1. Internal Rate of Return Criterion
Lecture No. 25
Chapter 7
Contemporary Engineering Economics
Copyright © 2016

2. Net Investment Test
What it is: Whether or not a firm borrows money from a project during the investment period
How to test: Passes a net investment testwhen the project balances computed at the project’s i* values, PB(i*)n, are either less than or equal to zero throughout the life of the investment.
Meaning: The firm does not overdraw on its return in any point and hence is not indebted to the project.

3. Pure versus Mixed Investment
Pure Investment
Mixed Investment
Definition: An investment in which a firm never borrows money from the project.
How to Determine: If the project passes the net investment test, it is a pure investment.
Relationship: A simple investment is always a pure investment.
Definition: An investment in which a firm borrows money from the project during the investment period.
How to Determine: If a project fails the net investment test, it is a mixed investment.
Relationship: If a project is a mixed investment, it is a nonsimple investment.

4. Example 7.6: Pure versus Mixed Investments
Sample Calculation for Project B:
Use 21.95% as an interest rate to find the project balances.

5. Decision Rules for Pure Investment
Example
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 incremental analysis (see Lecture No. 26).

6. Decision Rule for Mixed Investments
We need an external interest rate for mixed investments. We will use the MARR as the established external interest rate—the rate earned by money invested outside of the project.
We calculate a rate of return on the portion of capital that remains invested internally—commonly known as the return on invested capital (RIC).
Then select the investment if RIC > MARR.

7. Procedure to Calculate the RIC

8. Computational Logic for RIC
Borrowing
from project
Lending
to project

9. Example 7.8: RIC for a Mixed Investment
NPW plot for a nonsimple investment
with multiple rates of return
A mixed investment

10. Solution Case 1: i< 1.6 PB(i,25%)1 > 0
Step 1: External interest rate = MARR = 25%
Step 2: Calculate PB(i,25%)n
Figure: 07-07EXM
RIC = 25.60% > 25%, Accept

11. Finding RIC Using Cash Flow Analyzer
External interest rate
Example 7.8
Input cash flows
RIC at 25%

12. Example 7.9
Given: RIC for a Mixed Investment by Trial and Error Approach
External interest rate = 6%
Find: RIC

13. Solution Guess i = RIC at 8%: Guess i = RIC at 6.13%:
PB(8%,6%)3 < 0, indicating that our guess I = 8% is in error.
We need to lower the guess value and try again.

14. Summary of IRR Criteria
Figure: 07-09

15. Modified Internal Rate of Return (MIRR)
Idea: Can we avoid a multiple ROR problem? Is there a way to come up with a single ROR for nonsimple investment?
Procedure: Use two interest rates: (1) positive cash flows (cash inflows) are invested at the firm’s MARR, and (2) negative cash flows (cash outflows) are financed at the firm’s cost of capital.
Decision Rule: Accept the investment if:
MIRR > MARR

16. Example 7.10: Calculation of MIRR
Given: MARR (i) = cost of capital (k) = 6%
Find: MIRR

17. Solution
MIRR (6.026%) > 6%, accept the investment.