75% | 66,980.28 | `=4521.17/6.75%` | | Selling costs | 1.5% x 66,980.28 | 1,004.70 | `=1.5%*66980.28` | | Net sale proceeds | 66,980.28 - 1,004.70 | 65,975.58 | | | Loan repaid | balance after 5 years | 32,072.16 | `=-FV(5.5%,5,-2683.78,36000)` | | Reversion to equity | 65,975.58 - 32,072.16 | 33,903.42 | | ### Step 4: returns (USD thousand) | Year | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | Unlevered cash flow | -60,900.00 | 3,800.00 | 3,917.00 | 4,037.51 | 4,161.64 | 70,265.06 | | Levered cash flow | -25,260.00 | 1,116.22 | 1,233.22 | 1,353.73 | 1,477.86 | 35,509.13 | | Measure | Unlevered | Levered | |---|---|---| | IRR | 8.02% | 10.79% | | Multiple | 1.42x | 1.61x | | Profit | 25,281.21 | 15,430.16 | Reading: the Gordon approximation says a 6.50% cap rate with 3% growth implies about 9.5% unlevered. The model gives 8.02% because the Fund pays closing and selling costs, sets aside a reserve, and assumes the exit cap rate widens by 25 basis points. Remove all three and the model returns exactly 9.50%, the Gordon answer. Leverage adds 2.77 points of IRR. About 87% of the levered cash returned arrives in year 5 (`=35509.13/40690.16`), so the exit assumption carries most of the return. ### Step 5: positive and negative leverage Two comparisons answer "does debt help?", and they can disagree: | Comparison | Property side | Debt side | Verdict in Worked example A | |---|---|---|---| | Cash yield in year 1 | Cap rate 6.50% (unlevered cash yield on price) | Mortgage constant 7.45% | Negative: cash-on-cash falls to 4.42% | | Total return over the hold | Unlevered IRR 8.02% | Interest rate 5.50% | Positive: levered IRR rises to 10.79% | The mortgage constant includes principal repayment, which is the equity's own money coming back as a smaller loan at exit, so the year 1 cash yield understates the benefit of leverage. Over the hold, what matters is whether the property's total return (income plus growth) beats the interest rate. When the interest rate approaches the unlevered IRR, leverage stops adding return but keeps adding risk (Exercise C2). ### Step 6: exit cap rate sensitivity | Exit cap rate | 6.25% | 6.50% | 6.75% (base) | 7.00% | 7.25% | |---|---|---|---|---|---| | Unlevered IRR | 9.42% | 8.70% | 8.02% | 7.38% | 6.76% | | Levered IRR | 13.65% | 12.20% | 10.79% | 9.41% | 8.06% | | Equity multiple | 1.82x | 1.71x | 1.61x | 1.52x | 1.43x | ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Northfield distribution centre sale-leaseback: IRR against exit cap rate, Example values computed in Python", "width": 420, "height": 240, "data": { "values": [ {"exit_cap": 6.25, "measure": "Levered IRR", "irr": 13.65}, {"exit_cap": 6.25, "measure": "Unlevered IRR", "irr": 9.42}, {"exit_cap": 6.5, "measure": "Levered IRR", "irr": 12.2}, {"exit_cap": 6.5, "measure": "Unlevered IRR", "irr": 8.7}, {"exit_cap": 6.75, "measure": "Levered IRR", "irr": 10.79}, {"exit_cap": 6.75, "measure": "Unlevered IRR", "irr": 8.02}, {"exit_cap": 7.0, "measure": "Levered IRR", "irr": 9.41}, {"exit_cap": 7.0, "measure": "Unlevered IRR", "irr": 7.38}, {"exit_cap": 7.25, "measure": "Levered IRR", "irr": 8.06}, {"exit_cap": 7.25, "measure": "Unlevered IRR", "irr": 6.76} ] }, "mark": {"type": "line", "point": true}, "encoding": { "x": {"field": "exit_cap", "type": "quantitative", "title": "Exit cap rate (%)", "scale": {"domain": [6.2, 7.3]}}, "y": {"field": "irr", "type": "quantitative", "title": "IRR (%)"}, "color": {"field": "measure", "type": "nominal", "title": "Return"} } } ``` A quarter point of exit cap moves the levered IRR by about 1.4 points and the unlevered by about 0.7: leverage doubles the sensitivity, in both directions. ### Step 7: the joint venture waterfall The Fund's equity is a joint venture: a capital partner (LP) contributes 90% (22,734.00) and the sponsor (GP) 10% (2,526.00). Tier 1: all distributions go 90/10 until the partners have their capital back plus an 8% compounded preferred return. Tier 2: the rest goes 80% to the LP and 20% to the GP. There is no catch-up. | Year | Distribution | Preferred return balance after payment | Tier 1 (90/10) | Tier 2 (80/20) | |---|---|---|---|---| | 1 | 1,116.22 | 26,164.58 | 1,116.22 | 0.00 | | 2 | 1,233.22 | 27,024.52 | 1,233.22 | 0.00 | | 3 | 1,353.73 | 27,832.75 | 1,353.73 | 0.00 | | 4 | 1,477.86 | 28,581.51 | 1,477.86 | 0.00 | | 5 | 35,509.13 | 0.00 | 30,868.03 | 4,641.10 | Year 1: the balance grows to `=25260*1.08` = 27,280.80 before the payment and is 26,164.58 after it; year 5: the balance before payment is `=28581.51*1.08` = 30,868.03, which tier 1 pays in full. | Partner | Contributed | Distributed | IRR | Multiple | |---|---|---|---|---| | LP (90%) | 22,734.00 | 36,157.03 | 10.50% | 1.59x | | GP (10%) | 2,526.00 | 4,533.13 | 13.32% | 1.79x | | Total | 25,260.00 | 40,690.16 | 10.79% | 1.61x | The GP's promote is 464.11: it receives 928.22 of tier 2 (`=20%*4641.10`) instead of its pro rata 464.11 (`=10%*4641.10`). The waterfall moves 0.29 points of IRR from the LP to the GP, the reward for finding the deal and managing it. ```mermaid flowchart TD A["Equity distribution from the property"] --> B{"Partners repaid with 8% preferred return?"} B -->|"No"| C["Tier 1: 90% LP, 10% GP, pro rata"] B -->|"Yes"| D["Tier 2: 80% LP, 20% GP"] C --> E["Reduce preferred return balance"] E --> B ``` ## Worked example B (half solved): a build-to-suit for Corvane Robotics *Example* situation (fictional): a developer proposes to build an assembly and test facility for Corvane Robotics, which will sign a 12-year lease from completion. Costs (USD thousand): land 4,000, hard costs 18,000, soft costs (design, permits, fees) 3,000, financing costs during construction 1,500. Stabilised NOI is 1,855. Comparable new industrial buildings with similar tenants sell at a 5.75% cap rate. | Item | Computation | Result | |---|---|---| | Total development cost | 4,000 + 18,000 + 3,000 + 1,500 | [ ] | | Yield on cost | 1,855 / [TDC] | 7.00% | | Value on completion | 1,855 / 5.75% | [ ] | | Development profit | [value] - [TDC] | [ ] | | Profit on cost | [profit] / [TDC] | [ ] | | Development spread | 7.00% - 5.75% | [ ] | | Value on completion if the market cap rate rises to 6.25% | 1,855 / 6.25% | 29,680.00 | Questions to answer: 1. Is the spread wide enough for the risks the developer takes (construction cost, delay, the tenant's credit)? Name one risk that a 125 basis point spread may not cover. [ ] 2. What happens to the profit if the market cap rate rises to 6.25% during construction? [ ] 3. Corvane could build the facility itself. What would it compare the lease cost with? [ ] ## Exercise C (unsolved): maximum loan and a higher rate C1. A lender offers a 5.50% 25-year amortising loan with three tests: LTV at most 65%, year 1 DSCR at least 1.35x and going-in debt yield at least 9%. What is the maximum loan under each test, which one binds, and what is the resulting levered IRR and equity multiple (keep the 1% fee)? C2. Keep 60% LTV, but the rate is 6.75% instead of 5.50%. What are the year 1 DSCR and the levered IRR? Would a lender with a 1.30x DSCR covenant accept the loan? What does the result say about leverage when the interest rate approaches the unlevered IRR? C3. Northfield receives 60,000 for the building and pays 4,100 of rent in year 1, rising 3% a year. In one paragraph, list what Northfield should compare to decide whether the sale-leaseback is cheap or expensive financing. ## Connections to other cards | Card or template | Connection | |---|---| | mba/mba-npv-irr-card | IRR, NPV and the reinvestment caveat behind every return in this card | | mba/mba-capital-structure-card | Why leverage raises expected equity return and risk together (Modigliani and Miller) | | mba/mba-capm-wacc-card, mba/mba-dcf-valuation-card | The required return behind the cap rate, and DCF valuation of uneven cash flows | | mba/mba-pe-fund-economics-card | Fund-level waterfalls, catch-up and carried interest, the same logic at fund scale | | mba/mba-lbo-model-card, mba/mba-paper-lbo | Debt sizing and returns for an operating company instead of a building | | mba/mba-fixed-income-card | Loan pricing, spreads and interest rate risk | | mba/mba-options-real-options-card | Development timing and land as an option | | finance/lease-accounting-memo | How the tenant accounts for the leaseback | | finance/credit-memo, finance/collateral-valuation-review, finance/covenant-compliance-certificate | The lender's side of the loan | | real-estate/property-valuation-report, real-estate/lease-abstract, real-estate/property-due-diligence-checklist | Practice documents behind the inputs | ## Common mistakes and misconceptions 1. **Treating the cap rate as a return.** It is a current yield; the total return adds growth and the change in value. 2. **Putting debt service or capital spending above the NOI line.** NOI is before both, so that properties can be compared regardless of financing. 3. **Using year 0 NOI for the exit value.** Buyers pay for next year's income: exit value is year 6 NOI over the exit cap rate for a five-year hold. 4. **Forgetting closing costs, selling costs and the financing fee.** Closing and selling costs alone cost about 0.6 points of unlevered IRR in Worked example A (8.66% without them, 8.02% with them); the fee lowers the levered IRR. 5. **Comparing the cap rate with the interest rate** to judge leverage. Compare the cap rate with the mortgage constant for the cash yield, and the unlevered IRR with the interest rate for the total return. 6. **Sizing the loan on one test.** Lenders apply all their tests; the lowest loan wins. 7. **Assuming the exit cap equals the going-in cap** for an ageing building in a rising-rate market. 8. **Reporting the levered IRR without the equity multiple.** A high IRR on a short hold can be a small profit. 9. **Ignoring the lease term against the loan term.** A loan that outlasts the lease carries re-leasing risk. 10. **Splitting a waterfall pro rata after the hurdle.** Above the hurdle the GP's share rises; that is the promote. 11. **Reading a development spread without the risks.** A spread is compensation for construction, leasing and market risk; a thin spread may not cover them. ## Self-test questions 1. Define NOI and list three items that are not deducted in it. 2. A property has NOI of 2,600 and trades at a 6.5% cap rate. What is its value? 3. Using Gordon, what total return does a 5.5% cap rate with 2.5% expected growth imply? 4. Define LTV, DSCR and debt yield, and say which one does not depend on the interest rate. 5. In Worked example A, what are the year 1 DSCR and cash-on-cash return? 6. Why is the levered IRR higher than the unlevered IRR in Worked example A even though year 1 leverage is negative? 7. How much does a 25 basis point change in exit cap rate move the levered IRR in Worked example A? 8. What is a mortgage constant, and why is it higher than the interest rate on an amortising loan? 9. Define yield on cost and development spread. 10. In the waterfall of Worked example A, why does the GP earn a higher IRR than the LP? 11. What three markets link in the DiPasquale and Wheaton framework? 12. A seller asks for a price that implies a 5.0% cap rate. The market for similar buildings is at 5.75%. What NOI growth or risk story would justify the price? ## My notes and next steps | Date | Model or exercise | Time (minutes) | Errors found | Next step | |---|---|---|---|---| | *Example:* YYYY-MM-DD | Worked example A from blank sheet | 45 | Valued the exit on year 5 NOI | Rebuild the exit block | | [YYYY-MM-DD] | [ ] | [ ] | [ ] | [ ] | ## Sources and further reading Primary works: - Gordon, M. J. (1959). Dividends, earnings, and stock prices. *The Review of Economics and Statistics*, 41(2), 99-105. https://doi.org/10.2307/1927792 - Modigliani, F. and Miller, M. H. (1958). The cost of capital, corporation finance and the theory of investment. *The American Economic Review*, 48(3), 261-297. - DiPasquale, D. and Wheaton, W. C. (1992). The markets for real estate assets and space: a conceptual framework. *Real Estate Economics* (then the *Journal of the American Real Estate and Urban Economics Association*), 20(2), 181-198. https://doi.org/10.1111/1540-6229.00579 Textbooks (further reading, by name only): Geltner, Miller, Clayton and Eichholtz, *Commercial Real Estate Analysis and Investments* (OnCourse Learning; use the latest edition); Brueggeman and Fisher, *Real Estate Finance and Investments*. ## Answer key Worked example B: total development cost 26,500.00; value on completion 32,260.87 (`=1855/5.75%`); profit 5,760.87; profit on cost 21.74%; spread 1.25 points (125 basis points). At a 6.25% market cap rate the value falls to 29,680.00 and the profit to 3,180.00, so a half-point move in cap rates removes 45% of the profit. A 125 basis point spread may not cover a large cost overrun, a delay that pushes completion into a weaker market or the risk that Corvane, a venture-backed company, cannot pay the rent over 12 years; a lender will ask for a guarantee or a deposit. Corvane would compare the lease cost with the after-tax cost of owning: the capital it would tie up at its own cost of capital, the debt it could raise, the operating flexibility and the residual value at the end of the lease. Exercise C: - C1: LTV test 39,000.00 (`=65%*60000`); DSCR test 38,751.36 (`=PV(5.5%,25,-3900/1.35)`); debt yield test 43,333.33 (`=3900/9%`). The DSCR test binds at 38,751.36 (64.59% LTV). Equity 22,536.15, debt service 2,888.89, levered IRR 11.31%, equity multiple 1.65x. - C2: debt service `=PMT(6.75%,25,-36000)` = 3,019.93; year 1 DSCR 1.29x, below a 1.30x covenant, so the lender would cut the loan. Levered IRR falls to 9.28% and the multiple to 1.52x. The gap between unlevered IRR (8.02%) and the rate (6.75%) has narrowed, so leverage adds only about 1.3 points of return for the same risk. - C3: Northfield should compare the implied cost of the leaseback (the IRR that equates 60,000 today with the rents it will pay and the value of the building it gives up at the end of the lease) with its cost of debt and its WACC; the operating flexibility it loses or gains (relocation, expansion, renewal options); the covenants and rating effects of the lease liability; and the tax and accounting effects, checked with qualified advisers. Self-test: 1. NOI is effective gross income less operating expenses. Not deducted: debt service, income tax, depreciation and capital expenditure (any three). 2. `=2600/6.5%` = 40,000. 3. About 8.0% (5.5% + 2.5%). 4. LTV is loan over value; DSCR is NOI over debt service; debt yield is NOI over loan. Debt yield does not depend on the interest rate (LTV depends on value, which depends on cap rates). 5. DSCR 1.45x (`=3900/2683.78`), cash-on-cash 4.42% (`=1116.22/25260`). 6. Because over the hold the property's total return (8.02%) exceeds the interest rate (5.50%); the year 1 cash yield comparison counts principal repayment as a cost. 7. About 1.4 points (10.79% to 9.41% for 25 basis points wider, 12.20% for 25 basis points tighter). 8. Annual debt service over the loan; it includes principal repayment as well as interest. 9. Yield on cost is stabilised NOI over total development cost; the spread is yield on cost less the market cap rate for the completed property. 10. Above the 8% hurdle, the GP receives 20% of distributions for a 10% share of the capital. 11. The market for space (rents), the market for assets (cap rates and prices) and the construction sector (new supply). 12. Expected NOI growth well above the market (below-market leases rolling to market rent, an expansion option), or a lower-risk income stream (a long lease to a strong tenant); otherwise the price is too high. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First build of Worked example A from the inputs | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Added monthly debt service and an interest-only period | ## Standard and licence note Based on standard commercial real estate finance practice and the primary works listed above, with the textbook framework of Geltner, Miller, Clayton and Eichholtz named as further reading. The text, the model, the numbers and the exercises are original; no textbook, lender or valuation material or published case is copied or paraphrased, and the Fund, Northfield Outdoor Co., Corvane Robotics and every number in this card are fictional. The template is independent and not affiliated with or endorsed by any lender, fund, valuation body, business school or publisher. Check current market evidence, loan terms, tax and accounting rules with qualified professionals before you rely on them. Template licence: MIT.