Consider a project to supply Detroit with 40,000 tons of machine screws annually

Question

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 return of 15 percent and face a marginal tax rate of 30 percent on this project. a. Suppose you’re confident about your own projections, but you’re a little unsure about Detroit’s actual machine screw requirement. 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.) OCF/Q $ 49 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.) NPV/Q $ 185.416 c. 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, e.g., 32) Minimum level of output

Explanation / Answer

The above is base-case NPV.

OCF/Q is the change in OCF when the quantity is increased by 1 unit at 40,001

OCF = 1,730,049 =>  OCF/Q = $49.00

Similarly, NPV/Q is the change in NPV when the quantity is increased by 1 unit at 40,001

NPV = $49,392.58 =>  NPV/Q = $164.26

Minimum level of Output = 40,000 - 49,228.32 / 164.26 = 39,700

Detroit 0 1 2 3 4 5 6 Investment -$5,200,000 NWC -$550,000 $550,000 Salvage $600,000 Sales $14,800,000 $14,800,000 $14,800,000 $14,800,000 $14,800,000 $14,800,000 VC -$12,000,000 -$12,000,000 -$12,000,000 -$12,000,000 -$12,000,000 -$12,000,000 FC -$700,000 -$700,000 -$700,000 -$700,000 -$700,000 -$700,000 Depreciation -$866,667 -$866,667 -$866,667 -$866,667 -$866,667 -$866,667 EBT $1,233,333 $1,233,333 $1,233,333 $1,233,333 $1,233,333 $1,233,333 Tax (30%) -$370,000 -$370,000 -$370,000 -$370,000 -$370,000 -$370,000 Net Income $863,333 $863,333 $863,333 $863,333 $863,333 $863,333 Cash Flows -$5,750,000 $1,730,000 $1,730,000 $1,730,000 $1,730,000 $1,730,000 $2,700,000 NPV $49,228.32

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