MATHS
tutorial_8

# As a supervisor of a facilities engineering

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As a supervisor of a facilities engineering department, you are evaluating the purchase of a new crane. The economic estimates for the two best alternatives are shown in the table below. You have selected the longest useful life (9 years) for the study period and would lease a crane for the final three years under Alternative A. Based on the previous experience, the estimated annual leasing cost at that time will be \$66,000 per year(plus the annual expenses of \$28,800 per year). The MARR is 15% per year. Show the selection made with (a) the IRR method. (b) the ERR method. Tutorial 8 of SEEM 2440 A/B Alternatives A B Capital investment \$272,000 \$346,000 Annual expenses \$28,800 \$19,300 Useful life(years) 6 9 Market value(at the end of life) \$25,000 \$40,000

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Solution 2 (a) IRR method: the incremental analysis procedure Alternative A is the base alternative because it requires less capital investment. Evaluate △（ B-A Tutorial 8 of SEEM 2440 A/B year (B-A) cash flows 0 -(\$346,000-\$272,000)=-\$74,000 1-5 -(\$19,300-\$28,800)=\$9,500 6 -(\$19,300-\$28,800)-\$25,000=-\$15,500 7-8 -(\$19,300-\$66,000-\$28,800)=\$75,500 9 \$40,000-(\$19,300-\$66,000-\$28,800)=\$115,500
Solution 2 (a) IRR method: the incremental analysis procedure Evaluate △（ B-A By trial and error, 𝑖 % = 22.5% > 𝑀𝐴𝑅𝑅 . Therefore the incremental investment is justified and Alternative B should be selected. Note that there are more than one sign change in the cash flow, it is possible that there are multiple IRRs . Let’s use ERR method. Tutorial 8 of SEEM 2440 A/B ' ' ' ( ) ' ' ' ( %) \$74,000 \$9,500( / , %,5) \$15,500( / , %,6) \$75,500( / , %,2)( / , %,6) \$115,500( / , %,9) B A PW i P A i P F i P A i P F i P F i  

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Solution 2 (b) ERR method: Using the incremental cash flows computed in part (a), the ERR is found by solving the following equation: |−\$74,000 − \$15,500(P/F,15%,6 )| (F/P, i ′%, 9) = \$9,500(F/A,15%,5)(F/P,15%,4) + \$75,500(F/A,15%,3) + \$40,000 ERR=19.9%>MARR. Therefore, select Alternative B. Tutorial 8 of SEEM 2440 A/B
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