Question

Consider a project to supply Detroit with 25,000 tons of machine screws annually for automobile production. You will need an initial $4,500,000 investment in threading equipment to get the project started; the project will last for 5 years. The accounting department estimates that annual fixed costs will be $1,075,000 and that variable costs should be $200 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the 5-year project life. It also estimates a salvage value of $450,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $302 per ton. The engineering department estimates you will need an initial net working capital investment of $430,000. You require a return of 11 percent and face a tax rate of 22 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 answer to 2 decimal places, e.g., 32.16.)

Answer 1

If the quantity demand for machine screws decreases by 1%, the net cash flows for the first 4 years will decrease by 1.48%, and the net cash flow for the last year will decrease by 0.93%. If the quantity demanded falls by more than 7%, the NPV will become negative since the IRR will be 11%.

Step-by-step explanation:

expected revenue = 25,000 tons x $302 = $7,550,000 per year

initial investment = $4,500,000 + $430,000 = $4,930,000

contribution margin per unit = $302 - $200 = $102

total contribution margin = $102 x 25,000 = $2,550,000

annual fixed costs = $1,075,000

depreciation expense per year = $900,000

tax rate = 22%

required return rate = 11%

after tax salvage value = $450,000 x (1 - 22%) = $351,000

NCF₀ = -$4,930,000

NCF₁ = [($2,550,000 - $1,075,000 - $900,000) x 0.78] + $900,000 = $1,348,500

NCF₂ = $1,348,500

NCF₃ = $1,348,500

NCF₄ = $1,348,500

NCF₅ = $1,348,500 + $351,000 + $430,000 = $2,129,500

NPV = $517,402.62

IRR = 14.83%

if the demand falls by 10%, then total contribution margin will be $2,295,000

NCF₁₋₄ = $1,149,600

NCF₅ = $1,930,600

NPV = -$217,711.30

TIR = 9.36%

the first 4 net cash flows will decrease by 14.75%

the last cash flow will decrease by 9.34%

if the demand falls by 20%, then total contribution margin will be $2,040,000

NCF₁₋₄ = $950,700

NCF₅ = $1,731,700

NPV = -$952,825.22

TIR = 3.63%

the first 4 net cash flows will decrease by 29.5%

the last cash flow will decrease by 18.68%

This means that if the demand for machine screws decreases by 1%, the net cash flows for the first 4 years will decrease by 1.48%, the net cash flow for the last year will decrease by 0.93%