Question

In: Finance

You can choose between Machine A or B. Your annual interest rate is 9%. You need...

You can choose between Machine A or B. Your annual interest rate is 9%. You need a Machine for 6 years (required service period).

Machine A costs $42,000 and lasts for 2 years. It has no salvage value, and costs an additional $15,000 each year to operate.

Machine B costs $90,500 and lasts for 3 years. It has a salvage value of $20,000 and costs $8,000/year to operate.

What is the Annual Cost of the lowest cost machine?

Solutions

Expert Solution

Machine A Machine B
Annual Costs $ -38,875.69 $-31,592.30
Thus, Annual Cost of Lowest cost Machine that is Machine B is $ -31,592.30
Working;
Machine A:
Year Cost of Machine Annual Operating Costs Cash flow Discount factor Present Value
0 -42000 -42000                            1.0000 $     -42,000.00
1 -15000 -15000                            0.9174 $     -13,761.47
2 -42000 -15000 -57000                            0.8417 $     -47,975.76
3 -15000 -15000                            0.7722 $     -11,582.75
4 -42000 -15000 -57000                            0.7084 $     -40,380.24
5 -15000 -15000                            0.6499 $       -9,748.97
6 -15000 -15000                            0.5963 $       -8,944.01
                           4.4859 $ -1,74,393.20
(Sum of Year 1 to 6)
Annual Cost of Machine A = $            -1,74,393.20 /      4.4859
= $ -38,875.69
Machine B:
Year Cost of Machine Annual Operating Costs Cash flow Discount factor Present Value
0 -42000 -42000                            1.0000 $     -42,000.00
1 -15000 -15000                            0.9174 $     -13,761.47
2 -15000 -15000                            0.8417 $     -12,625.20
3 -42000 -15000 -57000                            0.7722 $     -44,014.46
4 -15000 -15000                            0.7084 $     -10,626.38
5 -15000 -15000                            0.6499 $       -9,748.97
6 -15000 -15000                            0.5963 $       -8,944.01
                           4.4859 $ -1,41,720.49
(Sum of Year 1 to 6)
Annual Cost of Machine A = $            -1,41,720.49 /      4.4859
= $ -31,592.30

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