Question

Given the following data, determine which machine is better. Use the B/C method, a study period of 10 years, and a MARR of 10%. Machine A Machine B First cost: Salvage value: Annual receipts: Annual disbursements: $20,000 2,000 150,000 138,000 $30,000 0 180,000 170,000 Determine the B/C values for each machine by using both the conventional and the modified formulations.

Answer 1

Machine A

Initial cost = $20,000

Salvage value = $2,000

Annual receipts = $150,000

Annual disbursements = $138,000

Conventional B/C Ratio = Present worth of benefits/ (Initial cost + Present worth of operating cost - Present worth of salvage value)

= 150,000 x (PVAF_{10% , 10} ) / {20,000 + 138,000 x  (PVAF_{10% , 10} ) - 2,000 x (PVF_{10%, 10} ) }

= 150,000 x 6.145 / { 20,000 + 138,000 x 6.145 - 2,000 x 0.386 }

= 921,750 / (20,000 + 848,010 - 772)

= 921,750 / 867,238

= 1.06

Modified B/C Ratio = (Present worth of benefits - Present worth of operating costs)/ (Initial cost - Present worth of salvage value)

= {150,000 x (PVAF_{10% , 10} ) - 138,000 x  (PVAF_{10% , 10} ) } / {20,000 - 2,000 x (PVF_{10%, 10} )}

= {150,000 x 6.145 - 138,000 x 6.145 } / (20,000 - 2,000 x 0.386 )

= (921,750 - 848,010)/ (20,000 - 772)

= 73,740/19,228

= 3.83

Machine B

Initial cost = $30,000

Salvage value = $0

Annual receipts = $180,000

Annual disbursements = $170,000

Conventional B/C Ratio = Present worth of benefits/ (Initial cost + Present worth of operating cost - Present worth of salvage value)

= 180,000 x (PVAF_{10% , 10} ) / {30,000 + 170,000 x  (PVAF_{10% , 10} ) - 0 }

= 180,000 x 6.145 / { 30,000 + 170,000 x 6.145 }

= 1,106,100 / (30,000 + 1,044,650)

= 1,106,100 / 1,074,650

= 1.03

Modified B/C Ratio = (Present worth of benefits - Present worth of operating costs)/ (Initial cost - Present worth of salvage value)

= {180,000 x (PVAF_{10% , 10} ) - 170,000 x  (PVAF_{10% , 10} ) } / (30,000 - 0)

= {180,000 x 6.145 - 170,000 x 6.145 } / 30,000

= (1,106,100 - 1,044,650)/ 30,000

= 61,450/30,000

= 2.05