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 $3,600,000 investment in threading equipment to get the project started; the project will last for four years. The accounting department estimates that annual fixed costs will be $850,000 and that variable costs should be $250 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the four-year project life. It also estimates a salvage value of $250,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $380 per ton. The engineering department estimates you will need an initial net working capital investment of $360,000. You require a return of 16 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

a.

Using the tax shield approach, the OCF at 20000 tons will be:

OCF = [(P – v)Q – FC](1 – tC) + tC(D)

OCF = [($380 – 250)(20000) – 850000](0.62) + 0.38(3600000/4)

OCF = $1427000

We will calculate the OCF at 21000 units. The choice of the second level of quantity sold is arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So, the OCF at this level of sales is:

OCF = [($380 – 250)(21000) – 850000](0.62) + 0.38(3600000/4)

OCF = $1507600

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

Sensitivity = DOCF/DQ = ($1507600 - 1427000)/(21000 – 20000)

DOCF/DQ = +$80.60

OCF will increase by $80.60 for every additional unit sold.

b. At level of 21000,

NPV = -3600000 - 360000 + (1507600 x Cumulative PVF @ 16% for 4 years) + (360000 x PVF @ 16% for 4th year) + (250000 x PVF @ 16% for 4th year)

= -3960000 + (1507600 x 2.798) + (360000 x 0.552) + (250000 x 0.552)

= $594985

At level of 20000 units,

NPV = -3600000 - 360000 + (1427000 x Cumulative PVF @ 16% for 4 years) + (360000 x PVF @ 16% for 4th year) + (250000 x PVF @ 16% for 4th year)

= -3960000 + (1427000 x 2.798) + (360000 x 0.552) + (250000 x 0.552)

= $369466

Sensitivity of NPV to changes in quantity supplied = (594985 - 369466) / (21000 - 20000)

= $225.52

c. You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes $225.52 for every unit sale, so we can divide the NPV for 20000 tons by the sensitivity to get a change in quantity. Doing so, we get:

369466 = 225.52(DQ)   

DQ = 1638 tons.

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