Mars Inc. Is Considering Purchasing A New Machine
Mars Inc Is Considering The Purchase Of A New Machine Which Will Redu
Mars Inc. is evaluating a capital investment in a new machine that aims to reduce manufacturing costs by $5,000 annually. The machine is classified under the MACRS 3-year depreciation schedule, which allocates depreciation as follows: 33%, 45%, 15%, and 7%. At the end of its 2-year operational lifespan, the machine will be sold for $1,800. Installation costs amount to $1,000, and the machine's purchase price is $6,000. The acquisition will increase net working capital (NWC) by $2,000, which will be recovered upon sale of the machine at the end of year 2. The company's marginal tax rate is 40%, and it employs a 12% discount rate to evaluate projects of this kind. The question is: what is the net present value (NPV) of this project?
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The decision to invest in new equipment involves multiple financial considerations, including initial costs, depreciation, working capital requirements, salvage value, and the company's tax implications. This analysis explores whether the proposed acquisition of a new machine by Mars Inc. is financially viable based on the given parameters, focusing on calculating the project's net present value (NPV).
Initially, the purchase price of the machine is $6,000, with an additional installation cost of $1,000, bringing the total initial investment to $7,000. The acquisition also raises net working capital (NWC) by $2,000, which is recovered at the end of Year 2, adding to the cash flow considerations. The machine’s annual cost savings amount to $5,000, which directly impacts the project's cash flows.
The depreciation schedule per MACRS 3-year class directs depreciation as 33% in Year 1, 45% in Year 2, 15% in Year 3, and 7% in Year 4. For the two-year project, the depreciation deductions are based on these percentages of the initial cost (excluding salvage value and NWC recovery). The depreciation provides tax shield benefits that reduce taxable income, thus affecting net cash flows.
Calculating depreciation each year:
- Year 1 depreciation: 33% of $6,000 = $1,980
- Year 2 depreciation: 45% of $6,000 = $2,700
- Remaining depreciation in the third year (ignored for this project duration) is not relevant as the project ends after Year 2.
The after-tax savings from depreciation, combined with cost savings and changes in working capital, determine annual cash flows:
- Year 1: Cost savings of $5,000, less depreciation tax shield of 40% of $1,980 = $792, so net tax shield benefit = 0.4*1,980 = $792
- Year 2: Cost savings of $5,000, less depreciation tax shield of 0.4*2,700 = $1,080
- Tax savings also result from the decline in taxable income due to depreciation.
The net operating cash flow for Year 1:
- Cost savings: $5,000
- Less taxes on operating savings: 40% of ($5,000 - $1,980) = 40% of $3,020 = $1,208
- After-tax operating cash flow: $5,000 - $1,208 = $3,792
- Plus depreciation add-back (non-cash): $1,980
- Total Year 1 cash flow: $3,792 + $1,980 = $5,772
Similarly, for Year 2:
- Cost savings: $5,000
- Taxes: 40% of ($5,000 - $2,700) = 40% of $2,300 = $920
- After-tax operating cash flow: $5,000 - $920 = $4,080
- Plus depreciation: $2,700
- Total Year 2 cash flow: $4,080 + $2,700 = $6,780
At the end of Year 2, the machine is sold for $1,800, which is taxed accordingly:
- Book value after 2 years: initial cost minus accumulated depreciation: $6,000 - ($1,980 + $2,700) = $6,000 - $4,680 = $1,320
- Salvage value: $1,800
- Gain on sale: $1,800 - $1,320 = $480
- Tax on salvage gain: 40% of $480 = $192
- After-tax salvage proceeds: $1,800 - $192 = $1,608
- Recovery of NWC: $2,000, which increases the cash flow at the end of Year 2
Total cash flow in Year 2 includes:
- Operating cash flow: $6,780
- After-tax salvage value: $1,608
- NWC recovery: $2,000
- Total Year 2 cash flow: $6,780 + $1,608 + $2,000 = $10,388
The initial investment is:
- Machine and installation: $7,000
- Increase in NWC: $2,000
- Total initial outlay: $9,000
Discounting all cash flows at the project's cost of capital (12%):
- PV of Year 1 cash flow: $5,772 / (1 + 0.12)^1 ≈ $5,157
- PV of Year 2 cash flow: $10,388 / (1 + 0.12)^2 ≈ $8,278
- Subtract initial outlay, adjusted for NWC recovery
Calculate NPV:
NPV = PV of benefits - initial investment
NPV ≈ ($5,157 + $8,278 + NWC recovery present value) - $9,000
Since NWC is recovered at the end, its present value is $2,000 / (1 + 0.12)^2 ≈ $1,591
Adding that, total present value of net cash inflows:
$5,157 + $8,278 + $1,591 = $15,026
Subtracting initial total investment ($9,000) results in:
NPV ≈ $15,026 - $9,000 = $6,026
Given this detailed analysis, the project yields a positive NPV, indicating it is financially attractive. The approximate NPV is around $6,026, which significantly exceeds the answer choice of $123.45. Therefore, based on the calculations, the project is economically viable.
References
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