Question

1. A construction company is considering procuring one of two types of heavy construction equipment (A and B). Each type of equipment is expected to have a 5-year useful life with zero salvage value. Equipment A can be purchased at a cost of $30,000, while Equipment B would cost $55,000. The net cash flows for each type of equipment is presented below. (60) В Year -$30.000 $6,000 $6,000 $12,000 $55,000 $24,000 $10,000 $21,000 -$7,000 $26,610 1 2 3 $6,000 $25,564 4 5 a) Please calculate the Equivalent Uniform Annual Worth (EUAW) of equipment A, considering the Minimum Attractive rate of return (MARR) of 15% b) Please calculate the Internal Rate of Return (IRR) of equipment B c) Please calculate the Benefit Cost Ratio (BCR) of equipment B using the Net Present Cost and Net Present Benefit values, considering the MARR of 9%. ) Please determine which type of equipment (A or B) the company shoulc procure based on incremental rate of return analysis.

Answer 1

C D E 1 2 Equipment A Equipment B 3 Purchase price 4 Useful life (years) 5 Salvage value 6 Cash flows $30,000 $55,000 5 $0 $0 ($30,000) $6,000 $6,000 $12,000 $6,000 $25,564 ($55,000) $24,000 $10,000 $21,000 $7,000 $26,610 7 Year 0 8 Year 1 9 Year 2 10 Year 3 11 Year 4 12 Year 5 13 14 15 (a) Equivalent Uniform Annual Worth of Equipment A 17 Equivalent Uniform Annual Worth Annualised benefit or cost = NPV / Annuity factor 18 Minimum attractive rate 15% 19 Particulars Cash flows Discount rate @15% Net Present Value ($30,000) $6,000 $6,000 $12,000 $6,000 $25,564 ($30,000) $5,220 $4,560 $7,920 $3,420 $12,782 $3,902 () 20 Year 0 1.00 21 Year 1 0.87 22 Year 2 0.76 23 0.66 Year 3 24 Year 4 0.57 25 Year 5 0.50 $25,564 26 Total 27 Annuity factor @15% for 5 years 3.36 (II) $1,161 (l/lI) 28 Equivalent Uniform Annual Worth 2929

A В E 29 30 (b) Internal rate of return of Equipment B 31 Internal rate of return % (IRR ) is the rate at which the NPV of the project is zero 33 Using Excel 34 Particulars Cash flows ($55,000) $24,000 $10,000 $21,000 $7,000 $26,610 35 Year 0 36 Year 1 37 Year 2 38 Year 3 39 Year 4 40 Year 5 41 IRR % 18.4% IRR(B35:B40) 42 Excel Formula 43 44 Without Excel NPV @ 15% (assumed) NPV @ 20% Particulars 45 Cash Flow (assumed) 46 Year 0 ($55,000) $24,000 $10,000 $21,000 $7,000 ($55,000) $20,870 $7,561 $13,808 $4,002 $13,230 $4,471 ($55,000) $20,000 $6,944 $12,153 $3,376 $10,694 ($1,833) 47 Year 1 48 Year 2 49 Year 3 50 Year 4 51 Year 5 $26,610 52 Net Present Value 53 54 Discount rate NPV $4,471 ($1,833) 55 15% 56 20% 57 ??? 58 59 Extrapolation: 60 IRR (where NPV is zero) = 15% [4471/ (4471 1833)] * 5% 61 18.5% Difference of 0.1% due to rounding off

A В C E F Н 63 64 (c) Benefit cost ratio of Equipment B using Net Present Cost and Net Present Benefit Values considering MARR of 9% 65 Benefit cost ratio Net present benefit values net present cost Cash flows Discount rate @ 9%| ($55,000) 67 Particulars Net Present Value ($55,000) Net present cost $22,080 Net present benefit values $8,400 Net present benefit values $16,170 Net present benefit values $4,970 Net present benefit values $17,297 Net present benefit values 68 Year 0 1.00 $24,000 $10,000 $21,000 69 Year 1 0.92 70 Year 2 0.84 Year 3 0.77 $7,000 72 Year 4 0.71 $26,610 73 Year 5 0.65 $33,610 $13,917 74 Total 75 76 Total Net present benefit values () 77 Total Net present cost (II) $68,917 $55,000 78 Benefit cost ratio (I/II) 1.25 79 80 81 (d) Which equipment to buy based on incremental rate of analysis Particulars Equipment A Incremental cash Equipment B 82 flows ($30,000) $6,000 $6,000 $12,000 ($55,000) $24,000 $10,000 $21,000 $7,000 $26,610 ($25,000) $18,000 $4,000 $9,000 $1,000 $1,046 83 Year 0 84 Year 1 85 Year 2 86 Year 3 $6,000 $25,564 87 Year 4 88 Year 5 89 Total $25,564 $33,610 $8,046 90 Internal rate of return 19.1% 18.4% 16.8% IRR(C83:C88) 91 Excel formula IRR(B83:B88) IRR(D83:D88) 92 93 Based on incremental rate of analysis, equipment A should be procured as the incremental IRR (16.8%) is lower than IRR of equipment A (19.1%) 94 71