Consider a project to supply Detroit with 20,000 tons of machine screws annually

Question

Consider a project to supply Detroit with 20,000 tons of machine screws annually for automobile production. You will need an initial $2,800,000 investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be $750,000 and that variable costs should be $260 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the five-year project life. It also estimates a salvage value of $220,000 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 $280,000. You require a return of 14 percent and face a marginal tax rate of 38 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 $

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 $

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

Solution:

a. Using the tax shield approach, the OCF is:

OCF = [($370 – 260)(20,000) – $750,000](0.62) + 0.38($2,800,000/5)

OCF = $1,118,000

And the NPV is:

NPV = –$2,500,000 – 280,000 + $1,118,000(PVIFA 14%, 5) + [$280,000 + $220,000(1 – .38)]/1.14^5

NPV = $1,253,164.53

To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 21,000.

The OCF at this level of sale is:

OCF = [($360 – 300)(21,000) – $750,000](0.62) + 0.38($2,800,000/5)

OCF = $1,180,000

The sensitivity of changes in the OCF to quantity sold is:

OCF/Q = ($1,118,000 – 1,180,000)/(20,000 – 21,000)

OCF/Q = +$62.00

b. The NPV at this level of sales is:

NPV = –$2,500,000 – $280,000 + $1,180,000 (PVIFA14%,5) + [$280,000 + $220,000(1 – 0.38)]/1.14^5

NPV = $1,487,300.66

And the sensitivity of NPV to changes in the quantity sold is:

NPV/Q = ($1,253,164.53 – 1,487,300.66))/(20,000 – 21,000)

NPV/Q = +$234.14

c. You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes$234.14 for every unit sold, so we can divide the NPV for 20,000 units by the sensitivity to get a change in quantity. Doing so, we get:

$1,253,164.53 = $234.14(Q)

Q = 5,352

For a zero NPV, we need to decrease sales by 5,352 units, so the minimum quantity is:

QMin= 20,000 – 5,352

QMin= 14,648

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