Problem 11-28 Sensitivity Analysis [LO1] Consider a project to supply Detroit wi
ID: 2761936 • Letter: P
Question
Problem 11-28 Sensitivity Analysis [LO1]
Consider a project to supply Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial $3,000,000 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 $800,000 and that variable costs should be $250 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 $650,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $360 per ton. The engineering department estimates you will need an initial net working capital investment of $420,000. You require a 15 percent return and face a marginal tax rate of 38 percent on this project.
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))
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))
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.)
Consider a project to supply Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial $3,000,000 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 $800,000 and that variable costs should be $250 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 $650,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $360 per ton. The engineering department estimates you will need an initial net working capital investment of $420,000. You require a 15 percent return and face a marginal tax rate of 38 percent on this project.
Explanation / Answer
Answer: a. Using the tax shield approach, the OCF is:
OCF = [($360 – 250)(30,000) – $800,000](0.62) + 0.38($3,000,000/3)
OCF = $1930000
And the NPV is:
NPV = –$3,000,000 – 420,000 + $1930,000(PVIFA 15%,3 ) + [$420,000 + $650,000(1 – .38)]/1.15 5
NPV = $1527760.34
To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 31,000. The OCF at this level of sale is:
OCF = [($360 – 250)(31,000) – $800,000](0.62) + 0.38($3,000,000/3)
OCF = $1998200
The sensitivity of changes in the OCF to quantity sold is:
OCF/Q = ($1930000 – 1998200)/(30,000 – 31,000)
OCF/Q = +$68.20
Answer:b The NPV at this level of sales is:
NPV = –$3,000,000 – $420,000 + $1998200(PVIFA 15%,3 ) + [$420,000 + $650,000(1 – 0.38)]/1.15 5
NPV = $1683476.29
And the sensitivity of NPV to changes in the quantity sold is:
NPV/Q = ($1527760.34 – 1683476.29))/(30,000 – 31,000)
NPV/Q = +$155.72
Answer:c
You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes $155.72 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:
$1527760.34= $155.72(Q)
Q =9811
For a zero NPV, we need to decrease sales by 1,633 units, so the minimum quantity is:
Q Min = 30000-9811=20189
Q Min = 23,367