Real Estate and Infrastructure: formula sheet

Key formulas

Four-form grid

Private equity | Private debt | Public equity | Public debt

Place every real estate investment in one cell first. Direct ownership and mortgage loans are private; REITs and MBS are public.

Direct vs indirect

Direct = own property or make loan yourself; Indirect = hold via fund, REIT or security

Indirect gives pooling, smaller ticket size and professional management at the cost of fees and less control.

Equity return sources

Total return ≈ income return + capital appreciation

Income is net rent after operating costs. Debt return is interest and principal, with no share in appreciation.

Appraisal smoothing effect

Appraisal-based returns → lower reported volatility and correlation than true values

Applies to private real estate. Unsmoothing is used to estimate true risk.

Net operating income

NOI = Potential gross income − vacancy and collection loss + other income − operating expenses

Exclude depreciation, interest and income taxes.

Direct capitalization value

Value = NOI₁ ÷ Cap rate

Use next year's (forward) NOI unless the question states otherwise.

Cap rate

Cap rate = NOI ÷ Value

Approximately equals discount rate minus NOI growth rate (for a constant-growth perpetuity).

Terminal value (DCF)

Terminal value = NOI in year after sale ÷ terminal cap rate

Discount it back with the other cash flows. Deduct selling costs if given.

DCF value

Value = Σ CFt ÷ (1 + r)^t + Terminal value ÷ (1 + r)^N

Use the required return r, not the cap rate, as the discount rate.

Cost approach

Value = Replacement cost new − depreciation and obsolescence + land value

Depreciation here covers physical, functional and external obsolescence.

Appraisal-based index source

Return ≈ income return + appraised value change

Values come from appraisers, not trades. Expect smoothing and lag.

Effect of smoothing on risk

Reported σ < true σ; reported correlation with equities < true correlation

Smoothing understates volatility and correlation, so Sharpe ratio is overstated.

Repeat-sales method

Uses price change of the same property across two sales

Needs properties that sell more than once; may miss changes in the property.

Hedonic method

Price = f(property characteristics) estimated by regression

Adjusts for quality differences; depends on model and data.

REIT index basis

Return = change in REIT share price + dividends

Market-priced, timely, more equity-like and volatile.

FFO

FFO = Net income + Depreciation + Amortization + Losses on property sales − Gains on property sales (and other non-cash or non-recurring items)

Adds back real estate depreciation and removes one-off sale gains and losses.

AFFO

AFFO = FFO − Straight-line rent adjustments − Recurring maintenance capex (and tenant improvements, leasing commissions)

Closer to recurring cash earnings. Other adjustments (e.g., non-cash interest) may appear; follow the question.

P/FFO and P/AFFO

P/FFO = Share price ÷ FFO per share; P/AFFO = Share price ÷ AFFO per share

Lower multiples can signal cheaper value, but compare with similar REITs.

NAV per share

NAV per share = (Estimated market value of assets − Liabilities) ÷ Shares outstanding

Use market values, not book values.

Property value via cap rate

Value = Forward NOI ÷ Cap rate

Use the NOI the question specifies (forward or trailing) and no depreciation or interest in NOI.

Levered return

Return on equity ≈ [Property return × Assets − Interest rate × Debt] ÷ Equity

Equity = Assets − Debt. Shows how leverage magnifies gains and losses.

Implied value from multiple

Target price = Target P/FFO × FFO per share

Often used with a peer-average multiple.

Economic infrastructure

Transportation + Utilities (energy, water) + Communication

Supports economic activity. Examples: toll road, airport, power grid, cell tower.

Social infrastructure

Education + Health care + Justice and corrections + Social housing

Supports community welfare. Often paid by government via availability payments, which are also used for some economic assets.

Greenfield vs brownfield

Greenfield = new build; Brownfield = existing operating asset

Greenfield: higher risk, higher expected return, delayed cash flows. Brownfield: lower risk, immediate income.

Typical risk and return ordering

Brownfield (lower risk, income-driven) < Greenfield (higher risk, growth-driven)

A general tendency, not a guarantee in every deal.

DCF asset value

Value = Σ CFt ÷ (1 + r)^t, for t = 1 to N

Use cash flows over the concession or asset life. Add a terminal value only if the asset continues beyond the forecast period.

Value with terminal value

Value = Σ CFt ÷ (1 + r)^t + TV ÷ (1 + r)^N, where TV = CF(N+1) ÷ (r − g)

Needs r > g. Terminal value is not used when the concession ends with no residual value.

Greenfield vs brownfield

Greenfield: higher risk, higher return potential. Brownfield: lower risk, more stable income.

A rule of thumb for ranking required returns, not a formula.

Quick revision

• Real estate can be held in private or public form, as equity or debt.
• Infrastructure assets are long-lived, provide essential services and often have high barriers to entry.
• Income approach: value = NOI ÷ cap rate for direct capitalization.
• NOI is rental income less operating expenses, before financing costs and income taxes.
• A lower cap rate, with NOI unchanged, gives a higher value.
• Cost approach estimates value from replacement cost less depreciation, plus land.
• Sales comparison approach adjusts recent sales of similar properties.
• Appraisal-based indexes are smoothed, so they understate volatility and correlation.
• Transaction-based indexes use actual sales and reflect market changes more quickly.
• REITs are listed, trade like equities and usually offer more liquidity than direct property.
• Leverage magnifies both gains and losses in property and infrastructure.
• Greenfield projects carry construction risk; brownfield assets are existing and usually carry less.

Common mistakes

• Treating REITs as direct real estate ownership. Fix: You own shares of a company that owns property. That is indirect, public equity.
• Assuming private real estate is truly less volatile than listed real estate. Fix: Appraisals lag market prices and smooth returns. Reported volatility and correlation are understated.
• Deducting depreciation or interest when computing NOI Fix: NOI uses only operating expenses. Leave out depreciation, financing costs and income taxes.
• Using the wrong year's NOI Fix: Use the forward (next year) NOI for Value = NOI₁ ÷ cap rate unless told otherwise.
• Saying smoothing overstates volatility. Fix: Smoothing dampens changes, so reported standard deviation is understated and the Sharpe ratio overstated.
• Calling NCREIF a transaction-based or REIT index. Fix: Treat NCREIF as an appraisal-based index of unleveraged institutional direct property, with income return included.
• Adding gains on property sales to FFO instead of subtracting them. Fix: FFO removes non-recurring items: subtract gains, add back losses.
• Deducting growth or acquisition capex when computing AFFO. Fix: Deduct only recurring maintenance capex, tenant improvements and similar items needed to sustain income.
• Calling a hospital or airport the wrong type of infrastructure Fix: Ask whether it mainly supports commerce (economic) or community welfare (social). Hospitals and schools are social; airports and ports are economic.
• Thinking greenfield means land that is undeveloped farmland only Fix: Greenfield simply means a new project built from scratch. Brownfield means an existing asset, even if it is being expanded.

Exam tips

• Always start with the equity/debt and public/private grid; most questions are solved by placement alone.
• Watch for stems about appraisal-based data. The expected answer is usually understated risk.
• Keep vehicle liquidity separate from underlying asset liquidity.
• Options with absolute words such as always or guaranteed about inflation hedging or diversification are usually wrong.
• With no penalty for wrong answers, never leave a question blank; eliminate one option and choose.
• Questions are three-option MCQs, so quickly compute NOI and test it against the options; the wrong options often come from including depreciation or using the wrong NOI year.
• Know the direction rule: a higher cap rate means a lower value.
• For approach-choice items, match the approach to the property: income for leased assets, comparison for active markets, cost for new or special-use buildings.