Lesson 13 Exercises – Derivation of Yield Rates (The Income Approach to Value)

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  1. Derive a yield rate from this sale assuming a straight line declining terminal income premise.

    The subject property is improved with an one-story commercial building. The original date of construction is 1939. The previous owner did major remodeling to the interior of the store prior to the transaction. The RCN of the improvements is $1,150,000.

    1. The sale price is $1,000,000.
    2. The anticipated monthly income is $12,000. The indicated market rent is $150,000 per year.
    3. The anticipated and market vacancy and collection losses are approximately 3 percent per year.
    4. The anticipated and market operating expenses are $54,000 for the first year.
    5. The anticipated property taxes are $12,500 per year.
    6. The buyer believes that the land alone is worth $400,000.
    7. The buyer anticipates a 30-year remaining economic life for the improvements.

Anticipated Gross Income (GI): $12,000 x 12
$144,000
Anticipated Vacancy & Collection Loss (V&CL): $144,000 × .03
-
$4,320
Anticipated Effective Gross Income (EGI)
=
$139,680
Anticipated Operating Expenses (OE)
-
$54,000
Anticipated Net Income Before deducting Recapture and Taxes (NIBT)
=
$85,680
Anticipated Property Taxes (PT)
-
$12,500
Anticipated Net Income Before Recapture (NIBR)
=
$73,180
Anticipated Recapture ($1,000,000 - $400,000) ÷ 1/30
-
$20,000
Anticipated Net Income
=
$53,180
Yield Rate =
Net Income / Sales Price
=
$53,180 / $1,000,000
= 0.0532 ≅ 5.3%

  1. Develop a yield rate from the sales information.

    A 25 year old building sold this year for $1,520,000. It is located directly across the street from the subject property. The buyer purchased the property for the future income benefits. The buyer paid $400,000 down and assumed two existing loans for the balance of the sale price.

    The anticipated gross annual income, as anticipated by the buyer, is $186,580 per year. The buyer anticipates a vacancy and collection loss of 2 percent of the annual gross income. Maintenance and insurance expenses are anticipated at $24,000 per year, and the annual property tax is estimated to be $17,500. The $560,000 investment in the building is expected to be recapture over the next 25 years.

    The owner projects the shape of the income stream to be level terminal.

Purchase Price
$1,520,000
Improvement Value (Buyer's Estimate)
$560,000
Land Value
$960,000
Remaining Economic Life (Buyer's Estimate)
25 Years
Anticipated Gross Income [GI]
$186,580
Anticipated Vacancy & Collection Loss [V&CL]: $186,580 × 2%
-
$3,732
Anticipated Effective Gross Income [EGI]
=
$182,848
Anticipated Operating Expenses [OE]
-
$24,000
Anticipated Net Income Before deducting Recapture and Taxes [NIBT]
=
$158,848
Anticipated Property Taxes [PT]
-
$17,500
Anticipated Net Income Before Recapture [NIBR]
=
$141,348

Derive the OverAll Rate as a starting point for the trial and error method:

$141,348 (NIBR) / $1,520,000 (Sale Price)
= 0.092992, or 9.3% (OAR)
TEST YIELD RATES [Yt] (start below 9.3%)
9.0%
8.5%
NIBR
$141,348
$141,348
Land Income (Land Value × Yield Rate Yt)
-
$86,400
$81,600
Improvement Income
=
$54,948
$59,748
PW1/P, Yt, Ann, 25 yrs
×
9.822580
10.234191
Indicated Improvement Value
=
$539,731
$611,472

Based on the above trial and error method, the buyer anticipates a yield return between 8½ and 9 percent. (Using a computer or financial calculator, 8.85% is calculated.)