13.1 Direct Capitalization and Multipliers

From NOI to Value: Direct Capitalization

Chapter 12 built stabilized net operating income. ECO VI.d Direct capitalization methods asks you to turn that income (or a gross income measure) into an indicated value in a single conversion step. ECO VI.g then requires you to apply those methods to fee simple, leased fee, and leasehold—Section 13.4 owns the rights detail; this section owns the math engines.

Direct capitalization estimates value by capitalizing a single year’s (or stabilized period’s) income with a capitalization rate or by multiplying income by an income multiplier. It does not explicitly forecast year-by-year cash flows and a reversion (that is yield capitalization / DCF, Section 13.3).

Income Approach weight reminder: about 21 scored items (19.1%) at Certified General, 9 (8.2%) at Certified Residential, and 5 (4.5%) at Licensed Residential. Direct cap and multipliers are high-frequency calculation items at all levels that test Income.

The IRV Relationship (Memorize Cold)

Appraisal “IRV” is the three-way relationship among Income (I), Rate (R), and Value (V):

Units must match. If I is annual NOI, R is an annual overall rate and V is property value. If someone hands you monthly income, annualize before using an annual Ro—or convert the rate—never mix months and years.

Worked IRV Set 1 — All Three Directions

Facts: Stabilized NOI = $96,000; market overall rate Ro = 8.0%.

1. Value: V = I ÷ R = $96,000 ÷ 0.08 = $1,200,000
2. Check rate: R = I ÷ V = $96,000 ÷ $1,200,000 = 0.08 = 8%
3. Check income: I = R × V = 0.08 × $1,200,000 = $96,000

Worked IRV Set 2 — Solve for Rate from a Sale

Comparable sold for $2,500,000. Reconstructed stabilized NOI at sale = $200,000.

Extracted Ro = $200,000 ÷ $2,500,000 = 0.08 = 8.0%

If the subject’s stabilized NOI is $180,000 and this 8% is the indicated overall rate:
Subject value = $180,000 ÷ 0.08 = $2,250,000

Worked IRV Set 3 — Implied Income

A property is under contract at $800,000. Investors require 9% overall. What NOI supports that price at 9%?

I = R × V = 0.09 × $800,000 = $72,000

If reconstructed NOI is only $60,000, either price is high, rate must be higher (riskier/lower growth expectations), or both—exam stems often ask only the arithmetic implication.

Worked IRV Set 4 — Rate Sensitivity

NOI fixed at $120,000:

Higher cap rate → lower value for the same income. Cap rates rise when risk rises, income growth expectations fall, or financing/equity requirements toughen (Section 13.2).

Overall Capitalization Rate (Ro)

The overall capitalization rate (Ro) is the ratio of a single year’s NOI to the property’s overall value (or to sale price when extracting):

Ro = NOI ÷ Value (or Price)
Value = NOI ÷ Ro

Ro is an overall rate on the entire property (land + improvements as a unit), not a land residual rate or a building residual rate unless the stem says residual technique.

For basic direct cap of whole-property NOI, you need Ro and NOI on a consistent definition (before/after reserves, market vs contract income—match comps).

Worked Problem — Full Direct Cap Path

Subject (fee simple, stabilized):

• PGI $500,000
• V&C 5% → EGI = $475,000
• OE $175,000 → NOI = $300,000
• Market Ro from comps: 7.5%

Indicated value = $300,000 ÷ 0.075 = $4,000,000

Trap: Capitalizing EGI ($475,000 ÷ 0.075 = $6,333,333) is wrong if Ro is an NOI rate. Capitalizing PGI is worse. Match the income level to the rate level.

Net Income Multiplier (NIM)

NIM = Value ÷ NOI = 1 ÷ Ro
If Ro = 8%, NIM = 1 / 0.08 = 12.5
Value = NOI × 12.5 = same as NOI ÷ 0.08.

Exams may say “net income multiplier of 12” instead of “cap rate of 8.33%.” Convert: Ro = 1 / 12 ≈ 8.33%.

Gross Rent Multiplier (GRM)

GRM relates sale price to gross rent. Residential teaching problems often use monthly rent:

GRM = Sale price ÷ Gross monthly rent
Value = Subject monthly rent × GRM

Some markets and commercial problems use annual GRM (price ÷ annual rent)—read the stem. A monthly GRM is roughly 12× an annual GRM for the same property if rent is level.

Worked GRM Extraction and Application

Reconciled GRM ≈ 153 (simple mid/average illustration).

Subject market rent $2,480/month → Value = 2,480 × 153 = $379,440 ≈ $379,000.

When GRM Is Appropriate

Critical assumption: Comps and subject have similar expense ratios and vacancy so that gross rent is a stable proxy for net income. If Comp A is owner-paid utilities and Comp B is tenant-paid, raw GRMs are not comparable without adjustment.

Worked Trap — Expense Structure Breaks GRM

Two duplexes each rent for $4,000/month total.

GRM both ≈ 480k/4k = 120 vs 620k/4k = 155—same rent, different prices because expenses (and risk) differ. Blind GRM application fails; NOI capitalization (or adjusted multipliers) is safer.

Gross Income Multiplier (GIM)

GIM = Sale price ÷ Annual gross income
Value = Subject annual gross income × GIM

“Gross income” may mean PGI or EGI—extract and apply on the same definition. Commercial properties often use annual GIM; residential small income may use monthly GRM instead.

Worked GIM Problem

Indicated GIM ≈ 9.2
Subject EGI = $220,000 → Value = 220,000 × 9.2 = $2,024,000

If you accidentally used subject PGI $240,000 × 9.2 while comps were on EGI, you overstate value.

GIM vs Cap Rate Relationship (Conceptual)

If OE ratio is stable, NOI ≈ EGI × (1 − OE ratio), and Ro ≈ (1 − OE ratio) / GIM when GIM is on EGI.

Example: GIM on EGI = 10; OE ratio = 40%; NOI ratio = 60% of EGI.
Ro ≈ 0.60 / 10 = 6%.
Check: EGI $100,000; NOI $60,000; Value = 100,000 × 10 = $1,000,000; Ro = 60,000/1,000,000 = 6%.

You do not need this conversion on every item, but it explains why changing expenses changes the valid GIM even when rents match.

Multipliers vs Overall Rates — Decision Framework

Both are direct capitalization under ECO VI.d. Neither is “better” in the abstract—market behavior and data quality choose the tool.

More Worked Problems (Exam Drill)

Problem A — NOI Cap

NOI $84,000; Ro 7%; value?
$84,000 ÷ 0.07 = $1,200,000

Problem B — Extract Ro, Apply to Subject

Comp: price $1,600,000; NOI $128,000 → Ro = 8%.
Subject NOI $140,000 → V = $140,000 ÷ 0.08 = $1,750,000

Problem C — Monthly GRM

Four comps GRMs: 140, 145, 142, 148; reconcile to 144.
Subject rent $3,100/month → V = 3,100 × 144 = $446,400

Problem D — Annual vs Monthly Confusion

Annual rent $36,000 (= $3,000/month). Price $450,000.
Annual GRM/GIM-style factor = 450,000 ÷ 36,000 = 12.5
Monthly GRM = 450,000 ÷ 3,000 = 150
Note: 12.5 × 12 = 150. If the stem says GRM 150 and gives annual rent, convert rent to monthly or GRM to annual.

Problem E — Wrong Income Level

Ro extracted as NOI/price = 8%. Subject EGI $400,000; OE $150,000; NOI $250,000.
Correct V = $250,000 ÷ 0.08 = $3,125,000
Wrong V using EGI = $5,000,000 — classic trap.

Problem F — Two Rates, Same NOI

NOI $200,000. Bullish market Ro 6% → $3,333,333. Bearish Ro 9% → $2,222,222. Difference ≈ $1.11 million from rate alone.

Problem G — NIM

NIM 11.5; NOI $92,000 → V = 92,000 × 11.5 = $1,058,000
Implied Ro = 1/11.5 ≈ 8.70%

Consistency Rules (Write These on Scratch Paper)

1. I, R, V same timing (annual with annual).
2. Same income definition used to extract R or multiplier as used on the subject.
3. Same rights (fee simple market income vs leased fee contract income—Section 13.4).
4. Stabilized income with market Ro unless the problem is explicitly current/year-one.
5. Reserves: if comps’ Ro is after reserves, subject NOI after reserves.

Common Exam Traps — Direct Cap & Multipliers

• Dividing monthly rent into price but applying the factor to annual rent
• Applying Ro to EGI or PGI
• Using GRM across properties with different expense regimes
• Extracting Ro with seller’s books that include debt service (fake NOI)
• Treating GIM on PGI comps as usable with subject EGI without adjustment
• Forgetting that higher Ro lowers value
• Confusing multiplier (price/income) with rate (income/price)—they are reciprocals only for the same income measure (NIM ↔ Ro, not GRM ↔ Ro)

Formula Card

1. V = I / R R = I / V I = R × V
2. Ro = NOI / Price; Value = NOI / Ro
3. NIM = 1 / Ro; Value = NOI × NIM
4. GRM = Price / Gross rent (match monthly/annual)
5. GIM = Price / Annual gross income (match PGI vs EGI)
6. Multipliers need similar expenses/vacancy; overall rates need supportable NOI

Bridge

You can convert a single income measure into value with IRV, Ro, GRM, and GIM. Section 13.2 develops where Ro comes from—market extraction and the band of investment—so the rate is not a guess. Section 13.3 introduces yield capitalization when one stabilized year is not enough. Section 13.4 applies direct and yield tools to fee simple, leased fee, and leasehold and reconciles the income approach indication.