1. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Internal Rate of Return Criterion Lecture No. 25 Chapter 7 Contemporary Engineering Economics Copyright © 2016

2. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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 test when 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. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Pure versus Mixed Investment Pure 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. Mixed 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. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Example 7.6: Pure versus Mixed Investments (−, +, +, 0)  Mixed investment Sample Calculation for Project B: Use 21.95% as an interest rate to find the project balances.

5. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Decision Rules for Pure Investment Decision Rules 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). Example

6. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Procedure to Calculate the RIC

8. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Computational Logic for RIC Lending to project Borrowing from project

9. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Example 7.8: RIC for a Mixed Investment NPW plot for a nonsimple investment with multiple rates of return A mixed investment

10. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Solution Case 1: i 0 Case 2: i > 1.6 PB(i,25%)1 < 0  Step 1: External interest rate = MARR = 25%  Step 2: Calculate PB(i,25%) n RIC = 25.60% > 25%, Accept

11. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Finding RIC Using Cash Flow Analyzer Example 7.8 RIC at 25% External interest rate Input cash flows

12. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Example 7.9  Given: RIC for a Mixed Investment by Trial and Error Approach External interest rate = 6%  Find: RIC

13. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Summary of IRR Criteria

15. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Example 7.10: Calculation of MIRR  Given: MARR (i) = cost of capital (k) = 6%  Find: MIRR

17. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Solution MIRR (6.026%) > 6%, accept the investment.