(12C Platinum) Property Value by Income and Reversion Method

[Eddie W. Shore]

Source: California Board of Equalization

"Lesson 4 - Time Value of Money (The Income Approach to Value)" California State Board of Equalization. Accessed March 27, 2023. https://www.boe.ca.gov/info/iav/lesson4.htm

"Lesson 18 - Property Reversion: Annuity plus Reversion Method (The Income Approach to Value" California State Board of Equalization. Accessed March 27, 2023. https://www.boe.ca.gov/info/iav/lesson18.htm

One way to calculate the value of property is by its income and reversion value.

In this case, the income is the estimated annual net income before taxes which is assumed to be "paid out" at the end of each year. This income stream is sometimes known as an Inwood annuity cash flow.

The reversion value of a property is its future value based on factors like inflation, anticipated selling price at the end of the project, and the current market value. The economic life of the property is not necessarily the remaining physical life of the property. In a time value of money timeline, the reversion value would be received at the end of the project.

Calculating the value of the property using this income method uses three steps, as illustrated by the Board of Equalization (see the Source section below):


1. Calculate the value of the income stream, called the net income before taxes (NBIT):

PV_income = NBIT ÷ (SFF + yield% + tax_rate%)

where:
SFF = yield% ÷ ((1 + yield%)^n - 1)

yield% and tax_rate% are expressed in decimal form (Example: 0.05 for 5%)

We can use the TVM keys to calculate ((1 + yield%)^n - 1) by setting the following values:

n, yield → I/YR%, -1 → PV, 0 → PMT, solve for FV.

Then: SFF = yield% ÷ FV


2. Value of the reversion value.

PV_reversion = reversion_value × (1 + (yield% + tax_rate%))^(-n)

We can use the TVM keys to calculate (1 + (yield% + tax_rate%))^(-n)
by setting the following values:

n, yield + tax_rate → I/YR%, 0 → PMT, -1 → FV, solve for PV.


3. Calculate the total property value.

Property Value = PV_reversion + PV_income



HP 12C Platinum Program: Property Value by Reversion Method

Store before running the program:

n = number of years of remaining economical life of the property
i = yield interest rate
R7 = property tax rate
R8 = net income before taxes (NBIT)
R9 = expected revision value of the property (the value of the property at the end of it's economic life)

Code:

Code:


step;  key code;  key

001;  0;  0
002;  44,0;  STO 0
003;  1;  1
004;  16;  CHS
005;  13;  PV
006;  0;  0
007;  14;  PMT
008;  15;  FV
009;  1;  1
010;  30; - 
011;  22; 1/x
012;  45,12;  RCL i
013;  25;  %
014;  45,12;  RCL i
015;  1;  1
016;  25;  %
017;  34;  x<>y
018;  33;  R↓
019;  40;  +
020;  45, 7;  RCL 7
021;  1;  1
022;  25;  %
023;  34;  x<>y
024;  33;  R↓
025;  40;  +
026;  45, 8;  RCL 8
027;  34;  x<>y
028;  10;  ÷
029;  44,40,0;  STO+ 0
030;  45, 12; RCL i
031;  45, 7;  RCL 7
032;  40;  +
033;  12;  i
034;  1;  1
035;  16;  CHS
036;  15;  FV
037;  0;  0
038;  14;  PMT
039;  13;  PV
040;  45, 9;  RCL 9
041;  20;  ×
042;  44,40,0;  STO+ 0
043;  45,12;  RCL i
044;  45,7;  RCL 7
045;  30;  -
046;  12;  RCL i
047;  45,0;  RCL 0
048;  43,33,000;  GTO 000

Examples


Example 1

NBIT: $7,588 (store in R8)
Reversion Value: $236,000 (store in R9)
Tax Rate: 1.3% (store 1.3 in R7)
Annual Rate: 8% (store in i)
Years of Economical Life Remaining: 5 (store in n)

Property Value: $180,092.06


Example 2

NBIT: $12,000
Reversion Value: $185,000
Tax Rate: 1.6%
Annual Rate: 7.34%
Years of Economic Life Remaining: 10

Property Value: $153,286.39