Internal Rate of Return Criterion Lecture No 25 Chapter Contemporary Engineering Economics Copyright © 2016 Contemporary Engineering Economics, 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 Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved 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 Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Example 7.6: Pure versus Mixed Investments Sample Calculation for Project B: Use 21.95% as an interest rate to find the project balances PB 21.95% = $1,000 PB 21.95% = $1,000 1+0.2195 +$1,600=$380.50 PB 21.95% =+$380.50 1+0.2195 $300=$164.02 PB 21.95% =+$164.02 1+0.2195 $200=0 (−, +, +, 0) Mixed investment Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Decision Rules for Pure Investment Decision Rules 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) Contemporary Engineering Economics, th edition Park PW i = $1,250,000+$731,500 P A, i,15 $80,000(P / F,i,15) =0 i* 58.71% Since i* > MARR(18%), accept the investment 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 Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Procedure to Calculate the RIC Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Computational Logic for RIC Borrowing from project Lending to project Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Example 7.8: RIC for a Mixed Investment $100 $260 $168 0 (1 i*) (1 i*) i1* 20% and i2* 40% A mixed investment NPW plot for a nonsimple investment with multiple rates of return Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Solution Step 1: External interest rate = MARR = 25% Step 2: Calculate PB( i ,25%) 100 PB( i ,25%) 100(1n i) 260 PB(i,25%) 160 100 i PB(i ,25%)2 ? • Case 1: i < 1.6 PB(i,25%)1 >i)(10 0.25) 168 PB(i ,25%) (160 100 125i 32 0 i IRR 25.60% 25% • Case PB(i ,25%) i)(1 i) 168 2: (160 i > 100 1.6 8 60i < 1000 i PB(i,25%)1 2 0 i 0.20 or 0.40 1.6 (not valid) RIC = 25.60% > 25%, Accept Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved External interest rate Finding RIC Using Cash Flow Analyzer Example 7.8 Input cash flows Contemporary Engineering Economics, th edition Park RIC at 25% 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 Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Solution • Guess i = RIC at 8%: • Guess i PB(8%,6%)3 < 0, indicating that our guess I = 8% is in error We need to lower the guess value and try =again RIC at 6.13%: Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Summary of IRR Criteria Contemporary Engineering Economics, 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 Contemporary Engineering Economics, 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 Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Solution MIRR (6.026%) > 6%, accept the investment Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved ... 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... Reserved Summary of IRR Criteria Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Modified Internal Rate of Return (MIRR) Idea:... with multiple rates of return Contemporary Engineering Economics, th edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Solution Step 1: External interest rate = MARR