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Company is considering the purchase of a new machine for the production of widgets
Company is considering the purchase of a new machine for the production of widgets. Machine Widget XS costs $260 000 and has three-year life. The annual cash operating costs (excluding depreciation) are $64 000 per year. Alternative machine Widget XL costs $450 000, has a five year life with the annual cash operating costs of $35 000 per year. For both machines, straight-line depreciation is used, The resulting book value will be zero for both machines but the salvage value is around 10% of the purchase price (e.g. this is the estimated market value). The tax rate is 30% and the cost of capital is 10%. Evaluate the after-tax cash flows for both alternatives and find the best alternative by considering equivalent annuities (more precisely equivalent annual cost, EAC). Focus
Expert Solution
Equivalent annual cost (EAC) is the cost per year of purchasing, operating and maintaining the project for its whole life.
The following formula is used for Equivalent Annual Cost (EAC) calculation-
Equivalent Annual Cost (EAC) = (r*NPV)/ (1-(1+r) ^-n)
Where,
NPV is equipment’s net present value =?
Cost of capital is r = 10% per years
Time period for Machine Widget XS is n = 3 years
Let’s first calculate the NPV of Machine Widget XS
| Year (t) | Value of Asset | Depreciation (straight line)D : asset/3 | Salvage value | Annual Cash Operating Cost | Before Tax cash Flow (BTCF) = (- operating cost + Salvage value) | Taxable Income = (BTCF - depreciation) | Income taxes = (Taxable Income *30%) | After tax cash flow (ATCF) = (BTCF - Income tax) | PV of after tax cash flow @10%= ATCF/ (1+10%)^t |
| 0 | $260,000 | N/A | 0 | 0 | -$260,000 | -$260,000.00 | |||
| 1 | $86,666.67 | $64,000 | -$64,000 | -$150,667 | -$45,200 | -$18,800 | -$17,090.91 | ||
| 2 | $86,666.67 | $64,000 | -$64,000 | -$150,667 | -$45,200 | -$18,800 | -$15,537.19 | ||
| 3 | $86,666.67 | $26,000 | $64,000 | -$38,000 | -$124,667 | -$37,400 | -$600 | -$450.79 | |
| NPV (sum of PVs) | -$293,078.89 |
Net present value (NPV) = -$293,078.89 (Negative sign is for cash outflow)
Equivalent Annual Cost (EAC) = (10%*$293,078.89)/ (1-(1+10%) ^-3)
= $117,851.36
Equivalent Annual Cost (EAC) of the Machine Widget XS is $117,851.36
Now, Time period for Machine Widget XL is n = 5 years
Let’s first calculate the NPV of Machine Widget XL
| Year (t) | Value of Asset | Depreciation (straight line)D : asset/5 | Salvage value | Annual Cash Operating Cost | Before Tax cash Flow (BTCF) = (- operating cost + Salvage value) | Taxable Income = (BTCF - depreciation) | Income taxes = (Taxable Income *30%) | After tax cash flow (ATCF) = (BTCF - Income tax) | PV of after tax cash flow @10%= ATCF/ (1+10%)^t |
| 0 | $450,000 | N/A | 0 | 0 | -$450,000 | -$450,000.00 | |||
| 1 | $90,000 | $35,000 | -$35,000 | -$125,000 | -$37,500 | $2,500 | $2,272.73 | ||
| 2 | $90,000 | $35,000 | -$35,000 | -$125,000 | -$37,500 | $2,500 | $2,066.12 | ||
| 3 | $90,000 | $35,000 | -$35,000 | -$125,000 | -$37,500 | $2,500 | $1,878.29 | ||
| 4 | $90,000 | $35,000 | -$35,000 | -$125,000 | -$37,500 | $2,500 | $1,707.53 | ||
| 5 | $90,000 | $45,000 | $35,000 | $10,000 | -$80,000 | -$24,000 | $34,000 | $21,111.32 | |
| NPV (sum of PVs) | -$420,964.01 |
Net present value (NPV) = -$420,964.01 (Negative sign is for cash outflow)
Equivalent Annual Cost (EAC) = (10% *$420,964.01)/ (1-(1+10%) ^-5)
= $111,049.25
Equivalent Annual Cost (EAC) of the Machine Widget XL is $111,049.25
As the Equivalent Annual Cost (EAC) is lower for the Machine Widget XL ($111,049.25); therefore the Machine Widget XL is best alternative
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