Question

Three alternatives Machines have the following cost data associated with them. Machine Y Machine Z 10 Data Useful Life, Years First Cost Annual Benefit Annual M&O Costs Annual additional M&O cost in Gradient Salvage Value Loan Payment Machine X 10 $1,325,000 $265,000 $95,000 $2,300 $1,980,000 $589,000 $97,000 $2,100 $1,650,000 $435,000 $91,000 $1,980 $145,000 $150,946 $205,000 $225,565 $178,000 $187,971 The loan payments are calculated using an interest rate of 10%, a life equal to the life of the machine, and a down payment of 30%. Use a MARR of 12% and determine which machine, if any, should be purchased. Use incremental analysis.

Answer 1

Particulars Purchase Price Down Payment -30% Pay by Loan Annuity factor (10%, 10 years) Installment Useful Life Machines A B C $13,25,000 $19,80,000 $16,50,000 $3,97,500 $5,94,000 $4,95,000 $9,27,500 $13,86,000 $11,55,000 6.14457 6.14457 6.14457 $1,50,946 $2,25,565 $1,87,971 10 101 10 Initial Cash Flow $3,97,500 $5,94,000 $4,95,000 Calculation of Annual Cash Flows: Annual Benefit $2,65,000 $5,89,000 $4,35,000 Annual M&O Costs $95.000 $97,000 $91,000 Annual addi M&O Costs $2,300 $2,100 $1,980 Net Annual Benefit $1,67,700 $4,89,900 $3,42,020 Less: Installment $1,50,946 $2,25,565 $1,87,971 Net Annual Cash Flows $16,754 $2.64,335 $1,54,049 Terminal Cash Flow (Salvage v1 $1.45,000 $2,05,000 $1,78,000

NPV Analysis PV Factor Cash flows Disc. Cash flows Year @ 12% A B C A B C 1 -$3,97,500-$5,94,000 - $4.95,000 -$3.97,500 -$5,94,000-$4,95,000 01-10 5.65022 $16,754 $2,64,335 $1,54,049 $94,664 $14,93,552 $8,70,411 10 0.32197 $1.45,000 $2.05.000 $1,78.000 $46,686 $66,005 $57,311 NPV -$2,56,150 $9,65,556 S4,32,722 Since NPV of Machine A is Negative, it cannot be selected for purchase

Incremental Analysis PV Factor Year CF(C) CF (B) Incremental Disc. Incremental @12% CF (B-C) Cash flows 0 1 -$4,95,000-$5.94,000 -$99,000 -$99,000 01-10 5.6502 $1,54,049 $2,64,335 $1,10,286 $6,23,140 10 0.3220 $1,78,000 $2,05,000 $27,000 $8,693 Incremental NPV $5,32,834| Since, B has higher NPV than C, Select Machine B Machine B to be selected