Please give an explanation to your answer.
Answer (a)
The cash outflow on buying and operating the machine is
Cash Outflow | |
Year 1 | 22000 |
Year 2 | 0 |
Year 3 | 0 |
Year 4 | 6500 |
Year 5 | 6500 |
Year 6 | 2500 |
Year 7 | 3500 |
Year 8 | 3500 |
Year 9 | 3500 |
Year 10 | 3500 |
The Equivalent Uniform Annual Cost is calculated as below
First calculate the Net Present Value (NPV) using the projected
cash flows
As a sample, we will illustrate the calculation for the entire 10
year period.
Discount Rate = 10%
NPV (10 year) = $34,681
Please note that since the EUAC will
To calculate the Equivalent Uniform Annual Cost, we use the PMT
formula in excel
Thus, EUAC (10 year) = $5,644
Using the above formulae, let us construct a table to determine
the lowest EUAC
Cash Outflow | NPV | EUAC | |
Year 0 | $22,000 | $22,000 | |
Year 1 | $0 | $20,000 | |
Year 2 | $0 | $18,182 | $10,476 |
Year 3 | $0 | $16,529 | $6,647 |
Year 4 | $6,500 | $24,036 | $7,583 |
Year 5 | $6,500 | $27,705 | $7,309 |
Year 6 | $2,500 | $28,988 | $6,656 |
Year 7 | $3,500 | $30,621 | $6,290 |
Year 8 | $3,500 | $32,105 | $6,018 |
Year 9 | $3,500 | $33,454 | $5,809 |
Year 10 | $3,500 | $34,681 | $5,644 |
Thus, the lowest EUAC is for the full 10 year period.
Answer (b)
If overhaul costs of $8,000 need to be paid at the end of year 5,
the table changes to
Cash Outflow | NPV | EUAC | |
Year 0 | $22,000 | $22,000 | |
Year 1 | $0 | $20,000 | |
Year 2 | $0 | $18,182 | $10,476 |
Year 3 | $0 | $16,529 | $6,647 |
Year 4 | $6,500 | $24,036 | $7,583 |
Year 5 | $14,500 | $32,221 | $8,500 |
Year 6 | $2,500 | $33,504 | $7,693 |
Year 7 | $3,500 | $35,137 | $7,217 |
Year 8 | $3,500 | $36,621 | $6,864 |
Year 9 | $3,500 | $37,970 | $6,593 |
Year 10 | $3,500 | $39,197 | $6,379 |
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