Consider A Project To Supply Detroit With 25,000 Tons Of Mac

Consider a project to supply Detroit with 25,000 tons of machine screw

Consider a project to supply Detroit with 25,000 tons of machine screws annually for automobile production. You will need an initial $2,600,000 investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be $650,000 and that variable costs should be $200 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the five-year project life. It also estimates a salvage value of $600,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $290 per ton. The engineering department estimates you will need an initial net working capital investment of $260,000. You require a return of 12 percent and face a marginal tax rate of 38 percent on this project. Suppose you’re confident about your own projections, but you’re a little unsure about Detroit’s actual machine screw requirement.

Paper For Above instruction

This analysis examines the financial viability of a manufacturing project to supply Detroit with 25,000 tons of machine screws annually for automobile production. The core focus involves evaluating the sensitivity of the project's operating cash flows (OCF) and net present value (NPV) to changes in the quantity supplied, which is a pivotal aspect in decision-making under uncertainty. Understanding these sensitivities enables managers to assess the potential impacts of demand fluctuations on project profitability and inform strategic choices regarding production levels.

Project Overview

The project's foundational parameters include an initial capital investment of $2,600,000 for manufacturing equipment, with an expected project duration of five years. Fixed costs are estimated at $650,000 annually, with variable costs of $200 per ton. The selling price is projected at $290 per ton, and the project requires an initial net working capital (NWC) investment of $260,000. Depreciation is calculated on a straight-line basis over five years, resulting in annual depreciation of $520,000, and the asset's salvage value is estimated at $600,000. The company seeks a return of 12%, and the project's tax rate is 38%.

Financial Calculations and Sensitivity Analysis

Operating Cash Flow (OCF) Sensitivity to Quantity Changes

The OCF's sensitivity to changes in the quantity supplied (Q) can be assessed by analyzing how incremental changes in production volume influence yearly cash flows. The formula for operating cash flow is:

OCF = (Revenue - Operating Expenses - Depreciation) × (1 - Tax Rate) + Depreciation

Where:

• Revenue = Price per ton × Quantity
• Operating Expenses = Fixed costs + Variable costs per ton × Quantity

Assuming a linear relationship, the change in OCF relative to a change in quantity (ΔQ) can be expressed as:

ΔOCF/ΔQ = (Price - Variable Cost) × (1 - Tax Rate)

Plugging in the values:

ΔOCF/ΔQ = ($290 - $200) × (1 - 0.38) = $90 × 0.62 = $55.80

Thus, the sensitivity of the OCF to changes in quantity supplied is approximately $55.80 per ton.

NPV Sensitivity to Quantity Changes

The net present value (NPV) sensitivity to changes in quantity considers how variations in volume affect the discounted cash flows over the project's life. Using the computed OCF sensitivity, we find the change in NPV per additional ton supplied as:

ΔNPV/ΔQ = ΔOCF/ΔQ × PV of Annuity Factor

Assuming the project's cash flows are discounted at 12% over five years, the present value of an incremental change can be approximated by multiplying the sensitivity by the capital recovery factor:

Capital Recovery Factor (CRF) = (1 - (1 + r)^-n) / r

Calculating CRF:

CRF = (1 - (1 + 0.12)^-5) / 0.12 ≈ (1 - 0.5674) / 0.12 ≈ 3.804

Therefore, ΔNPV/ΔQ ≈ $55.80 × 3.804 ≈ $212.33

In summary, the NPV increases by approximately $212.33 for each additional ton supplied, reflecting the marginal value of increasing production volume within the project's financial structure.

Minimum Operating Output Level

The minimum level of output corresponds to the point where the project's NPV equals zero, essentially where total revenues just cover fixed and variable costs, depreciation, and taxes. Setting NPV to zero and solving for Q involves calculating the break-even volume:

NPV = (Total Cash Flows over n Years) - Initial Investment - NWC

Focusing on operating cash flows, the break-even quantity Q* satisfies:

0 = [(Price - Variable Cost) × Q* - Fixed Costs - Depreciation × tax shield] × PV factor - Initial Investment - NWC

Solving for Q* gives:

Q* = (Fixed Costs + Depreciation × Tax Shield + Initial Investment + NWC) / [(Price - Variable Cost) × (1 - Tax Rate)]

Inserting known values:

Q* = ($650,000 + $520,000 × 0.62 + $2,600,000 + $260,000) / ($90 × 0.62) ≈ ($650,000 + $322,400 + $2,600,000 + $260,000) / 55.80 ≈ $3,832,800 / 55.80 ≈ 68,582 units

Therefore, the minimum operating level is approximately 68,582 units.

Conclusion

This analysis highlights that the operating cash flows are highly sensitive to the quantity supplied, with a dollar sensitivity of about $55.80 per ton. The NPV responds proportionally, with an estimated increase of approximately $212.33 for each additional ton. It also reveals that operating below roughly 68,582 units would render the project unprofitable under the given assumptions, indicating the critical importance of demand estimates and operational efficiency in strategic planning. Managers must consider these sensitivities to mitigate risks associated with demand fluctuations and to optimize production schedules.

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