Your Firm Is Considering Buying A New

Your Firm Is Considering Buying A N

Calculate the net cash flow your firm will realize from a new machine during the first year, considering its cost, revenue, operating costs, tax rate, and depreciation rate. Also, determine the payback period for a given project with initial investment and annual cash flows. Additionally, analyze the firm's breakeven point based on provided income statement data and produce a breakeven chart. Further, calculate the net present value (NPV) of a proposed project with specified cash flows and a required rate of return, and determine the internal rate of return (IRR) for another project based on given cash flows.

Paper For Above instruction

The process of capital budgeting is crucial for firms in making informed investment decisions. When contemplating the acquisition of new assets like machinery, firms must evaluate various financial metrics that gauge the project's profitability or viability. This paper explores the calculation of net cash flows, payback periods, breakeven points, net present value (NPV), and internal rate of return (IRR) based on specified scenarios, demonstrating essential analytical techniques in financial management.

Calculating the First-Year Net Cash Flow of the New Machine

The initial scenario involves purchasing a machine costing $200,000, expected to generate $110,000 in revenues annually, with operating costs of $45,000. The firm’s marginal income tax rate is 35%, and the machine depreciates at 20% for the first year under MACRS depreciation rules. Excluding the cost of the machine itself, the net cash flow must incorporate operating cash inflows and tax effects of depreciation.

The depreciation expense for Year 1, using MACRS 20% rate, equals $40,000 (20% of $200,000). The pre-tax income derived from operations is ($110,000 - $45,000) = $65,000. Tax savings from depreciation (depreciation tax shield) amounts to 35% of $40,000, which is $14,000. The taxable income after depreciation becomes ($65,000 - $40,000) = $25,000, with taxes of 35% equaling $8,750. The net income is then ($25,000 - $8,750) = $16,250, but the cash flow also includes non-cash depreciation expense.

The net cash flow during the first year is calculated as Operating cash flow = (Revenue - Operating costs) - Taxes + Depreciation. The tax on operational profit before depreciation is 35% of $65,000 = $22,750. However, since depreciation reduces taxable income, the after-tax cash flow combines net operational cash flow plus depreciation tax shield:

Operating cash flow = (Revenue - Operating costs) (1 - Tax rate) + Depreciation = ($110,000 - $45,000) (1 - 0.35) + $40,000 = $65,000 * 0.65 + $40,000 = $42,250 + $40,000 = $82,250.

Thus, the firm’s net cash flow during the first year from the new machine is approximately $82,250, capturing operational cash flows plus benefits from depreciation tax shield.

Payback Period Calculation

The second scenario involves evaluating a project with an initial investment of $50,000, expected to generate $10,000 annually over 8 years. The payback period is the time needed to recover the initial investment from cumulative cash flows. In this case, total cash inflows over 8 years equal $80,000, which exceeds the initial outlay.

Dividing the initial investment by annual cash flows gives: $50,000 / $10,000 = 5 years. Hence, the payback period is approximately 5 years, meaning the firm recovers its initial investment in five years.

Breakeven Point in Units and Chart

Using the provided income statement data, the breakeven point occurs where total sales revenue equals total costs, resulting in zero operating income. The revenue per unit is $2, and variable costs per unit are $0.80. Total fixed costs are $20. Correspondingly, the breakeven point in units is calculated as Fixed Costs / (Price per unit - Variable costs per unit):

Breakeven units = $20 / ($2 - $0.80) = $20 / $1.20 ≈ 16.67 units.

Graphically, the breakeven chart would plot total revenue and total costs against the number of units sold. The intersection point indicates the breakeven level, and beyond this point, the firm starts earning profit.

Calculating NPV of Project Alpha

Project Alpha involves a $10,000 initial outlay with varied cash inflows over three years. Using a discount rate of 10%, the NPV is computed as the sum of discounted cash inflows minus the initial investment:

NPV = (6,000 / (1 + 0.10)^1) + (4,000 / (1 + 0.10)^2) + (2,000 / (1 + 0.10)^3) - $10,000

Calculations:

- Year 1: 6,000 / 1.10 ≈ 5,454.55

- Year 2: 4,000 / 1.21 ≈ 3,305.79

- Year 3: 2,000 / 1.331 ≈ 1,501.13

Sum of discounted inflows = 5,454.55 + 3,305.79 + 1,501.13 ≈ 10,261.47

NPV = 10,261.47 - 10,000 ≈ $261.47

IRR Calculation

The IRR is the discount rate that makes the net present value of cash flows from the project equal to zero. Given the cash flow series:

- Year 0: -$30

- Year 1: $40,000

The IRR calculation involves solving for r in:

-30 + 40,000 / (1 + r) = 0

=> 40,000 / (1 + r) = 30

=> 1 + r = 40,000 / 30 ≈ 1,333.33

=> r ≈ 1,333.33 - 1 = 1,332.33 or 133,233%

This clearly indicates a typographical or conceptual error; usually, such a large cash flow suggests the project has very high returns. In reality, more data points would be necessary for a precise IRR, or use financial calculator or Excel's IRR function for an accurate estimation.

Conclusion

The analysis above illustrates fundamental financial evaluation techniques, emphasizing the importance of various metrics such as net cash flow, payback period, breakeven point, NPV, and IRR. These tools assist firms in making informed investment decisions, balancing profitability, risk, and strategic considerations in capital budgeting.

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