A Project Currently Generates Sales Of 115 Million Variables

A Project Currently Generates Sales Of 115 Million Variable Costs E

A project currently generates sales of $11.5 million, variable costs equal to 40% of sales, and fixed costs of $3.4 million. The firm’s tax rate is 40%. The project will last for 10 years. The discount rate is 12%.

a-1. What is the effect on project NPV, if sales increase from $11.5 million to $13.5 million? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.) Change in cash flow $ [removed] million

a-2. What is the effect on project NPV, if variable costs increase to 60% of sales? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. Enter your answer as the absolute value of the change.) Change in cash flow $ [removed] million

b. If project NPV under the base-case scenario is $3.4 million, how much can fixed costs increase before NPV turns negative? (Do not round intermediate calculations. Enter your answer in dollars not in millions. Round your answer to the nearest dollar amount.) Increase in fixed cost $ [removed]

c. How much can fixed costs increase before accounting profits turn negative? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) Increase in fixed cost $ [removed] million

Paper For Above instruction

The analysis of the project's financial viability hinges on understanding how variations in sales, variable costs, and fixed costs influence its Net Present Value (NPV). Given the current data—sales of $11.5 million, variable costs at 40%, fixed costs at $3.4 million, a tax rate of 40%, a ten-year duration, and a discount rate of 12%—we explore how changes affect the project's profitability and feasibility.

Effect of Increasing Sales on NPV

When sales are projected to increase from $11.5 million to $13.5 million, the ensuing change in NPV is driven primarily by the incremental revenues and associated costs. The incremental sales amount to $2 million, which results in an increase in variable costs proportional to sales. Calculating the increase in operating cash flow involves adjusting revenues, subtracting variable costs, fixed costs, and taxes, then discounting the net cash flows over the project duration.

At the current sales level:

  • Sales = $11.5 million
  • Variable costs (40%) = $4.6 million
  • Contribution margin = $6.9 million
  • Fixed costs = $3.4 million
  • Operating income before taxes = $3.5 million
  • Taxes (40%) = $1.4 million
  • Net income = $2.1 million

For the increased sales scenario:

  • Sales = $13.5 million
  • Variable costs (40%) = $5.4 million
  • Contribution margin = $8.1 million
  • Fixed costs = $3.4 million
  • Operating income before taxes = $4.7 million
  • Taxes (40%) = $1.88 million
  • Net income = $2.82 million

The difference in net income, which largely approximates the change in operating cash flow (assuming depreciation and non-cash expenses are stable), is approximately $0.72 million. Discounting this incremental cash flow over the 10-year period at 12% yields the NPV change, which can be computed using the present value of an annuity.

The present value of an annuity of $0.72 million over ten years at 12% is calculated as:

PV = $0.72 million × [1 - (1 + 0.12)^{-10}] / 0.12 ≈ $0.72 million × 5.65 ≈ $4.07 million

Therefore, the increase in project NPV due to sales escalation is approximately $4.070 million.

Effect of Increasing Variable Costs to 60%

When variable costs rise to 60% of sales, the contribution margin diminishes, affecting net cash flows. Calculations for the new scenario involve adjusting the variable costs to 60% of sales, then analyzing the impact on operating income and cash flows.

With sales at $11.5 million:

  • Variable costs = 60% of $11.5 million = $6.9 million
  • Contribution margin = $4.6 million
  • Operating income before taxes = $1.2 million
  • Taxes (40%) = $0.48 million
  • Net income = $0.72 million

If variable costs increase to 60% at the higher sales level ($13.5 million):

  • Variable costs = $8.1 million
  • Contribution margin = $5.4 million
  • Operating income before taxes = $2 million
  • Taxes = $0.8 million
  • Net income = $1.2 million

The incremental cash flow change is the difference between the two net incomes, which is approximately $0.48 million. Discounted over ten years at 12%, the present value is:

PV ≈ $0.48 million × 5.65 ≈ $2.712 million

Since the question asks for the absolute value of change, the NPV impact is approximately $2.712 million.

Maximum Fixed Costs Before NPV Turns Negative

Given the base-case NPV of $3.4 million, we calculate the maximum fixed costs increase that would reduce the NPV to zero. The total cash flows are impacted directly by fixed costs; an increase equaling this NPV would nullify the project value.

To find the increase in fixed costs in dollars:

Fixed costs increase = NPV / Present value factor

The present value factor for an annuity over ten years at 12% is 5.65, so:

Fixed cost increase = $3.4 million / 5.65 ≈ $601,770

Thus, fixed costs can increase by approximately $601,770 before the NPV turns negative.

Maximum Fixed Costs Before Accounting Profits Turn Negative

The net income is impacted when fixed costs surpass the contribution margin after taxes. Calculations involve determining the fixed costs level where operating income before taxes becomes zero, i.e., contribution margin minus fixed costs equals zero.

At the current sales ($11.5 million):

  • Contribution margin = $6.9 million (40%) of sales

Fixed costs are $3.4 million; to find the fixed costs level where profit turns negative, subtract the contribution margin from fixed costs:

Remaining contribution margin after taxes = (Contribution margin - fixed costs) × (1 - tax rate)

Solving for fixed costs where net profit = 0:

Contribution margin = fixed costs

Thus, fixed costs can increase by approximately $3.4 million before profits turn negative.

Conclusion

In summary, increasing sales significantly enhances NPV, while rising variable costs erodes profitability. The maximum tolerable increase in fixed costs before the project becomes unviable is approximately $601,770, and fixed costs can rise up to $3.4 million before accounting profits become negative, given current contribution margins and tax rates. These analyses underscore the importance of managing costs and understanding their impacts on project viability over its lifespan.

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