This document discusses methods for calculating the rate of return of an investment using cash flow diagrams and equations. It describes the Present Worth Method and Equivalent Uniform Annual Cost Method for calculating rate of return. An example calculation is shown using both methods to find a 5.16% rate of return for an investment of $5,000 that yields $100 annually for 10 years and $7,000 at the end of 10 years.

1. Building Economy ARE 431
Dr. Mohammad A. Hassanain ١
The Rate of Return Method
٢
The Present Worth Method.
The Equivalent Uniform Annual Worth Method.
Today’s Lecture

2. Building Economy ARE 431
Dr. Mohammad A. Hassanain ٢
٣
Rate of Return Method
The objective of the rate of return method is to find the
rate of return (% - percentage) for an investment over
a specific service life. The rate of return method
considers all the cash follows that occur during the life
cycle of an investment.
There are two methods to find the rate of return for an
investment. These are:
The Present Worth Method.
The Equivalent Uniform Annual Cost (EUAC)
Method.
٤
Rate of Return Method
Rate of Return Calculation by the Present Worth Method:
Procedure (3 Steps):
1. Draw a cash flow diagram.
2. Set up the rate of return equation in the form:
+_=0 P +
n
Σj = 1
F (P/F, i%, n) A (P/A, i%, n)+_
3. Select values of i by trail and error until the
equation is balanced.

3. Building Economy ARE 431
Dr. Mohammad A. Hassanain ٣
٥
Rate of Return Method
Rate of Return Calculation by the Present Worth Method:
Example: If $5,000 is invested now, this is expected to yield
$100 per year for 10 years and $7,000 at the end of 10
years, What is the rate of return?
A = $100
642
0
1 3 5 7 8
i = ?%
9
$5,000
10
$7,000
Draw the Cash Flow Diagram
٦
Rate of Return Method
Using the equation:
+_=0 P
n
Σj = 1
F (P/F, i%, n) A (P/A, i%, n)+_
_=0 5,000 + 7,000 (P/F, i%, 10)100 (P/A, i%, 10) +
Try i = 5%
_=0 5,000 + 7,000 (P/F, 5%, 10)100 (P/A, 5%, 10)+
=0 + $69.46
+_

4. Building Economy ARE 431
Dr. Mohammad A. Hassanain ٤
٧
Rate of Return Method
Try i = 6%
_=0 5,000 + 7,000 (P/F, 6%, 10)100 (P/A, 6%, 10)+
=0 _
$355.19
By interpolation
$69.46
_ $355.19
5%
0 i %
6%
$69.46 0_
$69.46 ( $355.19)_ _ =
5%
_ i %
5%
_ 6 %
i = 5.16%
٨
Rate of Return Method
Rate of Return Calculation by the EUAC Method:
Procedure (3 Steps):
1. Draw a cash flow diagram.
2. Set up the rate of return equation in the form:
3. Select values of i by trail and error until the
equation is balanced.
+_=0 P (A/P, i%, n) A+_ +_ F (A/F, i%, n)Σj = 1
n

5. Building Economy ARE 431
Dr. Mohammad A. Hassanain ٥
٩
Rate of Return Method
Rate of Return Calculation by the EUAC Method:
Example: If $5,000 is invested now, this is expected to yield
$100 per year for 10 years and $7,000 at the end of 10
years, What is the rate of return?
A = $100
642
0
1 3 5 7 8
i = ?%
9
$5,000
10
$7,000
Draw the Cash Flow Diagram
١٠
Rate of Return Method
Using the equation:
_=0 5,000 7,000 (A/F, i%, 10) + 100(A/P, i%, 10) +
Try i = 5%
=0 + $9.02
_=0 5,000 7,000 (A/F, 5%, 10) + 100(A/P, 5%, 10) +
+_=0 P (A/P, i%, n) A+_ +_ F (A/F, i%, n)Σj = 1
n

6. Building Economy ARE 431
Dr. Mohammad A. Hassanain ٦
١١
Rate of Return Method
Try i = 6%
=0 _
$48.26
By interpolation
$9.02
_ $48.26
5%
0 i %
6%
$9.02 0_
$9.02 ( $48.26)_ _ =
5%
_ i %
5%
_ 6 %
i = 5.16%
=0 5,000 7,000 (A/F, 5%, 10) + 100(A/P, 5%, 10) +_