In: Finance
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?
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 | |||||