# Lesson 11 – Derivation of Overall Rates (OARs) from Sales and by Band of Investment (The Income Approach to Value)

## Appraisal Training: Self-Paced Online Learning Session

Open All Close AllIn Lessons 8 and 10, we discussed some of the formulas for deriving an opinion of value. In this lesson, we will demonstrate how to derive overall rates by two different methods.

Rule 8(g) provides two methods of developing overall rates:

- By comparing the net incomes that could reasonably have been anticipated from recently sold comparable properties with their sales prices, … (the market-derived rate).
- By deriving a weighted average of the capitalization rates for debt and for equity capital … (the band-of-investment method).

This lesson discusses the following:

- Deriving Overall Rates from Sales
- Deriving Overall Rates by the Band-of-Investment Method

### Deriving Overall Rates from Market Sales of Comparable Properties

Rule 8(g)(1) states that a capitalization rate may be developed:

By comparing the net incomes that could reasonably have been anticipated from recently sold comparable properties with their sales prices, adjusted, if necessary, to cash equivalents (the market-derived rate). This method of deriving a capitalization rate is preferred when the required sales prices and incomes are available.

In much the same manner as processing the income stream to derive a multiplier, appraisers must use the anticipated income stream to derive an OverAll Rate [OAR]. When deriving a gross income multiplier, the income is processed to the level of anticipated gross income, to anticipated effective gross income when deriving an effective gross income multiplier. When deriving an OAR, the appraiser goes a step further: expenses are deducted from the effective gross income and the income is processed down to the level of Net Income Before deducting for Recapture [NIBR].

Subtracting the anticipated vacancy and collection losses and anticipated operating expenses from the anticipated gross income produces the anticipated Net Income Before deducting recapture and Taxes [NIBT]. Investors typically anticipate having to pay property taxes. They are a necessary expense to the property owner, and therefore, should be deducted as an operating expense when developing the OAR. NIBT less the anticipated property taxes produces NIBR.

The steps used in processing the income stream to value a property are summarized as follows:

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Income Stream

The anticipated NIBR divided by the sale price produces a market-derived OAR. An OAR is an income rate for a total property interest that reflects the relationship between a single year's net operating income expectancy and the total property value. The OAR makes no distinction between recapture (return OF an investment) and yield (return ON an investment). The basic formula for deriving an OAR is:

**Anticipated NIBR**

**Sale Price**

**= OAR**

#### EXAMPLE 11–1: Deriving Overall Rates by Market Derivation

A 20-unit apartment complex recently sold for $850,000. The current contracted rent is $525 per unit. The buyers stated that they anticipate a 5 percent vacancy and collection loss. The buyer also stated that they anticipate the following annual expenses:

The apartment owner's association dues, chamber of commerce dues, and income taxes are excluded from being a part of the operating expenses. (Operating expenses were discussed in Lesson 7, Processing the Income Stream). The association dues, chamber of commerce dues, and income taxes are expenses that are not necessary to maintain the income stream. In addition, Property Tax Rule 8 specifically excludes income taxes as an operating expense in the valuation process. However, property tax is an operating expense and may be deducted from the anticipated income stream in the process to derive OAR. For property tax purposes, however, it is recommended that the deduction be performed as a separate step from deduction of the other operating expenses. For the derivation of an OAR, the allowable operating expenses from the above expense roll, excluding property taxes, is $29,550.

- The processing of the income stream is as follows:

Anticipated GI$126,000Anticipated V&CL ($126,000 × 0.05)−$6,300Anticipated EGI=$119,700Anticipated ExpensesMaintenance & Repair $12,750Insurance $4,500Utilities $4,500Swimming Pool Contract $1,500Management $6,300−$29,550Anticipated NIBT−$90,150Anticipated Property Taxes−$8,500Anticipated NIBR=$81,650 - The derivation of the OAR is as follows:
Anticipated NIBR Sale Price= OAR$81,650 (Anticipated NIBR) $850,000 (Sale Price)= 0.096 or 9.6% (OAR)

### Deriving Overall Rates by Band-of-Investment

Rule 8(g)(2) provides that a capitalization rate may also be developed by deriving a weighted average of the capitalization rates for debt and equity, with weights based on the typical loan-to-value ratio for the property being appraised. This methodology is called the band of investment method.

The band-of-investment method is a technique in which the capitalization rates attributable to components of a capital investment are weighted and combined to derive a weighted average rate attributable to the overall investment. The rate developed is a weighted average between the mortgage investment (the lender's component) and the equity investment (the buyer's component). The property interests are separated into bands of investment based upon the financial investment of each participant in a transfer. The band-of-investment method is most useful when market investors are primarily concerned with equity capitalization rates.

Because OARs reflect the complete cash flow requirements of an investment, the components should reflect the complete cash flow requirements for each segment of capital. The cash flow requirement for the debt segment is simply the total requirement to service the debt, including the principal payments as well as the interest. The cash flow rate to the debt component [R_{m}] is the mortgage constant [ƒ] based on the effective interest rate and the term of the loan. The equity requirement should reflect the cash flow rate that will satisfy an equity investor (R_{e}) in the current market.

The ** debt capitalization rate** [R

_{m}] is the ratio of the annual debt service to the principal amount of a loan. In real estate appraisal, it is called the

*mortgage constant*[ƒ or MC]. The mortgage constant is a function of the interest rate, the frequency of amortization, and the term of the loan. The mortgage constant was discussed in detail in the

*Time Value of Money - Six Functions of a Dollar*, offered by the Board of Equalization at: http://www.boe.ca.gov/info/tvm/, and in Lesson 5 of this learning session. As previously discussed elsewhere, the factors for the mortgage constant for monthly payment, fully-amortizing, loans can be found in column 7 of Assessors' Handbook Section 505,

*Capitalization Formulas and Tables*. For interest‑only loans, the

*i*nterest rate is the Mortgage Constant; for annual payment, fully-amortizing, loans, the annual Periodic Repayment factor, column 6 of Assessors' Handbook Section 505,

*Capitalization Formulas and Tables*, is the Mortgage Constant.

The ** equity capitalization rate** [R

_{E}] is the ratio between the buyer's anticipated pre-tax cash flow to equity and the equity investment in the property. The pre-tax cash flow to equity is the buyer's anticipated NIBR less the annual debt service. The equity investment is the total property value less the outstanding loan balance. Equity capitalization rates can be derived from comparable sales or by surveying investors.

The formula for developing an OAR using the band of investment can be expressed as:

Capital Source | Formula |
---|---|

Equity Component: | + (1-M) × R_{e} =
OAR or R_{o} |

**M**

**M**=

**(1-M)**

**1 - M**=

**R**or

_{m}**ƒ**

*mortgage constant*[MC or ƒ]. It is the ratio of the annual debt service to the principal amount of a loan.

**R**

_{e}*cash flow rate*. It is the ratio of annual pre-tax cash flow expectancy to the amount of equity investment.

**R**

_{o}#### EXAMPLE 11–2: Deriving Overall Rates by the Band of Investment Method

Capital Source | Weighting | R_{m} or R_{e} |
Weighted Amount |
---|---|---|---|

Debt Component: | 85.30% × | 0.092618 [25 yrs @ 8%] [R_{m}] = |
0.079003 |

Equity Component: | 14.70% × | 0.100000 [R_{e}] = |
0.014700
WEIGHTED OAR (R = _{o})0.093703, or 9.4% |

If there is more than one mortgage or trust deed, the formula for developing an OAR using the band of investment, as shown above, can be expanded thusly:

Capital Source | Formula |
---|---|

1^{st} Trust Deed: |
M^{1} × ƒ^{1} + |

2^{nd} Trust Deed: |
M^{2} × ƒ^{2} + |

additional Trust Deeds: | M^{…} × ƒ^{…} + |

Down Payment | (1−(M^{1}+M^{2}+M^{…}) × R_{e} =
OAR or R_{o} |

Where the Trust Deeds percentages, M^{1}, M^{2}, M^{…}, etc. (with their corresponding rates or mortgage constants, ƒ^{1}, ƒ^{2}, ƒ^{…}, etc.) make up the Debt Component, and the Down Payment (and corresponding cash flow rate R_{e}) is the Equity Component.

R_{e} may be determined by interviewing investors of different types of property. If the R_{e} is not known (for example, when there are few or no sales), the R_{e} can be calculated by dividing the pre-tax cash flow of a property by the equity investment. * Pre-tax cash flow* (equity income) is the portion of net operating income that remains after total mortgage debt service is paid but before ordinary income tax on operations is deducted. Equity Income is calculated by subtracting the annual debt service from the NIBR. The debt service is calculated by multiplying the loan amount by the mortgage constant. The mortgage constant is based on the effective interest rate and the term of the loan. The equity income is converted to R

_{e}by dividing the equity income by the equity investment. This can be summarized using the following formulas:

**R**= Equity Income ÷ Equity Investment

_{e}**Equity Income**= NIBR − Debt Service

**Debt Service**= Loan Value × Mortgage Constant [ƒ or MC]

So: **R _{e}** = [NIBR − (Loan Value × MC)] ÷ Equity Investment

Where:

**Equity Income**

**Equity Investment**

**Debt Service**

Alternatively, R_{e} can also be derived using the following:

**Equity Income**

**R**=

_{e}#### EXAMPLE 11–3: Deriving Overall Rates by the Band of Investment Method

A new lease was negotiated six months ago. The contract rent is $9,500 per month. Historically, the operating expenses have consumed approximately 30 percent of the annual effective gross income. A vacancy and collection allowance of 7 percent would be typical. The annual property tax is $22,500. The OAR developed by market derived band-of-investment method would be as follows:

Using the formula:

Capital Source | Formula |
---|---|

Debt Component: | M × R_{m} + |

Equity Component: | (1-M) × R_{e} =
OAR or R_{o} |

**M**

**R**

_{m}**R**

_{e}We discover we have not been given the R_{e}. As such, we will need to use the following formula to derive R_{e} before we can continue.

**R**= Equity Income ÷ Equity Investment

_{e}**Equity Income**= NIBR − Debt Service

**Debt Service**= Loan Value × Mortgage Constant [ƒ or MC]

Before we work all three lines to determine R_{e}, we examine if we have enough information to process the first line. If not, we determine if we have enough information to process the second line. If not, we start with the third line. For this example, we do not have enough information to process the first or second line, so we will start with the third line.

Starting with the third equation, we need to derive the Debt Service.

**Debt Service**

**=**

**$117,156**

Next, we need to derive Equity Income. To do so, we will have to process the income stream to NIBR. The income stream is processed as follows:

**Anticipated NIBR**

**=**

**$51,714**

Now we can solve for Equity Income.

**Equity Income**

**=**

**($65,442)**

In this example, the R_{e} is a negative amount. This is not unusual. To increase leverage and increase profits through mortgage financing, many investors incur debt deliberately and seek maximum yields on minimum down payments. The R_{e} can be determined by dividing the equity income by the value of the property held in equity. In this illustration, the value of the property held in equity is $375,000 ($1,500,000 × 25 percent).

Now that we have the equity income, we can finally we can derive the R_{e}.

_{e}

_{e}

**R**

_{e}**=**

**(0.174512) − 17.4512%**

The OAR can be calculated by band-of-investment method as follows:

Capital Source | Weighting | R_{m} & R_{e} |
Weighted Amount |
---|---|---|---|

Debt Component: | 75% × | 0.1041388 [20 yrs @8.5%] = | 0.078104 |

Equity Component: | 25% × | (0.174512) = | (0.043628)
WEIGHTED OAR (R_{o}) = 0.034476, or 3.4% |

### Summary

The lesson you just read explained how to derive overall rates using two methods, by using data from comparable sales and the band-of-investment. The next lesson will address valuation using overall rates.

Note: Before proceeding on to the next lesson, be sure to complete the exercises for this lesson.