Answer:
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%.
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%
