Lesson 17 Exercises – The Land Residual Techniques of Income Capitalization (The Income Approach to Value)

Appraisal Training: Self-Paced Online Learning Session

Check Your Knowledge

Open All Solutions Close All Solutions
  1. You are asked to appraise an unimproved 100' × 125' vacant lot. The zoning regulations allow three possible uses of the lot:
    1. A service station;
    2. A one story office building covering 60 percent of the lot; and,
    3. A two story apartment house covering 80 percent of the lot.

    Proposal 1 – Service Station
    Current ground rents for service station sites are 15 cents per square foot of ground area per month. Lessee pays all expenses except the property taxes.

    Proposal 2 – Office Building
    The cost of a 7,500 square foot office building is $450,000. An economic monthly rent is $1.20 per square foot of gross building area. Normal operating expenses (excluding taxes) are estimated to be 25 percent of the effective gross income. A five percent vacancy allowance appears reasonable over a 50 year economic life.

    Proposal 3 – Apartment House
    The cost of a 20,000 square foot, two story, 12 unit, apartment house is $750,000. A schedule of economic rents shows gross annual rentals of $150,000. Expenses (excluding taxes) are estimated at 30 percent of effective gross income. A seven percent vacancy allowance appears reasonable over a 40 year economic life.

    For each proposal:

    • Property taxes are based on one percent of the taxable value.
    • For purposes of this exercise, use a six percent yield rate for each proposal.
    • For purposes of this exercise, consider the building incomes to be straight line declining terminal with straight line recapture.

    What is the value of the lot for property tax purposes?

Proposal 1 – Gas Station (Direct Land Capitalization)

Gross Income ($0.15 × 12,500 Sq. Ft. × 12 Months) / Capitalization Rate (6% Y + 1% ETR)
=
$22,500 / 7%
= $321,428

Proposal 2 – Office Building (Land Residual Technique)

Potential Gross Income [PGI]: 7,500 Sq. Ft. × $1.20 × 12 Months
$108,000
Vacancy & Collection Losses [V&CL]: $108,000 × 5%
−
$5,400
Effective Gross Income [EffGI]
=
$102,600
Operating Expenses: $102,600 × 25%
−
$25,650
Net Income Before deducting for recapture & Taxes [NIBT]
=
$76,950
Income Imputed to Buildings: $450,000 × (6% Y + 2%** CRR + 1% ETR)
−
$40,500
Residual Income to Land
=
$36,450
Income to Land / Cap. Rate for Land (6% Y + 1% ETR)
=
$36,450 / 7%
= $520,714 (Land Value)

Proposal 3 – Apartment House (Land Residual Technique)

Potential Gross Income [PGI]
$150,000
Vacancy & Collection Losses [V&CL]: $150,000 × 7%
−
$10,500
Effective Gross Income [EffGI]
=
$139,500
Operating Expenses: $139,500 × 30%
−
$41,850
Net Income Before deducting for recapture & Taxes [NIBT]
=
$97,650
Income Imputed to Buildings: $750,000 × (6% Y + 2½%†† CRR + 1% ETR)
−
$71,250
Residual Income to Land
=
$26,400
Income to Land / Cap. Rate for Land (6% Y + 1% ETR)
=
$26,400 / 7%
= $377,143 (Land Value)

Proposal 2 produces the highest land value; therefore, it represents the highest and best use of the subject site. The value of the lot, regardless how it is used in the future, is $520,000±.

** 2% CRR = 1 ÷ 50 yr REL
†† 2½% CRR = 1 ÷ 40 yr REL

  1. Use the same information from EXERCISE 17-1 for this exercise, except, for each proposal, and for purposes of this exercise, consider the shape of the building incomes to be level terminal.

Proposal 1 – Gas Station (Direct Land Capitalization)

Gross Income ($0.15 × 12,500 Sq. Ft. × 12 Months) / Capitalization Rate (6% Yo + 1% ETR)
=
$22,500 / 7%
= $321,428

Proposal 2 – Office Building (Land Residual Technique)

Potential Gross Income [PGI]: 7,500 Sq. Ft. × $1.20 × 12 Months
$108,000
Vacancy & Collection Losses [V&CL]: $108,000 × 5%
−
$5,400
Effective Gross Income [EffGI]
=
$102,600
Operating Expenses: $102,600 × 25%
−
$25,650
Net Income Before deducting for recapture & Taxes [NIBT]
=
$76,950
Improvement Income: $450,000 × (6% Y + 0.003444 SFF{6%,Ann,50yr} + 1% ETR
−
$33,050
Income Residual to the Land
=
$43,900
Income to Land / Cap. Rate for Land (6% Yo + 1% ETR)
=
$43,900 / 7%
= $627,143 (Land Value)

Proposal 3 – Apartment House (Land Residual Technique)

Potential Gross Income [PGI]
$150,000
Vacancy & Collection Losses [V&CL]: $150,000 × 7%
−
$10,500
Effective Gross Income [EffGI]
=
$139,500
Operating Expenses: $139,500 × 30%
−
$41,850
Net Income Before deducting for recapture & Taxes [NIBT]
=
$97,650
Improvement Income: $750,000 × (6% Y + 0.006462 SFF{6%,Ann,40yrs} + 1% ETR)
−
$57,347
Residual Income to the Land
=
$40,303
Income to Land / Cap. Rate for Land (6% Yo + 1% ETR)
=
$40,303 / 7%
= $575,757 (Land Value)

Assuming a constant terminal income stream, Proposal 2 still produces the highest land value; therefore, it represents the highest and best use of the subject site. The value of the lot, regardless how it is used in the future, is currently about $625,000.