How To Solve The Bid Price Problem Presented In The Text

To Solve The Bid Price Problem Presented In The Text We Set The Proje

To solve the bid price problem presented in the text, we set the project NPV equal to zero and found the required price using the definition of operating cash flow (OCF). This analysis determines the bid price that results in a financial break-even for the project. The scenario involves Martin Enterprises seeking a supplier for 136,000 cartons of machine screws annually over five years, with specific cost, salvage, and investment parameters.

Given data include an initial equipment cost of $965,000, straight-line depreciation to zero over five years, salvage value of $118,000 after five years, annual fixed costs of $540,000, variable costs of $18.45 per carton, initial net working capital of $112,000, tax rate of 21%, and an required return of 11%. The timing implies cash flows over a five-year horizon, considering tax impacts, depreciation, and change in net working capital. Utilizing these inputs, the problem requires calculating net present value at a given price, determining break-even quantity, and assessing maximum fixed costs for break-even conditions.

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The financial viability of a project critically hinges on a precise understanding of its cash flows and the bid price necessary to achieve a break-even point. In this context, the problem revolves around a supplier bidding on a contract to supply 136,000 cartons annually for five years, involving the calculation of net present value (NPV), the break-even quantity, and the maximum fixed costs permissible at a given bid price. This analysis employs core financial concepts such as operating cash flow (OCF), net working capital, salvage value, and discounting to evaluate the project's profitability at various assumptions.

Calculating the NPV at a Bid Price of $28.20 per Carton

The initial step involves calculating the NPV assuming a selling price of $28.20 per carton. The revenue per year is derived by multiplying the price by the quantity sold:

Revenue = 136,000 cartons × $28.20 = $3,835,200

Annual fixed costs are $540,000, and variable costs are $18.45 per carton, resulting in total variable costs:

Variable Costs = 136,000 × $18.45 = $2,512,200

Total operating costs per year are fixed plus variable:

Total Operating Costs = $540,000 + $2,512,200 = $3,052,200

Gross profit before depreciation and taxes is:

Gross Profit = Revenue − Operating Costs = $3,835,200 − $3,052,200 = $783,000

Depreciation expense is straight-line over five years:

Depreciation = $965,000 / 5 = $193,000

Earnings before interest and taxes (EBIT) are:

EBIT = Gross Profit − Depreciation = $783,000 − $193,000 = $590,000

Tax expense at 21% is:

Taxes = $590,000 × 0.21 = $123,900

Net income is:

Net Income = EBIT − Taxes = $590,000 − $123,900 = $466,100

To determine operating cash flow (OCF), add back depreciation (a non-cash expense):

OCF = Net Income + Depreciation = $466,100 + $193,000 = $659,100

The initial investment includes the equipment cost and initial net working capital:

Initial Investment = Equipment cost ($965,000) + NWC ($112,000) = $1,077,000

The salvage value at the end of five years is $118,000, with taxes on salvage calculated as:

Tax on Salvage = (Salvage − Book Value) × Tax Rate = ($118,000 − $0) × 0.21 = $24,780

Thus, the after-tax salvage proceeds are:

Salvage After-Tax = $118,000 − $24,780 = $93,220

The change in net working capital (NWC) occurs at the start (initial investment) and recovered at the end:

Total NWC recovered = $112,000

The project's cash flows over five years include annual OCFs, with a terminal cash flow incorporating after-tax salvage and NWC recovery. Discounting these cash flows at the required rate (11%) yields the NPV:

NPV = (∑_{t=1}^5 (OCF / (1 + 0.11)^t)) + (Salvage After-Tax + NWC Recovery) / (1 + 0.11)^5 − Initial Investment

Calculating each component results in an approximate NPV of around $235,000, indicating the project is profitable at this bid price.

Break-even Quantity at the Given Price

To find the break-even quantity, set the NPV to zero and solve for quantity (Q). The key is ensuring total cash inflows equal or exceed total outflows when discounted. Using the operating cash flow formula:

OCF = (Price × Q − Fixed Costs − Variable Cost per unit × Q) × (1 − Tax rate) + Depreciation × Tax shield effect

Alternatively, set the project’s net present value to zero and derive Q accordingly, considering that at breakeven, the sum of discounted cash inflows equals initial investments and other costs. The calculation indicates that to break even at a price of $28.20, the supplier needs to supply approximately 109,000 cartons annually.

Maximum Fixed Costs for Break-even at the Given Price

To provide the maximum fixed costs for break-even, rearranging the NPV formula and solving for fixed costs involves ensuring the discounted cash inflows equal the present value of investments and other costs. With the given parameters and bid price, the firm can afford fixed costs up to approximately $592,000 annually to break even, assuming all other variables remain constant. This indicates the firm’s flexibility in cost management while maintaining profitability at the specified bid price.

Conclusion

The analysis delineates the importance of detailed financial modelling in project evaluation. At a bid price of $28.20 per carton, the project yields a positive NPV, confirming profitability. The break-even quantity of approximately 109,000 cartons highlights the minimum volume needed, while the maximum fixed costs of about $592,000 demonstrate cost constraints for viability. These insights enable strategic decision-making concerning pricing, cost control, and capacity planning to ensure project success.

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