7.2 Allocation and Extraction Methods

Why Secondary Land Methods Exist

Direct sales comparison of vacant land is preferred when comps exist, but many residential and older urban markets produce few pure lot sales. Buyers purchase improved properties, and the land component is embedded in the total price. AQB ECO III lists allocation and extraction among land/site valuation methodologies for exactly this reason.

Both methods reverse-engineer a land indication from improved sales (or from the subject’s improved value). They are not guesses: they require market support for ratios (allocation) or for cost and depreciation (extraction). On exam day, expect arithmetic plus a judgment question about which method fits the data.

Allocation Method

Definition

Allocation estimates land or site value by applying a ratio of land value to total property value (or sometimes land value to improvement value) derived from the market to the property being analyzed.

Basic form:

Land value = Total property value × Land-to-value ratio

Equivalently, if the market supports land as L% of total and improvements as (1 − L%):

Land value = Total value × L%

Ratios may be observed from:

• Markets with occasional vacant lot sales paired with improved sales of similar houses
• Assessed values (use cautiously; exam may warn that assessments lag or are mass-appraisal averages)
• Developer budgets and residual studies
• Paired extraction studies on many sales (building a ratio set)

When allocation is appropriate

• Few or no vacant land sales, but many similar improved sales
• Relatively homogeneous housing or property type (similar age, quality, lot utility)
• Stable market where land share of value is predictable (for example, mature subdivision where lots are similar)
• Need for a supportable land component in cost approach when direct land comps are thin

When allocation is weak

• Mixed ages/qualities so land ratios swing wildly
• Subject has excess land, unusual view, or nonconforming lot vs the ratio sample
• Hot teardown markets where land ratio approaches 100% of price—ratio from ordinary improved sales misstates land
• Commercial properties with highly variable building-to-land relationships

Worked example 1 — Allocation from a ratio

Market evidence: In a suburban subdivision of similar 15–20-year-old homes on 8,000–9,000 SF lots, analysis of lot sales and improved sales supports a typical land-to-total-value ratio of 25%.

Subject: Improved residential property; current market value by sales comparison (total) = $400,000. Lot is typical for the tract; no excess land.

Allocation:

Land value = $400,000 × 0.25 = $100,000

Improvement contribution (residual check) = $400,000 − $100,000 = $300,000

Exam note: The $400,000 total must itself be credible. Allocation does not create total value; it splits a supported total (or splits comparable sales to read land).

Worked example 2 — Building the ratio from a land sale and improved sales

Vacant finished lot sale in the same tract: $95,000.
Typical improved sale of similar house on similar lot: $380,000.

Implied land-to-value ratio = $95,000 ÷ $380,000 = 25.0%.

Another improved sale at $400,000 with same lot type → allocated land = $400,000 × 0.25 = $100,000.

If a second lot sold for $110,000 against improved homes at $400,000, ratio = 27.5%. Reconcile ratios (for example, 25–27%) before applying to the subject.

Worked example 3 — Allocation on a comparable improved sale (then adjust land)

Sometimes you allocate land from each improved comp, then treat those land residuals like land sales:

If Comp C has a superior view lot worth +$10,000 land premium, adjusted land indication ≈ $105,000 − $10,000 = $95,000. Reconcile land indications $90,000–$100,000 for a typical subject lot.

Ratio applied to wrong base (trap)

If the stem gives improvement value only or cost new without depreciation, do not multiply the land ratio by the wrong base. Land-to-total value × total market value is the standard form. Land-to-improvement ratios require the matching algebra:

If land/improvement ratio = 1/3 (land is one-third of improvement value), and improvements contribute $300,000, land = $100,000, total = $400,000 (land is 25% of total). Read the stem’s ratio definition carefully.

Extraction Method

Definition

Extraction (sometimes called abstraction) estimates land value by subtracting the depreciated cost (contributory value) of improvements from the sale price of an improved property:

Land value = Sale price of improved property − Depreciated cost of improvements

Depreciated cost means reproduction or replacement cost new minus accrued depreciation (physical, functional, external) as of the date of sale—aligned with cost-approach thinking.

When extraction is appropriate

• Improved sales exist, but vacant land sales do not
• Improvements are of a type whose cost new can be estimated (Marshall-type data, local contractor costs)
• Depreciation can be supported (age-life, market extraction of depreciation, breakdown)
• Sales of properties with minor or typical improvements, or teardowns where building contribution is small
• Rural or transitional properties where a modest building sits on a large tract and land dominates

When extraction is weak

• Complex special-purpose buildings with uncertain cost and depreciation
• Old structures where depreciation could be 40% or 80% with equal “plausibility”—land residual becomes noise
• Super-adequate or unique improvements not reflective of subject land
• Ignoring entrepreneurial incentive or site improvements that are part of “improvements” vs land

Worked example 4 — Classic extraction

Improved sale price: $525,000
Replacement cost new of house and site improvements (driveway, landscaping): $400,000
Accrued depreciation (all causes): 30% of cost new
Depreciated cost of improvements: $400,000 × (1 − 0.30) = $400,000 × 0.70 = $280,000

Extracted land value: $525,000 − $280,000 = $245,000

If the subject site is similar to the sale’s site, $245,000 is a land indication. If the sale’s lot is larger or has a view, adjust the extracted land before applying to the subject.

Worked example 5 — Extraction with site improvements separated

Careful appraisers separate building from site improvements (utilities laterals already in, fencing, flatwork). Site improvements may be extracted with the building or partially left with land depending on whether the subject is valued as site (already improved with off-sites) or raw land.

Sale price: $300,000
House RCN: $220,000; depreciation 40% → depreciated house = $132,000
On-site improvements RCN: $30,000; depreciation 20% → depreciated = $24,000
Total depreciated improvements: $156,000
Land (site) extraction: $300,000 − $156,000 = $144,000

Worked example 6 — Teardown-style extraction

Sale price: $450,000
RCN of obsolete cottage: $120,000
Depreciation essentially 100% for contributory value in a teardown market (building contributes $0); demo cost buyer will incur: $20,000

If buyers pay $450,000 and will spend $20,000 to clear, land value indication ≈ $450,000 − $0 building contribution, but the cash outlay for land-ready site is related to $450,000 + $20,000 demo depending on whether price already reflects demo burden. Exam stems usually simplify:

Land ≈ price − contributory improvement value
If contributory value is zero: land ≈ $450,000, with demo as a buyer cost sometimes subtracted from price to read pure land: $450,000 − $20,000 = $430,000 if the stem frames demo as immediate expenditure after purchase.

Read the stem’s framing; both patterns appear. The principle: extraction isolates land by removing improvement contribution.

Worked example 7 — Side-by-side allocation vs extraction

Improved sale: $500,000
RCN improvements: $350,000
Depreciation: 20% → depreciated improvements = $280,000
Extraction land: $500,000 − $280,000 = $220,000
Implied L/V ratio: $220,000 ÷ $500,000 = 44%

Allocation using a neighborhood ratio of 30%: $500,000 × 0.30 = $150,000 land

Conflict! Extraction says $220,000; allocation says $150,000. Possible explanations:

1. Depreciation understated (building contributes less than $280,000) → true land higher (supports extraction direction) or lower if opposite error
2. Neighborhood 30% ratio from newer homes with costlier buildings does not fit this sale
3. Sale includes excess land or superior location not in the ratio sample
4. Cost new overstated → extraction overstates land

Exam skill: Recognize that methods can diverge; reconcile with which inputs are more reliable. If cost/depreciation is solid and sale is recent, extraction may win. If depreciation is guesswork but ratios are tight across dozens of similar homes, allocation may win.

Step-by-Step Procedures (Exam Checklist)

Allocation procedure

1. Confirm HBU and that subject’s land share should resemble the sample.
2. Derive land-to-value ratio(s) from market evidence.
3. Estimate total property value (usually sales comparison on improved basis) for subject—or allocate from each comp sale.
4. Multiply total value × ratio = land value.
5. Reasonableness check: land vs building split; compare to any scarce lot sales.

Extraction procedure

1. Select improved sales with sites comparable to the subject (or adjustable).
2. Estimate cost new of improvements as of sale date (match sale’s building).
3. Estimate accrued depreciation as of sale date.
4. Subtract depreciated improvement cost from sale price.
5. Adjust extracted land for site differences; reconcile multiple extractions.

Comparison Table — Which Method When?

Relationship to Cost Approach

In the cost approach:

Value ≈ Site value + Depreciated cost of improvements

Allocation and extraction are ways to get site value when you cannot grid vacant sales. Circular reasoning warning: do not (1) allocate land from a total value that was itself produced only by a cost approach that already assumed the land value, without independent support. On the exam, total value for allocation usually comes from sales comparison of the improved property.

Common Exam Traps

• Multiplying the land ratio by RCN instead of by total market value.
• Forgetting depreciation in extraction (subtracting full RCN → understates land).
• Double-counting site improvements in both land and building.
• Applying a commercial land ratio to a residential subject.
• Using allocation on a property with excess land without valuing the excess separately.
• Treating extraction of one weird sale as definitive without reconciliation.

Numeric Practice Set (Work Before Looking)

P1. Total value $360,000; land ratio 28%. Land?
→ $360,000 × 0.28 = $100,800.

P2. Sale $640,000; RCN $500,000; depreciation 25%. Land via extraction?
→ Depreciated improvements = $500,000 × 0.75 = $375,000; land = $640,000 − $375,000 = $265,000.

P3. Extracted land $120,000 on a $400,000 sale. Land ratio?
→ $120,000 ÷ $400,000 = 30%.

Bridge

Allocation and extraction recover land from improved market behavior. When the problem is a development tract, leased fee land, or a land residual against a proposed building, ECO methods shift to residual, subdivision development analysis, and ground rent capitalization—next section.