WARNING All rights reserved. No part of the course materials used in the instruction of this course may be reproduced in any form or by any electronic or mechanical means, including the use of information storage and retrieval systems, without written approval from the copyright owner. ©2006 Binghamton University State University of New York ISE 211 Engineering Economy Rate of Return Analysis (Chapter 7 & 8) Chapter 7 Rate of Return Analysis Calculating Rate of Return So far, we have learned how to use the Present Worth and Annual Cash Flow Analyses to compare alternatives. PW and Annual Cost Analyses depend on the interest rate chosen. Rate of return analysis finds the interest rate at which project costs = project benefits. This is called the Internal Rate of Return (IRR), i*. Calculating Rate of Return (cont’d) Now how can we use the Rate of Return analysis to compare alternatives? First convert the various consequences of the investment into a cash flow. Solve the cash flow for the unknown value of i*, which is the rate of return. Calculating Rate of Return (cont’d) This can be done by using one of the following two forms of the cash flow equation: 1. PW of benefits = PW of costs 2. EUAB = EUAC Example - 1: An $8200 investment returned $2000 per year over a five-year useful life. What was the rate of return on the investment? Example 2 An investment resulted in the following cash flow. Compute the rate of return. Year Cash Flow 0 –$700 1 + 100 2 + 175 3 + 250 4 + 325 Example 3 An investment resulted in the following cash flow. Compute the rate of return. Year Cash Flow 0 –$100 1 + 20 2 + 30 3 + 20 4 + 40 5 + 40 Example 4 (Problem 7.5 – page 263) For the diagram below, compute the interest rate at which costs are equivalent to benefits. 80 80 200 80 80 200 80 80 200 Plot of NPW vs. Interest Rate i The plot of NPW vs. interest rate i can be a very useful source of information. A cash flow representing an investment followed by benefits from the investment would have an NPW vs. i plot – lets call it the NPW plot for convenience. A typical NPW plot for an investment looks like this diagram: Plot of NPW vs. Interest Rate i (cont’d) A typical NPW plot for borrowed money looks like this diagram: Now, how can we use this kind of plot to determine the internal rate of return? Example 1 A new corporate bond was initially sold by a stockholder to an investor for $1000. The issuing corporation promised to pay the bond holder $40 interest on the $1000 face value of the bond every six months, and to repay the $1000 at the end of ten years. After one year the bond was sold by the original buyer for $950. a) What rate of return did the original buyer receive on his investment? b) What rate of return can the new buyer (paying $950) expect to receive if he keeps the bond for its remaining nine-year life? Example 2 (Problem 7.9 – page 263) A man buys a corporate bond from a bond brokerage house for $925. The bond has a face value of $1000 and pays 4% of its face value each year. If the bond will be paid off at the end of ten years, what rate of return will the man receive? Rate Of Return Analysis (ROR) ROR analysis is probably the most frequently used exact analysis technique in industry. Although problems in computing rate of return sometimes occur, its major advantage outweighs the occasional difficulty. The major advantage is that we can compute a single figure of merit that is readily understood. Consider these statement: The net present worth on the project is $32,000. The equivalent uniform annual net benefit is $2800. The project will produce a 23% rate of return. Rate Of Return Analysis (ROR) – (cont’d) In ROR analysis, find the IRR for any single project, then compare this IRR with a preselected MARR – the minimum attractive rate of return. The MARR is the interest rate used in PW and Annual Cost Analysis. When there are two alternatives, ROR analysis is performed by computing the incremental rate of return – ROR – on the difference between the alternatives. Note: we will deal with 3 or more alternatives in Chapter 8. Since we want to look at increments of investments, the cash flow for the difference between alternatives is computed. Rate Of Return Analysis (ROR) – (cont’d) This can be done by taking the higher initial cost alternative minus the lower initial cost alternative. Then, compare ROR with MARR and make your decision based on the following criteria: Two Alternative situation Decision IRR MARR Choose the higher-cost alternative IRR < MARR Choose the lower-cost alternative Caution – DO NOT compare IRR for each alternative. If you do so, you may choose the wrong alternative!!!!! Example – 1 (Problem 7.22 – page 265) Consider the following two alternatives. If 5% is considered the minimum attractive rate of return, which alternative should be selected? Year A B 0 -$2000 -$2800 1 + 800 + 1100 2 + 800 + 1100 3 + 800 + 1100 Example – 2 If an electromagnet is installed on the input conveyor of a coal processing plant, it will pick up scrap metal in the coal. The removal of this metal will save an estimated $1200 per year in machinery damage being caused by metal. The electromagnet equipment has an estimated useful life f five years and no salvage value. Two suppliers have been contacted: Leasseco will provide the equipment in return for three beginning-of-year annual payments of $1000 each; Saleco will provide the equipment for $2783. If the MARR is 10%, which supplier should be selected? Consideration of the Analysis Period The consideration of the analysis period is also important in the ROR analysis, just like it was in the PW and Annual Cash Flow analyses. The assumption that an alternative can be replaced with one of identical costs and performance appears to be the best option. Just be sure that all relevant costs and benefits are included when computing PW(costs) = PW(benefits), or EUAC = EUAB. Example 1 Two machines are being considered for purchase. If the MARR (here, the minimum required interest rate) is 10%, which machine should be bought? Initial Cost Uniform annual benefit End-of-useful-life salvage value Useful life (years) Machine X $200 95 50 6 Machine Y $700 120 150 12 Spreadsheets and ROR Analysis If a cash flow diagram can be reduced to at most one P, one A, and/or one F, then RATE investment function can be used. i = RATE(N,A,P,F,type,guess) Otherwise the IRR block function is used with a cash flow in each period. i = IRR(selected cash flow) Example 1 Consider the following cash flow: Cash flow amount Initial cost Annual benefit Salvage value Useful life -$8200 2000 0 6 years What is the rate of return on this investment? Example 2 Find the rate of return for the following cash flow using Excel: 1 2 A Year Cash flow B 0 -700 C 1 100 D 2 175 E 3 250 F 4 325 Chapter 8 Incremental Analysis Overview So far, we have learned how to: determine whether a single-project is desirable compare between two alternatives This chapter involves comparing between two or more alternatives using incremental rate of return analysis (IROR). Incremental analysis can be defined as the examination of the differences between alternatives. By emphasizing alternatives, we are really deciding whether or not differential costs are justified by differential benefits. Overview (cont’d) Although incremental analysis can be examined either graphically and numerically, we will focus on the numerical solutions of ROR analysis. We can solve multiple-alternative problems by PW and ACFA without any difficulties. ROR requires that, for two alternatives, the difference between them must be examined to see whether or not they are desirable. Now if we can choose between two alternatives, then by a successive examination we can choose from multiple alternatives. The following figure illustrates the method of comparing multiple alternatives: Overview (cont’d) Figure 1. Solving MultipleAlternative Problems by successive two-alternative analyses. Elements in Incremental Rate of Return Analysis 1) Check to see that all the alternatives in the problem are identified (including the null alternative “do-nothing”, if applicable). 2) (optional!) Compute the ROR for each alternative: any alternative that have a ROR less than the MARR may be immediately rejected. 3) Arrange the remaining alternatives in ascending order of investment. 4) Make a two-alternative analysis of the first two alternatives. 5) Take the preferred alternative from step 4, and the next alternative from the list created in step 3 – proceed with another two-alternative comparison. 6) Continue until all alternatives have been examined and the best of the multiple alternatives has been identified. Decision Criteria Decision Criteria for Increments of Investments If ROR MARR, retain the higher-cost alternative. If ROR MARR, retain the lower-cost alternative. Reject the other alternative used in the analysis. Decision Criteria for Increments of Borrowing If ROR MARR, the increment is acceptable. If ROR MARR, the increment is not acceptable. Reject the other alternative used in the analysis. Example 1 Using a 6% MARR, what is the preferred alternative using a twenty-year life and no salvage value? Initial Cost Uniform Annual Benefit Alternative A B C $2,000 $5,000 $4,000 410 700 639 Example 2 The following information is provided for five mutually exclusive alternatives that have twenty-year lives. If the MARR 6%, which alternative should be selected? Initial Cost Uniform Annual Benefit Rate of Return A $2,000 410 20% Alternative B C D $6,000 $4,000 $1,000 761 639 117 11% 15% 10% E $9,000 785 6% Example 3 Two mutually exclusive alternatives are being considered. Both have a four year useful life. Alternatives A and B have initial costs of $1000 and $500, respectively. The uniform annual benefits from the alternatives are $350 and $165, respectively. If the MARR is 16% and “donothing” is an option, determine which alternative should be selected using rate of return analysis? Example 4 Owing to perennial complaints by students and faculty about the lack of parking spaces on campus, a parking garage on university property is being considered. Since there are no university funds available for the project, it will have to pay for itself from parking fees over a 15-year period. A 10% MARR is deemed reasonable for consideration of the question of how may levels should be constructed. Based on the cost data shown below, determine whether a parking garage should be constructed. If a parking building should be built, how many levels should be built? # of levels Construction costs Operating Costs Yearly Income 1 $600,000 $35,000 $100,000 2 $2,200,000 $60,000 $350,000 3 4 $3,600,000 $4,800,000 $80,000 $95,000 $570,000 $810,000 Spreadsheets and Incremental Analysis An incremental analysis of two alternatives is easily done with the RATE or IRR functions when lives of the alternatives are the same. However, when the lives are different the problem is more difficult. As discussed earlier, when comparing alternatives with different length lives, the usual approach is to assume that the alternatives are repeated until the next least common multiple of their lives. This can be done easier with a spreadsheet – Excel supports an easier approach. Excel has a tool called GOAL SEEK that identifies a formula cell, a target value, and a variable cell. Spreadsheets and Incremental Analysis Using this tool the variable cell is changed automatically by the computer until the formula cell equals the target value. To find an IRR for an incremental analysis, the formula cell can be the difference between two equivalent annual worth with a target value of 0. Then if the variable cell is the interest rate, GOAL SEEK will find the IRR. Example Two different asphalt mixes can be used on a highway. The good mix will last 6 years, and it will cost $600,000 to buy and lay down. The better mix will last 10 years, and it will cost $800,000 to buy and lay down. Find the incremental IRR for using the more expensive mix. Homework # 7/8 (Chapters 7 & 8) 5 14 19 24 31 43 45 46 49 52 53 58 2 5 8 12 16 19 24 30 34

© Copyright 2018