Two machines are under consideration for a new production line. Machine X costs
ID: 1099588 • Letter: T
Question
Two machines are under consideration for a new production line. Machine X costs $50,000 and is expected to have a salvage value of $6500 at the end of its useful life of 5 years. It will have a fixed cost of $16,000 per year and a variable cost of $55 per unit per year. On the other hand, machine Y costs $55,000 and is expected to have a salvage value of $7000 at the end of its useful life of 7 years. It will have a fixed cost of $14,500 per year and a variable cost of $58 per unit per year. Determine the quantity that must be produced for the two machines to break even at an interest rate of 3% per year.
Explanation / Answer
Equivalkent annual cost = pmt(interest rate, number of years, Present value)
where pmt is a function in excel
Machine X
0
1
2
3
4
5
year 0
year 1
year 2
year 3
year 4
year 5
Machine Cost
-50000
Salvage Value
6500
Present value
-50000
5606.957
Net Present Value of Machine
-44393.0429
Equivalent annual cost of Machine
9,693.42
Annual Fixed Cost
16,000.00
Total Equivalent annual cost(Fixed)
25,693.42
Variable cost per unit
55
Breakeven Quantity
467.15
Machine Y
0
1
2
3
4
5
6
7
year 0
year 1
year 2
year 3
year 4
year 5
year 6
year 7
Machine Cost
-55000
Salvage Value
7000
Present value
-55000
5691.641
Net Present Value of Machine
-49308.3594
Equivalent annual cost of Machine
7914.30
Annual Fixed Cost
14,500.00
Total Equivalent annual cost(Fixed)
22,414.30
Variable cost per unit
58
Breakeven Quantity
386.45
Machine X
0
1
2
3
4
5
year 0
year 1
year 2
year 3
year 4
year 5
Machine Cost
-50000
Salvage Value
6500
Present value
-50000
5606.957
Net Present Value of Machine
-44393.0429
Equivalent annual cost of Machine
9,693.42
Annual Fixed Cost
16,000.00
Total Equivalent annual cost(Fixed)
25,693.42
Variable cost per unit
55
Breakeven Quantity
467.15
Machine Y
0
1
2
3
4
5
6
7
year 0
year 1
year 2
year 3
year 4
year 5
year 6
year 7
Machine Cost
-55000
Salvage Value
7000
Present value
-55000
5691.641
Net Present Value of Machine
-49308.3594
Equivalent annual cost of Machine
7914.30
Annual Fixed Cost
14,500.00
Total Equivalent annual cost(Fixed)
22,414.30
Variable cost per unit
58
Breakeven Quantity
386.45
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