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  • ADDITIONAL PRACTICE PROBLEMS

The following are some additional practice problems with suggested solutions.

Applying the Income (Capitalization) Approach

  • A 50 unit apartment building and lot are being appraised. The 30 two-bedroom units rent for $600 and the 20 one-bedroom units rent for $475 monthly, which is comparable to market rent in the area. Vacancy and collection losses are estimated to be 5% of potential gross income. The parking structure and laundry facility contribute an additional estimated $1,200 income per month. What is the property's (land and building) total estimated annual effective gross income?
Analysis Figures
30 x $600 = $18,000 x 12
20 x $475 = $9,500 x 12

Apartment rental income
Plus other income: $1200 x 12

Potential Gross Annual Income
Less 5% vacancy/collection loss
=
=

=
=

=
=
$ 216,000
114,000

330,000
14,400

$344,400
- 17,220
Total Annual Effective Gross Income = $ 327,180
  • The owner's operating statement shows the following annual expenses:
Analysis Figures
Fixed Expenses:
Real Property Taxes
Insurance
License
Capital Improvements
Depreciation

Total Fixed Expenses

=
=
=
=
=

=

$ 7,200
2,200
200
22,000
10,000

41,600
Operating Expenses:
Water
Gas and Electricity
Pool Service
Gardening Maintenance
Entertainment Expenses
Building Maintenance
Resident Manager Salary
Refuse Service

Total Fixed Expenses

=
=
=
=
=
=
=
=

=

$ 9,000
6,000
4,800
1,200
750
10,000
12,000
1,200

44,950
Reserves for Replacements:
Appliances, carpets, drapes
Building components

Total Reserves for Replacements

=
=

=

$ 6,000
4,000

10,000
Total Annual Expenses = $ 96,550
  • After reconstructing the owner's statement (determining proper allowable expense items), what is property's annual estimated net income?
  • Deduct $32,000 (Capital Improvements and Depreciation) from fixed expenses and $750 (Entertainment Expense) from operating expense, as being improper deductions.
Analysis Figures
From problem #1, the effective annual gross income is = $ 327,180
Fixed Expenses
Operating Expenses
Replacement Reserves

Total Expenses
=
=
=

=
$ 9,600
44,200
10,000

- 63,800
Estimated Annual Net Property Income = $ 263,380
  • The appraiser determined a proper capitalization rate for the above property is 9.5%. What is the estimated property value?
Analysis Figures
$263,380 net income divided by .095 cap rate = $ 2,772,421
Estimated Property Value = $ 2,772,421
  • Suppose the net income of the property is only $189,000 and similar properties are valued at $1,929,000. What is the indicated overall cap rate?
Analysis Figures
$189,000 (Income) / $1,925,000 (Value) = 9.8%
Overall Cap Rate = 9.8%
  • Given, based on comparative sales technique:
Analysis Figures
Sale price of an income property

Building value
=

=
$ 230,000

170,000
Remaining estimated life of building = 40 years
Annual net income of property = $ 23,500
  • What is the indicated interest rate for the property?
  • (Improved properties have both an interest rate and a recapture rate included in the capitalization rate. The recapture rate applies only to the improvements, while the interest rate applies to both land and improvements.)
Analysis Figures
Estimated net income before recapture = $ 23,500
Recapture for building:
100% / 40 yrs. = 2.5% x $170,000

Net income after building recapture

=

=

4,250

19,250
Interest Rate = $19,250 / $230,000 = 8.3%
  • Building Residual Technique Problem (Land value known; building value unknown.)
Analysis Figures
Assume the following:
Annual net income from the whole property
Land value

Recapture rate for building (25 yrs. remaining economic life)
Interest rate

=
=

=
=

$ 14,000
42,000

4%
8%
  • What is (1) the building value and (2) the property value?
Analysis Figures
Net income of property
Income attributable to land: $42,000 x .08

Income attributable to building
=
=

=
$ 14,000
3,360

10,640
Capitalization rate: 12% (8% + 4%)
Formula: Present Value = Net income / Capitalization Rate

Therefore, Indicated value of building = $10,640 / .12
Plus land value



=
=



88,667
42,000
Property Value by Building Residual Technique (rounded) = $ 130,700
  • Land Residual Technique Problem (Building value known; land value unknown.) Assume the same figures as above in building residual technique problem, except building value is $88,700 and land value is unknown.
  • What is (1) land value and (2) property value?
Analysis Figures
Net income
Less income attributable to improvements ($88,700 x .12)

Income attributable to land
=
=

=
$ 14,000
- 10,644

3,356
Indicated value of land = $3,356 / .08 = $41,950 (rounded)
Add improvement value
=
=
42,000
88,700
Property Value by Land Residual Technique (rounded) = $ 130,700
  • Assume that comparisons show comparable single-family houses in a neighborhood rent for about $380 per month and sell for an average of $45,600. What is the indicated gross rent multiplier for a subject property in this neighborhood?
Analysis Figures
Formula:
sales price divided by gross monthly rent

=

gross rent multiplier
$45,600 / $380 = 120
Gross Rent Multiplier = 120
  • Suppose that, when compared to other rentals, the above property lost $24 per month rental income due to poor kitchen location. What is the estimated depreciation attributable to incurable functional obsolescence?
Analysis Figures
120 x $24 = $ 2,880
Depreciation Attributable to Incurable Functional Obsolescence = $ 2,880
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