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 $4,000,000 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 $700,000 and that variable costs should be $200 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 $440,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $320 per ton. The engineering department estimates you will need an initial net working capital investment of $400,000. You require a return of 11 percent and face a marginal tax rate of 30 percent on this project.

Given the sensitivity number you calculated, is there some minimum level of output below which you wouldn’t want to operate?

Consider a project to supply Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial $4,000,000 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 $700,000 and that variable costs should be $200 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 $440,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $320 per ton. The engineering department estimates you will need an initial net working capital investment of $400,000. You require a return of 11 percent and face a marginal tax rate of 30 percent on this project.

Explanation / Answer

Solution.

At the cash break-even, the OCF is zero. Setting the tax shield equation equal to zero and solving for the quantity, we get:

OCF = 0 = [($320 – 200)QC – $700,000](0.70) + 0.30($4,000,000/3)

QC= 1,071

The accounting breakeven is:

QA= [$700,000 + ($4,000,000/3)]/($320 – 200)

QA= 16,944

Using the tax shield approach, the OCF is:

OCF = [($320 – 200)(30,000) – $700,000](0.70) + 0.30($4,000,000/3)

OCF = $2,430,000

And the NPV is:

NPV = –$4,000,000 – 400,000 + $2,430,000(PVIFA11%,3) + [$400,000 + $440,000(1 – .30)]/1.113

NPV = $2,055,910.26

To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 31,000. The OCF at this level of sales is:

OCF = [($320 – 200)(31,000) – $700,000](0.70) + 0.30($4,000,000/3)

OCF = $2,514,000

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

OCF/Q = ($2,430,000 – 2,514,000)/(30,000 – 31,000)

OCF/Q = +$84.00

The NPV at this level of sales is:

NPV = –$4,000,000 – $400,000 + $2,514,000(PVIFA11%,3) + [$400,000 + $440,000(1 – 0.30)]/1.113

NPV = $2,261,182.29

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

NPV/Q = ($2,055,910.26 – 2,261,182.29))/(30,000 – 31,000)

NPV/Q = +$205.27

You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes $205.27 for every unit sold, so we can divide the NPV for 30,000 units by the sensitivity to get a change in quantity. Doing so, we get:

$2,055,910.26 = $205.27(Q)

Q = 10,016

For a zero NPV, we need to decrease sales by 10,016 units, so the minimum quantity is:

QF = 30,000 – 10,016

QF = 19,984

At the cash break-even, the OCF is zero. Setting the tax shield equation equal to zero and solving for the quantity, we get:

OCF = 0 = [($320 – 200)QC – $700,000](0.70) + 0.30($4,000,000/3)

QC= 1,071

The accounting breakeven is:

QA= [$700,000 + ($4,000,000/3)]/($320 – 200)

QA= 16,944

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