Ch4. The Income Approach — Direct Capitalization and DCF

The Logic of the Income Approach

Income Approach: Value is estimated by converting expected future income into a present value indication.

Theoretical basis: The Principle of Anticipation — the value of income-producing real estate is the present worth of the future benefits it is expected to produce.

Two income approach methods:
① Direct Capitalization:    Value = NOI ÷ Cap Rate
② Discounted Cash Flow (DCF): Value = Σ PV of annual NOI + PV of reversion

Best-suited property types:

Income-producing commercial real estate (office, retail, industrial, multifamily)
Any property for which reliable income and expense data are available

Net Operating Income (NOI)

Potential Gross Income (PGI)         [All income if fully leased at market rent]
  − Vacancy & Credit Loss            [Allowance for vacant units and bad debt]
= Effective Gross Income (EGI)
  + Other Income                     [Parking, laundry, ancillary revenue]
  − Operating Expenses (OE)          [Taxes, insurance, management, maintenance,
                                      reserves — NOT mortgage payments or depreciation]
= Net Operating Income (NOI)

Key: NOI excludes debt service and book depreciation

Direct Capitalization

Value = NOI ÷ Overall Capitalization Rate (OAR / Cap Rate)

Cap Rate: the investor's required return on a one-year income basis

Cap Rate Selection Methods

① Market Extraction (most reliable):
   Cap Rate = NOI / Sale Price  (derived from comparable sales)
   R = $60,000 NOI / $1,000,000 sale price = 6.0%

② Band of Investment (Mortgage-Equity):
   R = Mortgage Constant × LTV Ratio
     + Equity Dividend Rate × (1 − LTV Ratio)
   Blends the lender's and equity investor's required returns

③ Build-Up Method:
   R = Safe Rate + Illiquidity Premium + Management Burden + Risk Premium
   (Similar to a yield build-up for fixed income)

④ Discounted Cash Flow / IRR:
   Use the market-derived IRR from comparable investment sales as the cap rate

Worked example:

NOI = $60,000 per year
Cap Rate = 5.5%
Value Indication = $60,000 / 0.055 = $1,090,909 ≈ $1,091,000

Discounted Cash Flow (DCF)

DCF analysis projects income and expenses over a defined holding period, discounts each year’s NOI to present value, and also discounts a terminal (reversion) value at the end of the holding period.

Value = Σ [NOI_t / (1 + r)^t] + [Reversion / (1 + r)^n]

Reversion (Terminal Value):
= Projected NOI in year n+1 / Terminal Cap Rate
  (or estimated sale price based on market analysis)

r = Discount Rate (investor's required yield rate / IRR)

DCF example:

Holding period: 5 years
Annual NOI: $48,000 (constant)
Terminal value (end of year 5): $900,000
Discount rate: 8%

PV of NOI stream:
  $48,000/1.08 + $48,000/1.08² + ... + $48,000/1.08⁵ ≈ $191,760

PV of reversion:
  $900,000 / 1.08⁵ ≈ $612,520

Total Value Indication ≈ $804,280

Overall Rate vs. Equity Dividend Rate

Overall Capitalization Rate (OAR):
OAR = NOI / Total Property Value
→ Reflects the total property perspective (debt + equity combined)

Equity Dividend Rate (EDR):
EDR = Pre-Tax Cash Flow / Equity Investment
→ Reflects only the equity investor's perspective
   (NOI minus debt service, divided by down payment)

Value = NOI ÷ Cap Rate ★★★★★ : The direct capitalization formula. A lower cap rate implies lower perceived risk and therefore higher value for the same income. Memory trigger: Value = Income ÷ Rate — lower rate → higher value

NOI Derivation ★★★★★ : PGI → EGI (subtract vacancy) → NOI (subtract operating expenses). Debt service and depreciation are never deducted from NOI. Memory trigger: NOI = EGI − OE (no mortgage, no depreciation)

Market Extraction ★★★★☆ : The most direct method — derive the cap rate by dividing a comparable property’s NOI by its verified sale price. Reflects what the market is actually paying. Memory trigger: Market cap rate = NOI ÷ sale price (from comps)

Practice Quiz

Q. PGI = $80,000; vacancy & credit loss = 5%; other income =$ 3,000; operating expenses = $18,000. What is NOI?

EGI = $80,000 × 0.95 =$ 76,000. NOI = $76,000 +$ 3,000 − $18,000 =$ 61,000.

Q. Using the NOI above with a 6.5% cap rate, what is the value indication by direct capitalization?

Value = $61,000 / 0.065 ≈$ 938,462 ≈ $938,000 (rounded).