Contemporary Engineering Economics, 4 th edition, © 2007 Multiple Rates of Return Problem Lecture No. 26 Chapter 7 Contemporary Engineering Economics Copyright © 2006

Contemporary Engineering Economics, 4 th edition, © 2007 Net Investment Test What it is: A process to determine whether or not a firm borrows money from a project during the investment period. How to test: A project is said to be a net investment 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 investment is net in the sense that the firm does not overdraw on its return any point and hence is not indebted to the project

Contemporary Engineering Economics, 4 th edition, © 2007 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.

Contemporary Engineering Economics, 4 th edition, © 2007 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. (However, we can’t say that a nonsimple investment is also a mixed investment.)

Contemporary Engineering Economics, 4 th edition, © 2007 Example 7.6 Pure versus Mixed Investments n Project Cash Flows ABCD $1,000 1,000 2,000 1,500 -$1,000 1, $1, ,000 -$1,000 3,900 -5,030 2,145 i*i*33.64%21.95%29.95%(10%,30%,50%)

Contemporary Engineering Economics, 4 th edition, © 2007 Sample Calculation – Net Investment Test (Project B) (-, +, +, 0)  Mixed investment Use 21.95% as an interest rate to find the project balances

Contemporary Engineering Economics, 4 th edition, © 2007 Net investment test (Example 7.6)

Contemporary Engineering Economics, 4 th edition, © 2007 Multiple Rates of Return Problem Find the rate(s) of return: $1,000 $2,300 $1,320

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

Contemporary Engineering Economics, 4 th edition, © 2007 PW Plot for a Nonsimple Investment with Multiple Rates of Return

Contemporary Engineering Economics, 4 th edition, © 2007 n = 0n = 1n = 2 Beg. Balance Interest Charged Payment-$1,000 -$200 +$2,300 +$1,100 +$220 -$1,320 Ending Balance-$1,000+$1,100$0 Use either i* =20% or 10% Cash borrowed (released) from the project is assumed to earn the same interest rate through external investment as money that remains internally invested a mixed investment Fail the Net Investment Test

Contemporary Engineering Economics, 4 th edition, © 2007 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%, the answer is “yes”, because it represents the rate at which the firm can always invest the money in its investment pool. Then, the 20% is also true IRR for the project.. Suppose the firm’s MARR is 15% instead of 20%. The assumption used in calculating i* is no longer valid. In order to calculate i*, we assumed that all cash released from the project can be invested at the i* instead of MARR. Conclusion: Neither 10% nor 20% is a true IRR. Conceptual Issue:

Contemporary Engineering Economics, 4 th edition, © 2007 If NPW criterion is used at MARR = 15% PW(15%) = -$1,000 + $2,300 (P/F, 15%, 1) - $1,320 (P/F, 15%, 2 ) = $1.89 > 0 Accept the investment If you encounter multiple rates of return, abandon the IRR analysis and use the PW criterion. If you want to find the true rate of return (or return on invested capital) to the project, follow the procedure outlined in Section How to Proceed: