Question

For the below ME alternatives , which machine should be selected based on the PW analysis. MARR=10%

	Machine A	Machine B	Machine C
First cost, $	15000	21,476	10000
Annual cost, $/year	8,095	6,000	4,000
Salvage value, $	4,000	5,000	1,000
Life, years	3	6	2

Answer the below questions :

B- PW for machine B=

Answer 1

Present worth is calculated by bringing the future cash flows to present value by discounting at given interest rate and deducting initial cash flows from it.

For evaluating alternatives with different economic lives, we should calculate the LCM of economic lives and calculate the values accordingly.

Present worth of A = -Initial cost -Present value of annual costs for calculated economic life -Present value of cost of alternative after current economic life, i.e.(Initial cost-Salvage value) + Present value of salvage value

= -15,000 -8,095(P/A,10%,6) -11,000(P/F,10%,3) +4,000(P/F,10%.6)

= -15,000 -8,095(4.3553) -11,000(0.7513) +4,000(0.5645)

= -15,000 -35,256.2 -8,264.3 +2,258

= -56,262.5

Present worth of A = (-)$56,262.5

Present worth of B = -Initial cost -Present value of annual costs +Present value of salvage value

= -21,476 -6,000(P/A,10%,6) +5,000(P/F,10%.6)

= -21,476 -6,000(4.3553) +5,000(0.5645)

= -21,476 -26,131.8 +2,822.5

= -44,785.3

Present worth of B = (-)$44,785.3

Present worth of C = -Initial cost -Present value of annual costs for calculated economic life -Present value of cost of alternative after current economic life i.e.(Initial cost-Salvage) + Present value of salvage value

= -10,000 -4,000(P/A,10%,6) -9,000(P/F,10%,3) +1,000(P/F,10%.6)

= -10,000 -4,000(4.3553) -9,000(0.7513) +1,000(0.5645)

= -10,000 -17,421.2 -6,147 +564.5

= -33,003.7

Present worth of A = (-)$33,003.7

As Alternative-C has least costs at present therefore, Alternative-C should be chosen.