1. Internal Rate of Return Criterion
Lecture No. 27
Chapter 7
Contemporary Engineering Economics
Copyright © 2006
Contemporary Engineering Economics, 4th edition, © 2007

2. Decision Rule for Pure Investment
Decision Criterion for a Single Project:
If IRR > MARR, accept the project.
If IRR = MARR, remain indifferent.
If IRR < MARR, reject the project.
Decision Criterion for Mutually Exclusive Projects:
Use the incremental analysis (See Lecture No. 28)
Contemporary Engineering Economics, 4th edition, © 2007

3. Example 7.7 Investment Decision for a Pure Investment
Contemporary Engineering Economics, 4th edition, © 2007

4. Contemporary Engineering Economics, 4th edition, © 2007
Solution:
Contemporary Engineering Economics, 4th edition, © 2007

5. Decision Rule for Mixed Investments
Need for an external interest rate for mixed investments. We will use the MARR as established external interest rate—the rate earned by money invested outside of the project.
Calculate a rate of return on the portion of capital that remains invested internally—commonly known as the return on invested capital (RIC)
Select the investment if RIC > MARR.
Contemporary Engineering Economics, 4th edition, © 2007

6. Procedure to Calculate the RIC
Step 1: Identify the MARR (or external interest rate).
Step 2: Calculate PB(i, MARR)n (or simply PBn) according to the rule
Step 3: Determine the value of i by solving the terminal project balance equation
That interest rate i is the RIC (or IRR) for the mixed investment.
Contemporary Engineering Economics, 4th edition, © 2007

7. Computational Logic for RIC
Contemporary Engineering Economics, 4th edition, © 2007

8. Example 7.8 RIC for a Mixed Investment
MARR = 15% n An 1 2
-$1,000,000
2,300,000
-1,320,000
Contemporary Engineering Economics, 4th edition, © 2007

9. Contemporary Engineering Economics, 4th edition, © 2007
Solution:
PB(i,15%)0 = -$1,000
PB(i,15%)1 = -$1,000(1 + i) + $2,300
= 1,000(1.3 – i)
Case 1: i < 1.3 → PB(i,15%)1 > 0
PB(i,15%)2 = 1,000(1.3 –i)(1.15) – 1,320
= 175 – 1,150i
= 0
RIC = IRR = i = 15.22% > 15%
Case 2: i >1.3 → PB(i,15%)1 < 0
There is no solution.
Figure: 07-07EXM
Contemporary Engineering Economics, 4th edition, © 2007

10. Contemporary Engineering Economics, 4th edition, © 2007
Calculation of the IRR
Figure: 07-08EXM
Contemporary Engineering Economics, 4th edition, © 2007

11. Finding the RIC for Mixed Investments with Cash Flow Analyzer
MARR of 15%
Nonsimple Investment Cash Flows
0 -$1,000
2,300
-1,320
Return on invested capital
15.21% at MARR of 15%
Contemporary Engineering Economics, 4th edition, © 2007

12. Example 7.9 RIC for a Mixed Investment by Trial and Error1 2 3
-$1,000
3,900
-5,030
2,145
External interest rate = MARR = 6%
Find the RIC for the project.
Contemporary Engineering Economics, 4th edition, © 2007

13. Solution: RIC =6.13% > MARR, Select the investment
Guess i = RIC at 8%:
Guess i = RIC at 6.13%:
The net investment
is negative at the
end of the project,
indicating that our
trial i =8% is in error.
We lower the guess
value and try again.
Contemporary Engineering Economics, 4th edition, © 2007

14. Summary of IRR Criterion
Figure: 07-09
Contemporary Engineering Economics, 4th edition, © 2007