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

The investor decides to purchase property based on their anticipated income, expenses, and recapture. Appraisers use this direct relationship to derive multipliers and rates.

In Lessons 7 and 8, we discussed the use of anticipated income to derive income multipliers and the levels of the income stream to be processed to, in order to derive gross income multipliers and effective gross income multipliers.  The summary chart looked like this:

Where:

In this lesson, we will explain:

• How to develop a gross income and effective gross income multipliers.
• How to derive an opinion of value using the multipliers and applying the multiplier formula discussed in Lesson 8,
  V = I × M.

Income may be capitalized by the use of gross income [GIM and EGIM], gross rent [GRM], or gross production [GPM] multipliers, derived by comparing sales prices of closely comparable properties (adjusted, if necessary, to cash equivalents) with their gross income, gross rents, or gross production.

Typically, the GIM [Gross Income Multiplier] considers gross annual income from all sources; other multipliers may sometimes be used, such as those using monthly income. The GRM [Gross Rent Multiplier] is the same concept, but uses only rental income and usually excludes income from other sources, such as billboards, laundry machines, parking, storage, and vending machines.

When appraising smaller residential properties, appraisers commonly use a gross rent multiplier because such properties typically have no, or very little, non-rental income. Appraisers use GIM for properties, such as large apartment projects, that produce significant non-rental income attributable to the real property (e.g., income from parking, laundry facilities, or rental of storage areas). Gross production multipliers, also mentioned in Rule 8, are multipliers based on measures other than income. Appraisers seldom use them in real property appraisal.

Demonstration of Deriving a Multiplier

In this demonstration, we will show you how to derive a gross income multiplier for comparable sales.

The subject property is a 10-unit commercial office building. It has a potential gross income of $XXX.  There has been three recent sales of commercial office buildings. All of the sales are about the same age and condition as the subject property. They are also located in similar locations.

The cost estimates for the subject property indicate that it would cost $xxx to replace the existing improvements.

SOLUTION: In order to determine the gross income multiplier for each sale, you must first calculate the anticipated gross income for each property based on the number of units and monthly rent then annualize it. The gross income multiplier can then be calculated by dividing the sale price by the anticipated gross income.

In this demonstration, we will show you how to derive an effective gross income multiplier (EGIM). The subject property is a 45 unit two-story apartment building; all units have two bedrooms and one bathroom. The subject property recently sold for $2,750,000. Per returned income and expense questionnaire completed by the new owner, they purchased the property based on an anticipated monthly rental income of $1,250 per unit; based trends in the current rental market, they also anticipated vacancy and collection loss of 7% per month. Derive an EGIM for the subject property.

Steps for deriving an EffGIM for the subject property:

1. Calculate the annualized anticipated gross income based on the anticipated monthly rent and the number of units. In this case:

   Number of Units	Monthly Rent	Number of Months	Anticipated Gross Income
   45 ×	$1,250 ×	12 =	$675,000

2. Deduct the anticipated vacancy and collection loss from the anticipated gross income, to estimate the anticipated effective gross income.

   Anticipated Gross Income	Anticipated V&C loss	V&C Loss	Anticipated EffGI
   $675,000 ×	7% =	($47,250) =	$627,750

3. To derive the EffGIM for the subject property divide the subject's sales price by its indicated anticipated effective gross income.

   Sale Price	Anticipated EffGI	EffGIM
   $2,750,000 ÷	$627,750 =	4.381

In valuing the subject property three comparable apartment buildings were identified. Comparable properties are other apartments with all two bedroom and one bath units. The following table represents the buyers' anticipated income and vacancy and collection loss at the time of sale for each of the comparable properties.

To derive an Effective Gross Income Multiplier (EffGIM) for each of the comparable properties:

1. Calculate each property's anticipated potential gross income.

   Sale Number	Number of Units	Monthly Rent	Number of Months	Anticipated Gross Income
   1	50 ×	$1,200 ×	12 =	$720,000
   2	42 ×	$1,250 ×	12 =	$630,000
   3	46 ×	$1,175 ×	12 =	$648,600

2. Calculate each property's anticipated effective gross income.

   Sale Number	Number of Units	Monthly Rent	Number of Months	Anticipated Gross Income
   1	50 ×	$1,200 ×	12 =	$720,000
   2	42 ×	$1,250 ×	12 =	$630,000
   3	46 ×	$1,175 ×	12 =	$648,600

   Sale Number	Anticipated Gross Income	Anticipated V&C loss	V&C Loss	Anticipated EffGI
   1	$720,000 ×	6% =	($43,200) =	$676,800
   2	$630,000 ×	8% =	($50,400) =	$579,600
   3	$648,600 ×	5% =	($32,430) =	$616,170

3. Divide the property's sale price by the anticipated effective gross income.

   Sale Number	Sale Price	Anticipated EffGI	EffGIM
   1	$3,000,000 ÷	$676,800 =	4.433
   2	$2,625,000 ÷	$579,600 =	4.529
   3	$2,668,000 ÷	$616,170 =	4.330

Sales of certain commercial property types may on occasion include the purchase of personal property that is necessary for the operation of the business and the generation of income by the real estate. Examples of such property types with on-going businesses are motels, hotels, restaurants, etc. For these commercial property types you can derive an EffGIM that includes the value of the personal property.

For example, you have a sale of a 100 room hotel for $28,000,000. Included in the purchase price was $5,600,000 of personal property. The hotel has a stabilized occupancy factor of 70% and an average daily room rate of $125; the buyer expects the room rate and occupancy level will continue.

What is the indicated EffGIM for the total property, including the value of the personal property?

1. Calculate the subject property's anticipated gross income.

   Number of Rooms	Average Daily Rate	Days in a Year	Anticipated Gross Income
   100 ×	$125.00 ×	365 =	$4,562,500

2. Calculate the subject property's anticipated effective gross income.

   Anticipated Gross Income	Occupancy Factor	Anticipated EffGI
   $4,562,500 ×	70% =	$3,193,750

3. Derive EGIM by dividing the sales price attributed to the real estate and personal property by the effective gross income.

   Sale Price	EffGI	EffGIM
   $28,000,000 ÷	$3,193,750 =	8.767

Remember: When you derive a multiplier from a sale that includes personal property, that multiplier must only be applied to other properties that have income generated from a similar mix of real property and personal property.

Income multipliers are very useful in the valuation of income-producing properties; however, they are very sensitive to variations in comparable characteristics, and therefore, must be used with care. The properties analyzed, from which the income multipliers were derived, must be closely comparable to the subject property. Properties that are very similar physically can have very different operating expense ratios, and therefore, not be comparable enough to the subject property to be used for valuation purposes. The properties must be comparable in remaining economic life, use, expense ratios, amount of vacancy, risk, tax rates, and other units of comparison. Vacancy and collection losses are less important when using EGIMs.

The income multiplier must be applied on the same basis in which it was derived.  In other words, an income multiplier based on potential gross income can only be applied to the potential gross income of the subject property. Likewise, an income multiplier based on effective gross income can only be applied to the effective gross income of the subject property.

The basic formulas for valuing property using income multipliers, as discussed in Lesson 6, is to multiply the potential gross income (PGI) by a GIM derived or to multiply the effective gross income (EGI) by an EGIM. Note that the market income derived from sales of comparable properties and not the buyer's anticipated income is used. Thus:

GIMs are easily applied, but they should only be used when the comparable sales are very similar to the subject property. Thus, each comparable sale must be comparable to the subject property in terms of its income potential, expense ratios, location, land to building ratio, and physical characteristics.

When using a GIM, an appraiser capitalizes the market potential gross income of the subject property before allowing for property related expenses. Any variance in the relationship of net income to gross income, between the subject property and each comparable sale, will not be reflected in the resulting value estimate. Such a variance may distort the value estimate.

Demonstration of Deriving Value

In this demonstration, we will show you how to derive an estimate of value using a gross income multiplier. For purposes of this demonstration, the GIM will be given – it is 5.0.

The subject property is a 20 unit apartment building. A review of apartments that are in comparable locations to the subject, and whose units are comparable in size and amenities to the subject are renting for $1,000 per month; which you determine to be economic rent for the subject property as well. Using a GIM of 5.0, what is the indicated value of the subject property?

SOLUTION:

1. First calculate the subject property's potential gross income using economic rents:

   Number of Units	Economic Rent per unit per month	Number of Months in year	PGI
   20 ×	$1,000 ×	12 =	$240,000

2. Multiply the potential gross income by the market derived GIM of 5.0 to arrive at an indicated market value for the subject property.

   PGI	GIM	Market Value
   $240,000 ×	5.0 =	$1,200,000

In this demonstration, we will show you how to derive an estimate of value using gross income multipliers of comparable sales.

The property we are valuing is a non-franchise independently-owned 4,000 square foot fast food restaurant located on a one acre parcel. The following is sales and rent information from four other fast food restaurants.

1. To derive a GIM from each of the comparable sales, first determine each property's PGI:

   Sale Number	Building Area	Rent per square feet per month	Number of Months	PGI
   1	4,000 square feet ×	$2.25 ×	12 =	$108,000
   2	4,200 square feet ×	$2.25 ×	12 =	$113,400
   3	4,500 square feet ×	$2.00 ×	12 =	$108,000
   4	5,250 square feet ×	$2.75 ×	12 =	$173,250

2. To derive a GIM divide the sale price of each comparable property by its indicated potential gross income:

   Sale Number	Sale Price	PGI	GIM
   1	$1,050,000 ÷	$108,000 =	9.722
   2	$1,115,000 ÷	$113,400 =	9.833
   3	$950,000 ÷	$108,000 =	8.796
   4	$1,950,000 ÷	$173,250 =	11.255

3. Determine what economic rent for the subject property is and calculate its potential gross income.

   Sale Number	Sale Price	Building Area	Rent per square feet per month	Remarks
   Subject	N/A	4,000 square feet
   1	$1,050,000	4,000 square feet	$2.25	Similar location and parcel size
   2	$1,115,000	4,200 square feet	$2.25	Similar location and parcel size
   3	$950,000	4,500 square feet	$2.00	Inferior in location; smaller parcel size
   4	$1,950,000	5,250 square feet	$2.75	Superior location, larger parcel

   Comparable sales number 1 and 2 are most similar to the subject in location, building area, and parcel size. Economic rent of $2.25 per square foot is indicated for the subject property. Potential gross income for the subject is:

   Building Area	Rent per square feet per month	Number of Months	PGI
   4,000 square feet ×	$2.25 ×	12 =	$108,000

4. Select an appropriate GIM and derive the subject property's value.

   Sale Number	Building Area	PGI	GIM	Remarks
   Subject	4,000 square feet	$108,000
   1	4,000 square feet	$108,000	9.722	Similar location and parcel size
   2	4,200 square feet	$113,400	9.833	Similar location and parcel size
   3	4,500 square feet	$108,000	8.796	Inferior in location; smaller parcel size
   4	5,250 square feet	$173,250	11.255	Superior location, larger parcel

   Comparable sales number 1 and 2 are most similar to the subject with number 1 having the same building area as the subject as well being similar location and parcel size. A GIM of 9.722 is deemed appropriate.

   PGI	GIM	Indicated Value
   $108,000 ×	9.722 =	$1,050,000

The lesson you just read discussed the derivation of multipliers and how to arrive at an estimate of value using multipliers. The next lesson will reiterate some important information about rates and factors and provide definitions for the various types of rates, some which were discussed in previous lessons and others that will be newly introduced.