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

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

Determine the accounting rate of return, payback period, and net present value (NPV) for an equipment purchase with the following details: The equipment costs $80,000. It is expected to increase annual cash revenues by $45,000 and annual cash expenses by $12,000. The asset is depreciated on a straight-line basis over a seven-year lifespan with a salvage value of $10,000. The company’s tax rate is 34%. Calculate the following:

Paper For Above instruction

The purchase of equipment often signifies a significant investment for a company, impacting its financial statements and overall profitability. Evaluating such investments requires analyzing several financial metrics, including the accounting rate of return (ARR), payback period, and net present value (NPV). Each of these metrics offers insight into the investment’s profitability, liquidity impact, and contribution to the company’s value.

1. Calculation of the Accounting Rate of Return (ARR)

The ARR measures the return generated from the invested capital, based on accounting profit rather than cash flows. First, we need to determine the annual depreciation expense. Using the straight-line depreciation method:

• Cost of equipment = $80,000
• Salvage value = $10,000
• Useful life = 7 years

Annual depreciation expense = (Cost - Salvage value) / Useful life = ($80,000 - $10,000) / 7 = $70,000 / 7 ≈ $10,000.

Next, we determine the pre-tax operating profit:

• Revenue increase = $45,000
• Expense increase = $12,000

Annual operating profit before depreciation and tax = $45,000 - $12,000 = $33,000.

Adjusted operating profit after depreciation:

• Operating profit before tax = $33,000 - $10,000 (depreciation) = $23,000

Tax expense = 34% of $23,000 = 0.34 × $23,000 = $7,820.

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

The ARR is computed based on the average annual profit over the initial investment:

ARR = (Average annual profit) / (Initial investment) = $15,180 / $80,000 ≈ 0.18975 or 19%.

Rounding to the nearest percent, the ARR is approximately 19%.

2. Calculation of Payback Period

The payback period measures how long it takes to recover the initial investment from cash inflows. Since taxes affect cash flows and profit but not actual cash flows directly, focus primarily on cash flows:

• Annual cash revenues increase = $45,000
• Annual cash expenses increase = $12,000

Annual cash inflow before taxes = $45,000 - $12,000 = $33,000.

Assuming taxes are paid on profits, we need to determine the after-tax cash inflow. However, as cash flows are unaffected by depreciation, and we are focusing on cash payback, we consider the net increase in cash inflows directly:

• Cash inflow per year = $33,000

Initial investment = $80,000.

Payback period = Initial investment / Annual cash inflow = $80,000 / $33,000 ≈ 2.42 years.

Therefore, the investment is recovered in approximately 2.4 years.

3. Calculation of Net Present Value (NPV)

NPV evaluates the project's profitability by discounting future cash flows at the company's required rate of return, which is 8%. We need to calculate the annual net cash flows considering taxes, depreciation, and salvage value.

Assuming cash flows are after-tax operating cash flows, and depreciation changes the accounting profit but not cash flow, we proceed as follows:

• Annual operating cash flow before depreciation: $33,000
• Tax liability on operating profit: 34% of earnings, but since depreciation is a non-cash expense, cash flows are typically adjusted for depreciation in cash flow calculations. For simplicity, assume annual after-tax cash flows equal net cash inflows: $33,000 × (1 - 0.34) = $21,780.

However, for NPV calculation, we add back depreciation (a non-cash expense) and consider the salvage value at the end of 7 years. The cash flow at the end of each year is approximately $21,780.

Note: Since we want a more precise NPV, we use the after-tax cash flow with depreciation added back as a non-cash charge:

Annual after-tax cash flow = (Earnings before depreciation - taxes) + depreciation = ($33,000 - $7,820) + $10,000 = $25,180.

This is a more accurate representation of cash flows, as depreciation affects accounting profit but not cash flow. Using these cash flows:

NPV = ∑ (Cash flow for year t) / (1 + r)^t + Salvage value discounted at year 7 - initial investment.

Calculating the present value of cash inflows over 7 years:

PV of cash inflows = $25,180 × [(1 - (1 + 0.08)^-7) / 0.08] ≈ $25,180 × 5.747 = $144,593.

Present value of salvage value = $10,000 / (1 + 0.08)^7 ≈ $10,000 / 1.713 = $5,837.

Total present value of inflows = $144,593 + $5,837 = $150,430.

Subtract initial investment: $80,000.

NPV = $150,430 - $80,000 = $70,430.

This positive NPV indicates a profitable investment.

Conclusion

In conclusion, based on the calculations:

• The accounting rate of return is approximately 19%.
• The payback period is approximately 2.4 years.
• The net present value, considering a required rate of return of 8%, is approximately $70,430.

This analysis demonstrates that purchasing the equipment is financially advantageous, providing reasonable returns within a short period, with a substantial contribution to the company's value as reflected by the positive NPV.

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