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  11/22/2013
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  (Multiple Rates of Return Problem)
  Lecture No. 20 Professor C. S. Park Fundamentals of Engineering Economics Copyright © 2005
  • Example: A company invests $10. .021 over 3 years.Return on Invested Capital • Definition 3: Return on invested capital is defined as the interest rate earned on the unrecovered project balance of an investment project. It is commonly known as internal rate of return (IRR). The company is said to earn a return of 10% on its investment of $10.000.000 in a computer and results in equivalent annual labor savings of $4.
  . Since the return is internal to the project.656 -$1.979 3 -$3.979 -$3.000 1 -$10.656 0 The firm earns a 10% rate of return on funds that remain internally invested in the project.000 -$697 -$365 +$4. we call it internal rate of return.021 +$4.021 +$4.000 balance -$6.021 Ending project -$10.000 2 -$6.Project Balance Calculation: 0 Beginning project balance Return on invested capital Payment received -$10.
  how would you make an accept/reject decision? .Multiple Rates of Return If a project has more than one rate of return.
  Example: -$100. $300. $250. but are negative. series. +. -) ROR: A possibility of ROR: A unique ROR multiple RORs . -$120 (-. +) +. and only more than one sign one sign change changes in the occurs in the net cash remaining cash flow flows series. $300 (-. Example: -$100.Investment Classification Nonsimple Investment Simple Investment Def: Initial cash flows Def: Initial cash flows are negative.
  500 2.900 Project C +$1. Project B is a nonsimple investment.000 -450 2 3 4 800 1. Project C is a simple borrowing. .000 3.000 -500 -$1.000 -5.030 2.145 -450 -450 Project A is a simple investment.Perio d (N ) 0 1 Project A Project B -$1.
  6 Multiple Rates of Return Problem $2.Example 7.300 $1.320 PW (i ) $1.000 • Find the rate(s) of return: $1. 000 1 i (1 i ) 2 0 .320 $2.300 $1.
  000 $2.320 PW (i ) $1. Then. 1 i $2. x 10 / 11 or x 10 / 12 Solving for i yields i 10% or 20% .000 (1 i ) (1 i ) 2 $1.300 $1.300 x $1.320 x 2 0 Solving for x yields.1 Let x .
  PW Plot for a Nonsimple Investment with Multiple Rates of Return .
  .320 -$1.300 n=2 +$1.000 Ending Balance -$1.000 -$200 +$2.100 $0 Cash borrowed (released) from the project is assumed to earn the same interest rate through external investment as money that remains internally invested. Balance Interest Payment n=1 -$1.100 +$220 -$1.000 +$1.Project Balance Calculation i* =20% n=0 Beg.
  The assumption used in calculating i* is no longer valid. Then. • Conclusion: Neither 10% nor 20% is a true IRR.Conceptual Issue: Can the firm be able to invest the money released from the project at 20% externally in Period 1? • If the firm’s MARR is exactly 20%. because it represents the rate at which the firm can always invest the money in its investment pool. we assumed that all cash released from the project can be invested at the i* instead of MARR. . In order to calculate i*. the answer is “yes”. the 20% is also true IRR for the project. • Suppose the firm’s MARR is 15% instead of 20%. .
  320 (P/F.000 + $2. 2 ) = $1.$1.89 > 0 Accept the investment • If you want to find the true rate of return (or return on invested capital) to the project. abandon the IRR analysis and use the PW criterion. follow the procedure outlined in Appendix 7A. or use the Cash Flow Analyzer.How to Proceed: • If you encounter multiple rates of return. 15%. 1) . 15%. .300 (P/F. If NPW criterion is used at MARR = 15% PW(15%) = -$1.
  300 2 -1.000 1 2.21% at MARR of 15% .320 Return on invested capital 15.Finding the True ROR for Nonsimple Projects with Cash Flow Analyzer MARR of 15% Nonsimple Investment Cash Flows 0 -$1.
  IRR = ROR. Accept i* i If PW(i) plot looks like this. If PW (i) plot looks like this.Decision Rules for Nonsimple Investment A possibility of multiple RORs. PW (i) i* i* i . • Find the true IRR by using the procedures in Appendix A or. • Abandon the IRR method and use the PW method. then. Then. If IRR > MARR. IRR ROR (i*).
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