# Lesson 9 Exercises – Multipliers: Derivation and Valuation (The Income Approach to Value)

## Appraisal Training: Self-Paced Online Learning Session

1. A property recently sold for a cash equivalent sales price of \$2,225,000. Per the returned sales questionnaire completed by the new owner; he anticipates an annual potential gross income of \$570,000. What is the subject property's indicated Gross Income Multiplier?

#### Solution:

Sale Price
Anticipated
Gross Income
Indicated
GIM
\$2,225,000
÷
\$570,000
=
3.904
1. A 20 unit apartment building recently changed ownership for a reported sales price of \$1,650,000. There 10 two bedroom/one bath units and 10 one bedroom/one bath units. Per the returned sales questionnaire, the owner reported that she based her purchase price on receiving monthly rental of \$875 per month for the two bedroom units and \$715 per month for the one bedroom units.

Based on the information provided, what is the subject property's indicated Gross Income Multiplier?

#### Solution:

Determine subject property's anticipated potential gross income:

Unit Type
# of
Units
Monthly
Rent
PGI
One Bedroom
10
×
\$715
×
12
\$85,800
Two Bedroom
10
×
\$875
×
12
\$105,000
Total:
\$190,800

Sale Price ÷ Anticipated Gross Income = Gross Income Multiplier:

Sale Price
PGI
GIM
\$1,650,000
÷
\$190,800
=
8.648
1. The subject property is a 26-unit apartment house. It has a potential gross income of \$164,000. The market has been very active in the past year. You have confirmed the sale of four recent transactions of apartment houses. All of the sales are about the same age and condition as the subject property. They are also located in similar locations.
Sale Number Sale Price Number of Units Monthly Rent per Unit
1 \$1,290,000 32 \$490
2 \$1,000,000 25 \$490
3 \$950,000 23 \$500
4 \$1,285,000 30 \$520

The cost estimates for the subject property indicate that it would cost \$829,000 to replace the existing improvements. Develop a gross income multiplier for each of the sales.

#### Solution:

Sale Price ÷ Anticipated Gross Income = Gross Income Multiplier

Sale #
No. of
Units
Monthly
Rent
Anticipated
Gross Income
1
32
×
\$490
×
12
=
\$188,160
2
25
×
\$490
×
12
=
\$147,000
3
23
×
\$500
×
12
=
\$138,000
4
30
×
\$520
×
12
=
\$187,200
Sale #
Sale Price
Gross Income
GIM
1
\$1,290,000
÷
\$188,160
=
6.856
2
\$1,000,000
÷
\$147,000
=
6.803
3
\$950,000
÷
\$138,000
=
6.884
4
\$1,285,000
÷
\$187,200
=
6.864
1. A 25 unit apartment building recently sold for \$1,250,000. The buyer based the purchase on his anticipation of receiving \$975 per month rental income for each unit and anticipated vacancy and collection loss of 7%.

What is the indicated effective gross income multiplier for the subject property?

#### Solution:

# of
Units
Monthly
Rent
Months
Gross
Income
Vacancy &
Collection Loss
@ 7%
EffGI
25
×
\$975
×
12
=
\$292,500
(\$20,475)
\$275,025

Sale Price ÷ Anticipated Effective Gross Income = Effective Gross Income Multiplier

Sale Price
EffGI
EffGIM
\$1,250,000
÷
\$272,025
=
4.595
1. A 30-unit motel located at a downtown location rents rooms based on the following rental schedule:
• Daily\$115
• Weekly\$700
• Monthly\$2800

During the county fair, all of the available rooms rent for \$225 per day. The number of daily, weekly, and monthly tenants fluctuates throughout the year. However, during the fair the motel is 100 percent occupied for approximately 30 days. The motel owners' income tax statement for the motel indicated that expenses were approximately 45 percent of the reported \$925,000 rental income.

The motel was recently placed in escrow at a reported sale price of \$7,400,000 (including the personal property); when asked, the buyers said they based the price they were willing to pay on the owners' reported income.

What is the effective gross income multiplier for the land, buildings, and personal property?

#### Solution:

Effective Gross Income Multiplier = Sale Price ÷ Effective Gross Income.

It is not possible to calculate the anticipated gross income based on the information given, nor is there information on anticipated vacancy and collection losses. However, we are given the income the buyers expect to receive – the \$925,000 reported on the owner's income tax return is, for this sale, the anticipated effective gross income.

We are asked to calculate an effective gross income multiplier; we don't need to go beyond effective gross income, and therefore we do not need the expense ratio, which we could otherwise use to calculate a net income. The expense ratio information, however, would be useful in comparing the EffGIM from this sale with other comparables – the comparables, and the property (or properties) to be appraised, should have similar expense ratios.

After determining the effective gross income, the calculation of the Effective Gross Income Multiplier is straight forward.

EffGIM =
\$7,400,000 (Sale Price) / \$925,000 (EffGI)
= 8.00

It must be remembered that if the 8.00 EffGIM is used to value a motel, the resulting value will include the land, building, and personal property. If the business property section then assesses the personal property based on a 571-L report, there will be a double assessment of the personal property.

1. The subject property is a ten unit office condo project. Each unit has 750 square feet of rentable area. Other similar office condo units, in terms of location and income potential, are typically renting for \$1,250 per month. GIM of 5.5.

What is the indicated market value of the subject property?

#### Solution:

Calculate the subject property's PGI:

# of
Units
Monthly
Rent
Months
PGI
10
×
\$1,250
×
12
=
\$150,000

Potential Gross Income × GIM = Indicated Market Value

\$150,000 × 5.5 = \$825,000

1. A 40 unit apartment building recently transferred ownership and was determined to be 100% reappraisable change in ownership. It is located within your area of responsibility to value. You find the following information from the office database of comparable sales.
Sale Number Date of Sale Sales Price Number of Units Gross Income Remarks
Subject Transfer N/A 40 \$400,800
1 1 mo ago \$2,390,000 46 \$466,440 Similar to subject
2 Last week \$2,240,000 42 \$428,400 Similar to subject
3 1 year ago \$2,238,000 37 \$321,900 Similar but older sale

Derive a GIM for each of the comparable sales and determine the market value of the subject property for the change in ownership?

#### Solution:

Derive a GIM for each of the comparable sales.

Sale #
Sale Price
Anticipated
Gross Income
GIM
1
\$2,390,000
÷
\$466,440
=
5.124
2
\$2,240,000
÷
\$428,400
=
5.229
3
\$2,238,000
÷
\$321,900
=
6.952

Select appropriate GIM. All three sales are similar to the subject in location, quality of construction, effective age, and unit makeup. Sale #1 and #2 sold near in time to the subject; while sale #3 was a year old. Therefore, the value of the subject is between \$2,054 million and \$2,096 million;  using a Gross Income Multiplier of 5.2, we can calculate:

PGI
GIM
Indicated Value
Subject
\$400,800
×
5.2
=
\$2,084,160

Indicated market value of subject property by the use of GIMs is \$2,084,000, rounded.

1. Assume that the following data was taken from a homogeneous neighborhood:
Property Type of Data Data Age Building Quality Number of Apartment Units Building Age Sale Price Anticipated PGI
A SALE 1 Yr. Average 10 2 \$150,000 \$20,000
B SALE 2 Yrs. Average 15 30 \$180,000 \$30,000
C SALE Current Average 12 1 \$176,000 \$26,000
D LISTING 1 Yr. Average 15 4 \$240,000 \$32,000
E SALE 3 Yrs. Average 14 3 \$210,000 \$32,000
F SALE 2 Yrs. Average 4 3 \$60,000 \$8,000
G OFFER 1 Yr. Average 18 2 \$250,000 \$38,000
H SALE 2 Yrs. Fair 20 20 \$240,000 \$36,000
I SALE 1 Yr. Average 15 1 \$230,000 \$34,000
J SALE Current Average 40 2 \$560,000 \$76,000
K SALE 1 Yr. Good 20 3 \$360,000 \$48,000
L SALE Current Average 10 4 \$160,000 \$20,000
1. Buyer "E" says he paid too much for the property.

Buyer "L" says she paid too much for the property.

The subject property is a new 15-unit apartment complex. The building's quality is considered as average.

Estimate the value of the subject property using gross income multipliers. The subject property has a market indicated potential gross income of \$34,000.

#### Solution:

Property Sale Price Anticipated PGI GIM Remarks
A \$150,000 \$20,000 7.50 Smaller; 10 Units
B \$180,000 \$30,000 6.00 2 Yr. Old Sale; Older Building
C \$176,000 \$26,000 6.77
D \$240,000 \$32,000 7.50 Listing – Probably High
E \$210,000 \$32,000 6.56 3 Yr. Old Sale; "Paid Too Much"
F \$60,000 \$8,000 7.50 Smaller
G \$250,000 \$38,000 6.58 Offer; Probably Low
H \$240,000 \$36,000 6.67 Larger; Fair Quality
I \$230,000 \$34,000 6.76 Comparable
J \$560,000 \$76,000 7.37 Too Large
K \$360,000 \$48,000 7.50 Better Quality
L \$160,000 \$20,000 8.00 "Paid Too Much"

The value range is indicated by the GIMs developed from sales C and I, the two most comparable sales.

SALE
SUBJECT'S POTENTIAL
GROSS INCOME
GIM
INDICATED
VALUE
C
\$34,000
×
6.76
=
\$229,840
I
\$34,000
×
6.77
=
\$230,180