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

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

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

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

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

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

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

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

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

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

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

Example 7.9 RIC for a Mixed Investment by Trial and Error 1 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

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

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