Problem 1: Equipment Purchased At A Cost Of 80,000 227319

Problem 1equipment Is Purchased At A Cost Of 80000 As A Result Ann

Determine the accounting rate of return, payback period, and NPV for an equipment purchase costing $80,000 with an expected 7-year life, a salvage value of $10,000, and associated cash flows and depreciation, considering the tax bracket and required rate of return.

Paper For Above instruction

In this analysis, we evaluate the financial viability of an equipment purchase that costs $80,000. The equipment is projected to generate an increase in annual cash revenues of $45,000, with annual cash expenses of $12,000, used to calculate depreciation and profitability metrics. The straight-line depreciation method is applied over the equipment’s seven-year lifespan, with a salvage value of $10,000. The company's tax rate is 34%, which influences after-tax profit calculations, and the minimum required rate of return (discount rate) is set at 8% for NPV calculations.

1. Accounting Rate of Return (ARR)

The ARR measures the average annual accounting profit from the investment as a percentage of the initial cost, providing a straightforward profitability indicator. First, depreciation expense is calculated as:

Depreciation = (Cost - Salvage Value) / Useful Life = ($80,000 - $10,000) / 7 = $70,000 / 7 ≈ $10,000 per year.

The pre-tax operating profit before depreciation and taxes is:

Operating profit before tax = Cash revenues - Cash expenses = $45,000 - $12,000 = $33,000.

The accounting profit before tax, accounting for depreciation, is:

Profit before tax = Operating profit - Depreciation = $33,000 - $10,000 = $23,000.

Tax amount is 34% of profit:

Tax = 0.34 × $23,000 ≈ $7,820.

Net income after tax:

Net income = $23,000 - $7,820 ≈ $15,180.

The ARR is computed as:

ARR = (Average annual accounting profit / Initial investment) × 100 = ($15,180 / $80,000) × 100 ≈ 19.0%.

2. Payback Period

The payback period determines how long it takes for the project to recover its initial investment from after-tax cash flows. Assuming cash flows are effectively represented by net cash revenues minus cash expenses, and adjusting for taxes, the annual after-tax cash inflow is calculated.

The annual cash inflow before depreciation: $45,000 (revenue) - $12,000 (expenses) = $33,000. The depreciation is a non-cash charge, so to find the after-tax cash flow, we adjust net profit accordingly.

However, simplified payback calculation often considers cash flows: cash revenues minus cash expenses, adjusted for taxes:

Tax on cash inflows is: 34% × ($45,000 - $12,000) = 0.34 × $33,000 = $11,220.

After-tax cash inflow = ($45,000 - $12,000) - $11,220 = $33,000 - $11,220 = $21,780.

Given the initial investment of $80,000, the payback period is:

Payback period = Initial investment / Annual after-tax cash inflow ≈ $80,000 / $21,780 ≈ 3.67 years.

3. Net Present Value (NPV)

The NPV assesses the present value of all cash inflows and outflows discounted at the minimum required rate of 8%. The calculation considers the annual cash inflows, the salvage value at the end of 7 years, and the initial investment.

Annual cash inflows (after-tax): $21,780. The project's life is 7 years, with a salvage value of $10,000 at the end of year 7.

NPV = (Sum of discounted cash inflows) + (Present value of salvage value) - initial investment.

First, calculate the present value of annuity (cash flows):

PV of annuity = $21,780 × [(1 - (1 + r)^-n) / r] = $21,780 × [(1 - (1 + 0.08)^-7) / 0.08].

Calculating the annuity factor: (1 + 0.08)^-7 ≈ 0.582.

Present value of cash inflows = $21,780 × [(1 - 0.582) / 0.08] ≈ $21,780 × 5.227 ≈ $113,842.

Present value of salvage value = $10,000 / (1 + 0.08)^7 ≈ $10,000 / 1.713 ≈ $5,841.

NPV = $113,842 + $5,841 - $80,000 = $39,683.

Thus, the project’s NPV, accounting for taxes, is approximately $39,683, indicating a financially viable investment.

Summary

The equipment investment yields an ARR of approximately 19%, with a payback period of about 3.67 years and an NPV of roughly $39,683. These metrics suggest that, based on the given assumptions and tax implications, the project is financially sound, providing a healthy return well above the minimum required rate of 8%. The relatively short payback period further underscores the project's attractiveness, while the positive NPV confirms its profitability after discounting future cash flows.

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