# Lesson 14 Exercises – Review of Four Types of Income Streams and Methods of Capitalization (The Income Approach to Value)

## Appraisal Training: Self-Paced Online Learning Session

1. You are asked to estimate the present value to receive an unimproved 125' × 125' vacant corner lot. You look at current zoning regulations, which allow the development of a gasoline service station, and you conclude that this is the current highest and best use of the property. Ground rents for comparable vacant service station sites in the community lead you to believe the land would rent for 50¢ per square foot per month. Property taxes are one percent of the taxable value; and a nine percent yield rate is appropriate for use in the valuation. Since this will be ground lease to a major chain of gasoline stations, vacancy and collection losses are a minimal five percent; the property owner’s expenses, for insurance, management, and reserves for possible hazard remediation, are estimated to be 15 percent of the potential gross income.

What is the present value of this lot?

#### Solution:

Constant (Level) Perpetual Income Stream

Potential Gross Income:
50¢/sq. ft./mo × 15,625 sq. ft. × 12mos/yr
\$93,750
Vacancy & Collection Loss
5% × PGI
\$5,687.50
Effective Gross Income
PGI − V&CL
=
\$89,062.50
Expenses
15% × PGI
\$14,062.50
Net Income Before Taxes
EffGI − Expenses
=
\$75,000

Land “Cap” Rate [RL]
9% Yield + 1% ETR
÷
10%
Land Value
NIBT ÷ RL
=
\$750,000
2. You are asked to estimate the present value to receive an unimproved 125' × 125' vacant corner lot ten years in the future. You look at current zoning regulations, which allow the development a gasoline service station, and you conclude that this is the current highest and best use of the property. Looking at trends and growth patterns, you are convinced that will be the highest and best use ten years hence. Ground rents for service station sites lead you to believe the current land value is \$750,000; land, being a non-wasting asset, should maintain (ignoring inflation) this value into the future. Property taxes are one percent of the taxable value; and a nine percent yield rate is appropriate for use in the valuation.

What is the value of the right to receive this lot in ten years?

#### Solution:

Single Reversion – A Single Future Income Payment

Future Value of Land
=
\$750,000
PW1{(9%+1%),Ann,10yrs}
×
0.385543
Present Worth of Reversion
=
\$289,157 ≈ \$289,000±
3. Three modular buildings are placed on public school property. The buildings are for the use a for-profit school, Jupiter Academy. Jupiter is also leasing the underlying land from the school district; Jupiter is leasing the buildings from Venus PreFab Shelters, the manufacturer. The lease calls for monthly payments of \$5,000 at the beginning of each month for 12 years, at which time the buildings will have no value. An appropriate allowance for vacancy and collection losses is five percent of gross income, and typical expenses for this type of building and leases, for fire and hazard insurance, management, and reserves for repairs and maintenance, are typically 20 percent of the effective gross income; the tenant typically pays for cleaning (janitorial), electricity and other utilities, heating, and general expenses. Property taxes are paid by Venus; the effective tax rate is 1½ percent. Use a 12½ percent yield rate.

What is the present value of these three buildings?

#### Solution:

Level Terminal Income Stream – Annuity

Potential Gross Income:
\$5,000/mo × 12mos/yr
\$60,000
Vacancy & Collection Loss
5% × PGI
\$3,000
Effective Gross Income
PGI − V&CL
=
\$57,000
Expenses
20% × EffGI
\$11,400
Net Income Before Taxes
EffGI − Expenses
=
\$45,600

"Cap" Rate:
Y + SFF{Y,Ann,REL} + ETR
12½% Y +
0.040194 SFF{12½%,Ann,12yrs}
+ 1½% ETR
÷
0.180194
Building Value
NIBT × "Cap" Rate
=
\$253,061
4. Assume the lease of improvements, only; the current Net Income Before deducting recapture and property Taxes [NIBT] is \$50,000 per year. The Remaining Economic Life [REl] is 40 years, the appropriate interest (Yield) rate is 15 percent, the Effective Tax Rate is 1¾ percent, and the improvements will have no value at the end of the 40-year life. The income stream is straight-line declining terminal; the straight-line rate of depreciation – the Capital Recovery Rate [CRR] – is 2½% over a period of 40 years (CRR = 1 ÷ REL = 1 ÷ 40 years = 2½%/year).

What is the present value of the improvements?

#### Solution:

Stright-Line Declining Terminal Income Stream

Net Income Before Taxes
\$50,000
“Cap” Rate:
Y + CRR{1÷REL} + ETR
15% Y + 2½% CRR + 1¾% ETR
÷
19¼%
Improvement Value
NIBT ÷ "Cap" Rate
=
\$259,740
5. You are asked to use the future Net Incomes Before deducting recapture and property Taxes to estimate the present value of an engine with a Remaining Economic Life [REL] of four years. The NIBT for the engine will be \$37,500 this year, \$25,000 next year and the year thereafter, and \$10,000 the last (fourth) year; it also has a salvage value of \$50,000 at the end of it's REL. Property taxes are one percent of the taxable value; and a nine percent yield rate is appropriate for use in the valuation.

Based upon the incomes forecast, what is the present value of the engine?

#### Solution:

Variable Income Stream

Variable incomes may be thought of, and treated as, a series of irregular single reversionary income payments.

Year
NIBT
PW1{(9%+1%),Ann}
1
\$37,500
×
0.909091 PW1{10%,Ann,1yr}
=
\$34,091
2
\$25,000
×
0.826446 PW1{10%,Ann,2yrs}
=
\$20,661
3
\$25,000
×
0.751315 PW1{10%,Ann,3yrs}
=
\$18,783
4
\$10,000
×
0.683013 PW1{10%,Ann,4yrs}
=
\$6,830
Salvage
4
\$50,000
×
0.683013 PW1{10%,Ann,4yrs}
=
\$34,151
Engine Value:
\$114,516