Modern Artifacts Can Produce Keepsakes That Will Be Sold

Modern Artifacts Can Produce Keepsakes That Will Be Sold For 70 Each

Modern Artifacts can produce keepsakes that will be sold for $70 each. Nondepreciation fixed costs are $2,000 per year and variable costs are $35 per unit. a. If the project requires an initial investment of $4,000 and is expected to last for 5 years and the firm pays no taxes. The initial investment will be depreciated straight-line over 5 years to a final value of zero, and the discount rate is 10%. What are the accounting and NPV break-even levels of sales? (Do not round intermediate calculations.

Round your answers to the nearest whole number.) Accounting break-even levels of sales units NPV break-even levels of sales units -------------------------------------------------------------------------------- b. What will be the accounting and NPV break-even levels of sales, if the firm's tax rate is 40%? (Do not round intermediate calculations. Round your answers to the nearest whole number.) Accounting break-even levels of sales units NPV break-even levels of sales

Paper For Above instruction

In this analysis, we examine the financial viability of Modern Artifacts' keepsake project by determining its accounting and net present value (NPV) break-even sales levels under two different tax scenarios: zero taxes and a 40% tax rate. These calculations are critical for understanding at what sales volumes the project covers its costs and begins generating profit, both from an accounting perspective and in discounted cash flow terms.

Part A: Zero Tax Scenario

The initial setup involves identifying the relevant cash flows, depreciation, and cost structures. The project requires an upfront investment of $4,000, depreciated straight-line over five years to a book value of zero. The annual depreciation expense is therefore \(\frac{\$4,000}{5} = \$800\). Fixed costs are $2,000 annually, and variable costs are $35 per unit. The sale price per unit is $70. The discount rate is 10%, and there are no taxes to consider.

The accounting break-even point occurs when total sales revenue equals total costs, including depreciation. At this point, the operating income before taxes is zero. To find the accounting break-even sales units, we solve for units where:

  • Sales Revenue = Fixed Costs + Variable Costs + Depreciation

Let \(Q_{a}\) be the accounting break-even sales units:

\(70 \times Q_{a} = 2000 + 35 \times Q_{a} + 800\)

Rearranging the equation:

\(70Q_{a} - 35Q_{a} = 2000 + 800\)

\(35Q_{a} = 2800\)

\(Q_{a} = \frac{2800}{35} = 80\) units

Thus, the accounting break-even sales volume is 80 units.

Next, the NPV break-even point considers the discounted value of cash flows over the project's lifespan. The cash flows are computed as net operating cash flows excluding depreciation since depreciation is a non-cash expense.

The annual cash flow before tax is:

\(CF = (Sales - Variable Costs - Fixed Costs)\)

However, since depreciation affects accounting income but not cash flow, the relevant annual cash flow is:

\(CF = \text{Earnings Before Depreciation} + \text{Depreciation}\)

Alternatively, since taxes are zero, cash flow simplifies to revenue minus variable and fixed costs plus depreciation:

\(CF = (70Q - 35Q - 2000) + 800 = 35Q - 2000 + 800 = 35Q - 1200\)

For NPV break-even, the sum of discounted cash flows (over 5 years) must equal the initial investment. The present value of an annuity of cash flows \(CF\) over 5 years at 10% is:

\(PV = CF \times \frac{1 - (1 + r)^{-n}}{r}\)

Where \(r = 0.10\) and \(n=5\). The annuity factor is approximately 3.7908.

Setting the present value of cash flows equal to the initial investment:

\(PV = (35Q - 1200) \times 3.7908 = 4000\)

Solving for \(Q\):

\(35Q - 1200 = \frac{4000}{3.7908} \approx 1054.1\)

\(35Q = 1054.1 + 1200 = 2254.1\)

\(Q = \frac{2254.1}{35} \approx 64.40\)

Rounding to the nearest whole unit, the NPV break-even sales volume is 64 units.

Part B: 40% Tax Rate Scenario

In this case, taxes significantly influence the cash flows and break-even points. The main difference is incorporating the effect of taxes on earnings and adjusting cash flows accordingly.

First, the taxable income is:

\(Earnings Before Taxes (EBT) = Revenue - Variable Costs - Fixed Costs - Depreciation\)

\(EBT = 70Q - 35Q - 2000 - 800 = 35Q - 2800\)

The taxes payable are:

\(Tax = 0.40 \times EBT\), but only if EBT is positive. For the break-even calculation, we set EBT to zero to find the sales volumes where earnings just cover costs:

  • Accounting break-even units when EBT = 0:

\(35Q - 2800 = 0\)

\(Q = \frac{2800}{35} = 80\) units

The fixed costs are entirely covered at 80 units, aligning with the previous calculation, but we need to adjust for taxes in the cash flow calculations for the NPV level.

To incorporate taxes, after-tax cash flow is calculated as:

\(CF_{after-tax} = (Sales - Variable Costs - Fixed Costs) - Taxes + Depreciation\)

Where taxes are applied on the taxable income:

\(Taxes = 0.40 \times (70Q - 35Q - 2000 - 800)\) if positive; otherwise, zero (if negative, no tax benefit).

Taxes on positive earnings:

\(Taxes = 0.40 \times (35Q - 2800)\)

Operating cash flow after taxes becomes:

\(CF_{after-tax} = (35Q - 2000) + 800 - 0.40 \times (35Q - 2800)\)

Expanding and simplifying:

\(CF_{after-tax} = 35Q - 1200 - 0.40 \times 35Q + 0.40 \times 2800\)

\(CF_{after-tax} = 35Q - 1200 - 14Q + 1120\)

\(CF_{after-tax} = (35Q - 14Q) + (-1200 + 1120) = 21Q - 80\)

Next, the NPV break-even is computed by solving:

\(PV = CF_{after-tax} \times \frac{1 - (1 + r)^{-n}}{r} = 4000\)

Using the same present value factor of 3.7908:

\( (21Q - 80) \times 3.7908 = 4000 \)

Solving for \(Q\):

\(21Q - 80 = \frac{4000}{3.7908} \approx 1054.1\)

\(21Q = 1054.1 + 80 = 1134.1\)

\(Q = \frac{1134.1}{21} \approx 54.00\)

Thus, the NPV break-even sales volume at a 40% tax rate is approximately 54 units.

Summary of Findings

In the tax-free scenario, the accounting and NPV break-even units are 80 and 64, respectively. When a 40% tax rate is imposed, both break-even points decrease, with the accounting break-even remaining at 80 units (since it's based on covering fixed plus depreciation costs), but the NPV break-even dropping to approximately 54 units due to the tax shield effects on cash flows. These results highlight the influence of taxation on project profitability assessments, demonstrating that tax considerations can significantly alter the economic thresholds for project viability.

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