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

ID: 2726547 • Letter: C

Question

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 return of 16 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.) places, e.g,32.16.) 0CFIAQ 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.) er to 2 decimal places, e.g-,3 ANPV/AQ 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

A./

OCF AT 40000 TON LEVEL

NPV AT 40000 TON LEVEL

= (-$5400000 - $520000) + $2870000 * PVIFA16%, 6 YRS + [$520000 + $280000 (1 - 0.3)] * PVIF16%, 6YRS

= -$5920000 + $2870000 * 3.6847 + $716000 * 0.4104

= -$5920000 + $10575089 + $293846

= $4948935

SUPPOSE THE QUANTITY CHANGE TO 41000 TON

OCF AT 41000 TON LEVEL

NPV AT 41000 TON LEVEL

= (-$5400000 - $520000) + $2940000 * PVIFA16%, 6 YRS + [$520000 + $280000 (1 - 0.3)] * PVIF16%, 6YRS

= -$5920000 + $2940000 * 3.6847 + $716000 * 0.4104

= -$5920000 + $10833018 + $293846

= $5206864

CHANGE IN OCF / CHANGE IN QUANTITY

= ($2940000 - $2870000) / 1000

= $70000 / 1000

= $70

B./

CHANGE IN NPV / CHANGE IN QUANTITY

= ($5206864 - 4948935) / 1000

= $257929 / 1000

= $257.93

C./

MINIMUM LEVEL OF OUTPUT

AT A LEVEL WHERE THE NPV IS ZERO THE COMPANY WILL NOT OPERATE

= NPV FIRST CASE = SENSITIVITY OF NPV * CHANGE IN QUANTITY

= $4948935 = $257.93 * CHANGE IN QUANTITY

CHANGE IN QUANTITY = 19187

FOR A ZERO NPV, WE NEED TO DECREASE SALES BY 19187 UNITS, SO THE MINIMUM QUANTITY IS

= 40000 - 19187

= 20813 UNITS

DESCRIPTION AMOUNT SALES (40000 * $450) $18000000 LESS VARIABLE COST (40000 * $350) ($14000000) LESS FIXED COST ($800000) INCOME $3200000 LESS TAX @30% ($960000) INCOME AFTER TAX $2240000 ADD DEPERICATION NET OF TAX ($5400000 / 6) (1 - 0.3) $630000 OCF $2870000

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

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

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