2Comparing Mutually Exclusive Alternatives Based on IRR Issue: Can we rank the mutually exclusive projects by the magnitude of its IRR?n A1 A2-$1,000 -$5,000$2,000 $7,000100% > %$818 < $1,3641IRRPW (10%)
4Can’t Compare without Knowing Their Base Salaries BillHillaryBase Salary$50,000$200,000Pay Raise (%)10%5%Pay Raise ($)$5,000$10,000For the same reason, we can’t compare mutually exclusive projects based onthe magnitude of its IRR. We need to know the size of investment and its timingof when to occur.
5Incremental Investment Project A1Project A2Incremental Investment (A2 – A1)1-$1,000$2,000-$5,000$7,000-$4,000$5,000RORPW(10%)100%$81840%$1,36425%$546Assuming a MARR of 10%, you can always earn that rate from other investment source, i.e., $4,400 at the end of one year for $4,000 investment.By investing the additional $4,000 in A2, you would make additional $5,000, which is equivalent to earning at the rate of 25%. Therefore, the incremental investment in A2 is justified.
6Incremental Analysis (Procedure) Step 1: Compute the cash flow for the difference between the projects (A,B) by subtracting the cash flow of the lower investment cost project (A) from that of the higher investment cost project (B).Step 2: Compute the IRR on this incremental investment (IRR ).Step 3: Accept the investment B if and only ifIRR B-A > MARRB-ANOTE: Make sure that both IRRA and IRRB are greater than MARR.
7Example 7.7 - Incremental Rate of Return B1B2B2 - B1123-$3,0001,3501,8001,500-$12,0004,2006,2256,330-$9,0002,8504,4254,830IRR25%17.43%15%Given MARR = 10%, which project is a better choice?Since IRRB2-B1=15% > 10%, and also IRRB2 > 10%, select B2.
8IRR on Increment Investment: Three Alternatives Step 1: Examine the IRR for eachproject to eliminate any projectthat fails to meet the MARR.Step 2: Compare D1 and D2 in pairs.IRRD2-D1=27.61% > 15%,so select D1. D1 becomes thecurrent best.Step 3: Compare D1 and D3.IRRD3-D1= 8.8% < 15%,so select D1 again.Here, we conclude that D1 is the bestAlternative.nD1D2D3-$2,000-$1,000-$3,00011,50080021,0005002,0003IRR34.37%40.76%24.81%
9Practice ProblemYou are considering four types of engineering designs. The project lasts 10 years with the following estimated cash flows. The interest rate (MARR) is 10%. Which of the four is more attractive?ABCDInitial cost$150$220$300$340Revenues/Year$115$125$160$185Expenses/Year$70$65$60$80
10Incremental Analysis for Cost-Only Projects ItemsCMS OptionFMS OptionAnnual O&M costs:Annual labor cost$1,169,600$707,200Annual material cost832,320598,400Annual overhead cost3,150,0001,950,000Annual tooling cost470,000300,000Annual inventory cost141,00031,500Annual income taxes1,650,0001,917,000Total annual costs$7,412,920$5,504,100Investment$4,500,000$12,500,000Net salvage value$500,000$1,000,000
13Ultimate Decision Rule: If IRR > MARR, AcceptThis rule works for any investment situationsIn many situations,IRR = RORbut this relationship does not hold for an investmentwith multiple RORs.
14Predicting Multiple RORs (Chapter 7A) - 100% < i *< infinityNet Cash Flow Rule of SignsNo. of real RORs (i*s)<No. of sign changes in the project cash flows
15Example n Net Cash flow Sign Change 1 2 3 4 5 6 -$100 -$20 $50 $60 123456-$100-$20$50$60-$30$1001No. of real i*s 3This implies that the project could have (0, 1, 2, or 3) i*s but NOT more than 3.
16Accumulated Cash Flow Sign Test Find the accounting sum of net cash flows at the end of each period over the life of the projectPeriod Cash Flow Sum(n) (An ) SnIf the series S starts negatively and changes sign ONLY ONCE, there exists a unique positive i*.
17Example n An Sn Sign change -$100 -$20 $50 $60 -$30 $100 -$100 -$120 $60-$30$100-$100-$120-$70-$10-$40$601234561No of sign change = 1, indicating a unique i*.i* = 10.46%
18Example A.2 $3,900 $2,145 $1,000 $5,030 Is this a simple investment? 13$1,000$5,030Is this a simple investment?How many RORs (i*s) can you expect fromexamining the cash flows?Can you tell whether or not this investment has a unique rate of return?
19SummaryRate of return (ROR) is the interest rate earned on unrecovered project balances such that an investment’s cash receipts make the terminal project balance equal to zero.Rate of return is an intuitively familiar and understandable measure of project profitability that many managers prefer to NPW or other equivalence measures.Mathematically we can determine the rate of return for a given project cash flow series by locating an interest rate that equates the net present worth of its cash flows to zero. This break-even interest rate is denoted by the symbol i*.
20Internal rate of return (IRR) is another term for ROR that stresses the fact that we are concerned with the interest earned on the portion of the project that is internally invested, not those portions that are released by (borrowed from) the project.To apply rate of return analysis correctly, we need to classify an investment into either a simple or a nonsimple investment.A simple investment is defined as one in which the initial cash flows are negative and only one sign change occurs in the net cash flow, whereas a nonsimple investment is one for which more than one sign change occurs in the net cash flow series.Multiple i*s occur only in nonsimple investments. However, not all nonsimple investments will have multiple i*s either.
21For a simple investment, the solving rate of return (i For a simple investment, the solving rate of return (i*) is the rate of return internal to the project; so the decision rule is:If IRR > MARR, accept the project.If IRR = MARR, remain indifferent.If IRR < MARR, reject the project.IRR analysis yields results consistent with NPW and other equivalence methods.For a nonsimple investment, because of the possibility of having multiple rates of return, we need to calculate the true IRR, or known as “return on invested capital.” However, your objective is to make an accept or reject decision, it is recommended the IRR analysis be abandoned and either the NPW or AE analysis be used to make an accept/reject decision.When properly selecting among alternative projects by IRR analysis, incremental investment must be used.