Time Value of Money - Six Functions of a Dollar

Using Assessors’ Handbook Section 505 (Capitalization Formulas and Tables)

Appraisal Training: Self-Paced Online Learning Session

(Assessors’ Handbook 505, Column 7)

This lesson discusses the Mortgage Constant (*MC*), which is listed in the monthly tables of
Assessors’ Handbook Section 505 (AH 505), *Capitalization Formulas and Tables*. The lesson:

- Explains the meaning and purpose of the
*MC*, - Explains how to find
*MC*factors in AH 505 and calculate*MC*factors, and - Contains practical examples of how to apply the
*MC*factor.

The *MC* factor provides the annualized payment amount per $1 of loan amount for a fully-amortized loan with monthly compounding and payments.

Mathematically, the *MC* factor is simply the monthly PR factor multiplied by 12.
The *MC* factor is also known as the annualized mortgage constant or constant annual percent.
The *MC* factors are in column 7 of the monthly pages of AH 505.

To locate the *MC* factor for a term of 30 years at an annual interest rate of 6%, go to page 32 of AH 505, go down 30 years and across to column 7. The *MC* factor is 0.0719461.
*MC* factors are found in Column 7 of the monthly tables only.

You can confirm that the *MC* factor is the monthly periodic repayment factor multiplied by 12:

0.005996 × 12 = 0.071952 (small difference due to rounding)

This means that for every $1 of loan amount, the annual total of the 12 monthly payments will be $0.071952 (or $0.072). Or, stating it another way, the sum of the 12 monthly payments will be equal to 7.1952% (or 7.2%) of the loan amount.

We could have calculated the *MC* factor by first calculating the monthly PR factor and then
multiplying it by 12 (note that both *i* and *n* must be expressed in months, not years) using the formula below:

*MC*=*PR*× 12*MC*= 0.00599551 × 12*MC*= 0.0719461

**Example 1:**

A buyer takes out a mortgage loan for $250,000 at an annual rate of 8% with monthly payments for 30 years.
What percentage of the original loan amount will she pay on an annualized basis?

**Solution:**

- The problem simply asks for the
*MC*factor, which we can look up directly in AH 505. - Go to AH 505, page 40, column 7, 30 years, to find the
*MC*factor of 0.0880517. This is equivalent to 8.80517%

One can confirm the answer by calculating the monthly payment, multiplying it by 12, and dividing this product by the original loan amount *(difference between factor and table and calculation due to rounding)*:

*PMT*=*PV*×*PR*(8%, 30*years*,*annual*)*PMT*= $250,000 × 0.007338*PMT*= $1,834.50

*MC*= (*PMT*× 12) ÷*PV**MC*= ($1,834.50 × 12) ÷ $250,000*MC*= $22,014 ÷ $250,000*MC*= 0.088056, or 8.8056%

**Example 2:**

In the band of investment method for deriving an overall capitalization rate (*R _{O}*),
the rate is a weighted average of the equity dividend rate (

**Solution:**

- Find the
*MC*factor in AH 505, page 32, column 7, for 30 years. The correct*MC*factor is 0.0719461. - Use the band of investment method to estimate the overall rate (R
_{O}) using the calculation shown in the table below. - The estimated overall capitalization rate (R
_{O}) is**7.90%**.