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

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.

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.

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

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).

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.

Procedure to Calculate the RIC

Computational Logic for RIC Borrowing from project Lending to project

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

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

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

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

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.

Summary of IRR Criteria Figure: 07-09

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

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

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