1. Consider a project to supply Detroit with 40,000 tons of machine screws annua

Question

1. Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,400,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $800,000 and that variable costs should be $350 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-year project life. It also estimates a salvage value of $280,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $450 per ton. The engineering department estimates you will need an initial net working capital investment of $520,000. You require a 16 percent return and face a marginal tax rate of 30 percent on this project.

a. What is the sensitivity of NPV to changes in quantity supplied? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

NPV/Q =

b. Given the sensitivity number you calculated, what is the minimum level of output below which you wouldn’t want to operate? (Do not round intermediate calculations and round your final answer to the nearest whole number.)

Minimum level of output =

2. Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,200,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $700,000 and that variable costs should be $300 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-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 $370 per ton. The engineering department estimates you will need an initial net working capital investment of $500,000. You require a 15 percent return and face a marginal tax rate of 30 percent on this project.

a. Calculate the financial break-even quantities. (Do not round intermediate calculations and round your final answers to the nearest whole number. (e.g., 32))

Financial break even =

Explanation / Answer

a. Operating cash flow Sales = $450 x 40,000 tons $18,000,000 Less: Variable Cost = $350 x 40,000 tons -$14,000,000 Less: Fixed Cost -$800,000 Net Income $3,200,000 Tax Rate 30% -$960,000 Earning after Tax $2,240,000 Add: Tax Shield on Depreciation ($54,000,000/6years) x 30% $2,700,000 Operating cash flow $4,940,000 NPV Year Cash Flow PV @16% Present Value $5,400,000(Investment)+$520,000(working capital) 0 -$5,920,000 1.000 -$5,920,000 1 $4,940,000 0.862 $4,258,620.69 2 $4,940,000 0.743 $3,671,224.73 3 $4,940,000 0.641 $3,164,848.91 4 $4,940,000 0.552 $2,728,318.02 5 $4,940,000 0.476 $2,351,998.3 Salvage value after tax $280,000 x (1-30%) + $4,940,000 +$520,000 (WC) 6 $5,656,000 0.410 $2,321,461.39 NPV $12,576,472.04 To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 41,000. The OCF at this level of sale is Operating cash flow Sales = $450 x 41,000 tons $18,450,000 Less: Variable Cost = $350 x 41,000 tons -$14,350,000 Less: Fixed Cost -$800,000 Net Income $3,300,000 Tax Rate 30% -$990,000 Earning after Tax $2,310,000 Add: Tax Shield on Depreciation ($54,000,000/6years) x 30% $2,700,000 Operating cash flow $5,010,000 NPV Year Cash Flow PV @16% Present Value $5,400,000(Investment)+$520,000(working capital) 0 -$5,920,000 1.000 -$5,920,000 1 $5,010,000 0.862 $4,318,965.52 2 $5,010,000 0.743 $3,723,246.14 3 $5,010,000 0.641 $3,209,694.94 4 $5,010,000 0.552 $2,766,978.4 5 $5,010,000 0.476 $2,385,326.21 Salvage value after tax $280,000 x (1-30%) + $4,940,000 +$520,000 (WC) 6 $5,726,000 0.410 $2,350,192.35 NPV $12,834,403.56 Sensitivity of NPV to changes in quantity supplied ?NPV/?Q = ($12,834,403.56 - $12,576,472.04)/(41000-40000) $257.93 b. The quantity should not fall below the point where the NPV is zero. The NPV changes $257.93 for every unit sale, so we can divide the NPV for 40,000 units by the sensitivity to get a change in quantity Change in Quantity = $12,576,472.04/40000 314 units For a zero NPV, we need to decrease sales by 314 units, so the minimum quantity Minimum Quantity = 40,000 - 314 39,686 units

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