Ch10. Appraisal Theory Capstone — Comparing the Three Approaches and Key Exam Points

Comparing the Three Approaches

┌────────────────────┬──────────────────┬──────────────────┬──────────────────┐
│ Feature            │ Cost Approach    │ Sales Comparison │ Income Approach  │
├────────────────────┼──────────────────┼──────────────────┼──────────────────┤
│ Theoretical Basis  │ Substitution     │ Substitution     │ Anticipation     │
│ Value Indication   │ Depreciated Cost │ Adjusted Sale    │ Capitalized /    │
│                    │                  │ Price            │ Discounted NOI   │
│ Core Formula       │ RCN − Deprec.    │ Sale × Adj.      │ NOI ÷ Cap Rate   │
│                    │ + Land           │ Factors          │ or DCF           │
│ Best Suited For    │ Special-purpose, │ Residential,     │ Income-producing │
│                    │ new construction,│ active sales     │ commercial and   │
│                    │ insurance        │ markets          │ investment RE     │
│ Key Strength       │ Grounded in      │ Direct market    │ Investor logic   │
│                    │ actual cost data │ evidence         │ and cash-flow    │
│ Key Limitation     │ Depreciation is  │ Requires         │ NOI and rate     │
│                    │ judgmental       │ adequate comps   │ estimation risk  │
└────────────────────┴──────────────────┴──────────────────┴──────────────────┘

Master Formula Reference

Cost Approach

Depreciated Cost = Replacement Cost New × (1 − Depreciation Rate)
Depreciation Rate (straight-line) = Effective Age / Total Economic Life

Curable depreciation  = Cost to cure
Incurable depreciation = Market-measured loss in value

Sales Comparison Approach

Adjusted Price = Sale Price × Conditions-of-Sale Adj.
                           × Market Conditions Adj.
                           × Location Adj.
                           × Physical Characteristics Adj.

Conditions-of-Sale Adj. = 100 / (100 ± Distortion %)
Market Conditions Adj.  = Current Index / Sale-Date Index

Income Approach

Direct Capitalization:
Value = NOI / Overall Cap Rate (OAR)

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

NOI Derivation:
PGI − Vacancy & Credit Loss = EGI
EGI + Other Income − Operating Expenses = NOI

Rental Build-Up (Cost to Rent):
Market Rent = Property Value × Required Return + Annual Landlord Expenses

Cap Rate vs. Discount Rate — The Key Distinction

Overall Capitalization Rate (Cap Rate / OAR):
- Converts a single year's NOI into a value indication
- Used in Direct Capitalization (one-period model)
- Derived by market extraction: Cap Rate = NOI / Sale Price
- Reflects: yield rate minus expected growth rate

Discount Rate (Yield Rate / IRR):
- Converts a multi-period income stream into present value
- Used in Discounted Cash Flow analysis
- Represents the investor's total required return (IRR)
- Reflects: risk-free rate + risk premium for the asset class

Relationship (Gordon Growth Model analog):
Cap Rate ≈ Discount Rate − Expected Long-Term Growth Rate

Example:
  Required IRR: 9.0%
  Expected annual NOI growth: 2.5%
  Implied Cap Rate ≈ 6.5%

Approach Selection by Property Type

Residential (single-family, condo):
  Primary:    Sales Comparison (abundant comps, buyers reference sales)
  Secondary:  Cost (useful for new construction valuation check)

Commercial Income Property (office, retail, industrial):
  Primary:    Income Approach (investors price on cash flow)
  Secondary:  Sales Comparison (market transaction check)

Special-Purpose (church, school, hospital, factory):
  Primary:    Cost Approach (few comps or income transactions)
  Secondary:  Income (if income can be estimated)

Land (vacant site):
  Primary:    Sales Comparison (vacant land comps)
  Secondary:  Land Residual (Income Approach technique)
              Extraction or Allocation (when comps are unavailable)

Reconciliation Principles

Reconciliation sequence:
① Review each approach indication for internal consistency
② Assess data reliability and quantity for each approach
③ Weight each approach according to its relevance to the assignment
④ State the final value conclusion and its rationale

Reconciliation considerations:
- Outlier indications: investigate before discarding
  (outliers often reveal market trends or data errors)
- Assignment-specific weighting:
  Mortgage appraisal → conservative; lean toward Sales Comparison
  Eminent domain      → all three required; market value standard
  Estate / tax        → IRS-compliant; Sales Comparison primary for residential
- Market conditions: in thin markets, Cost Approach gains relative weight

Common Errors and How to Avoid Them

① Including debt service in NOI
   → NOI = EGI − Operating Expenses only
     (mortgage payments are a financing decision, not an operating cost)

② Conditions-of-sale adjustment direction error
   Distressed sale (price 10% below market):
   → Adjustment = 100/(100−10) = 100/90 = +11.1% (upward)
   Above-market sale (price 10% above market):
   → Adjustment = 100/(100+10) = 100/110 = −9.1% (downward)

③ Mixing up cap rate extraction methods
   Market Extraction: Cap Rate = NOI ÷ Sale Price (backward from comps)
   Band of Investment: weighted average of debt and equity returns

④ Depreciating land
   → Land is NEVER depreciated in appraisal — it has indefinite economic life

⑤ Curable vs. incurable depreciation misapplication
   Curable → always measure as cost to cure (not the larger market loss)
   Incurable → measure as market-observed value loss (may be larger than repair cost)

⑥ Chronological age vs. effective age confusion
   → Use Effective Age (condition-based), not birth-certificate age

⑦ Forgetting lease concessions in effective rent
   → Effective Rent = Headline Rent minus amortized concessions (TI, free rent)

Three Approaches — Theoretical Basis ★★★★★ : Cost and Sales Comparison both rest on the Principle of Substitution. The Income Approach rests on the Principle of Anticipation. Only the Income Approach uses a different theoretical basis. Memory trigger: Cost · Sales Comp = Substitution · Income = Anticipation

NOI Exclusions ★★★★★ : Debt service (mortgage principal and interest) and book depreciation are never deducted in computing NOI. Only operating expenses are subtracted. Memory trigger: NOI = EGI − OE; never touch debt service or depreciation

Conditions-of-Sale Adjustment Direction ★★★★★ : If the comparable sold below market (distressed), adjust upward (denominator < 100 → result > 1). If it sold above market, adjust downward (denominator > 100 → result < 1). Memory trigger: Below-market comp → numerator stays 100, denominator shrinks → factor > 1

Capstone Practice Quiz

Q. PGI = $90,000; vacancy = 10%; other income =$ 4,000; operating expenses = $22,000. What is NOI?

EGI = $90,000 × 0.90 =$ 81,000. NOI = $81,000 +$ 4,000 − $22,000 =$ 63,000.

Q. Using the NOI above at a 7.0% cap rate, what is the direct capitalization indication?

Value = $63,000 / 0.07 =$ 900,000.

Q. A comparable sold for $300,000 three years ago under a distressed condition (5% below market). Annual appreciation has been 4%. Location adjustment: subject is 2% superior. Physical adjustment: subject is 3% inferior. What is the adjusted price?

Conditions-of-Sale: 100/95 ≈ 1.0526. Market Conditions (3 yrs at 4%): 1.04³ ≈ 1.1249. Location: 1.02. Physical: 0.97. Adjusted Price = $300,000 × 1.0526 × 1.1249 × 1.02 × 0.97 ≈$ 352,000.