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

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?

### Solution:

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

2. 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.

### Solution:

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.