Consider a project to supply Detroit with 30,000 tons of machine screws annually

Question

Consider a project to supply Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial $3,000,000 investment in threading equipment to get the project started; the project will last for three years. The accounting department estimates that annual fixed costs will be $800,000 and that variable costs should be $250 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the three-year project life. It also estimates a salvage value of $650,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $360 per ton. The engineering department estimates you will need an initial net working capital investment of $420,000. You require a return of 15 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.

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Suppose you'e onident about your own projections, b o're it's actual machine screw requirement. a. What is the sensitivity of the project OCF to changes in the quantity supplied? (Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).) b. 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).) ANPVIAC c. Given the sensitivity number you calculated, is there some 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 units

Explanation / Answer

Operating cash flow= [[quantiy*(Sp-CP)]-fixed cost]*(1-tax rate)]+(taxrate* depreciation)

Depreciation= invenstment/no of years
=3,000,000/3=1,000,000
=[30000*(360-250)-800000]*(1-0.38)]+(0.38*1000000)
=$1,930,000

NPV of the project= -invesntment-working capital+ present value of cash flows
=-3,000,0000-420,000+1930000*pvifa(15%,3)+[420000+650000*(1-.38))]
the last value in the formuale is working capital reover and after tax salvage value
=$1,527,760

let us increase the quantity to 31000
then OCF=1,998,200

Change in OCF/Change in qunatiy=(1,998,200-1,930,000)/(31000-30000)
=68.2

NPV at 31,000 level of slaes
NPV=$1,683,476

Change in NPV/Change in qunatiy=(1,683,476-1,527,760)/(31000-30000)
=155.72

We dont want the quantity to fall below point where NOV is Zero and NpV changes for every $155.72 for every unit sold then
1527760=155.72* change in qunatity

change in qunatity=9811
For a Zero NPV we need to decrease sales by 9811 units so minimum qunatity is
=30000-9811=20,189

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