Consider a project to supply Detroit with 40,000 tons of machine screws annually
ID: 2799002 • Letter: C
Question
Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,200,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $700,000 and that variable costs should be $300 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-year project life. It also estimates a salvage value of $600,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $370 per ton. The engineering department estimates you will need an initial net working capital investment of $500,000. You require a return of 15 percent and face a marginal tax rate of 30 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
Calculation Of Operating Cash flows
40000 Unit
30000 Unit
Particulars
Amount
Amount
Revenue 40,000Tonne * 370
$ 148,00,000.00
$ 111,00,000.00
Variable Cost per Tonne 40000*300
$ 120,00,000.00
$ 90,00,000.00
Contribution
$ 28,00,000.00
$ 21,00,000.00
(-) Annual fixed cost
$ 7,00,000.00
$ 7,00,000.00
(-)Depreciation
$ 7,66,666.67
$ 7,66,666.67
PBT
$ 13,33,333.33
$ 6,33,333.33
(-) Tax 30%
$ 4,00,000.00
$ 1,90,000.00
PAT
$ 9,33,333.33
$ 4,43,333.33
OCF = PAT+ Depreciation
$ 17,00,000.00
$ 12,10,000.00
a) For calculating change in operating cash flows units taken be 30000 and cash flows calculated as above
Sensitivity of the project OCF to changes in quantity = (1,700,000-1,210,000)/ (40000-30000)
= $ 49 for 1 quantity changed.
b) Calculation of NPV
Cash outflow = Cost of machine + working capital requirement = $ 5,700,000
Cash inflow Terminal = Salvage Value+ Working capital surrendered = $600,000(1-0.3) +$500,000 = $920,000
At 40000 units NPV = 1,700,000*PVAF (15%, 6) + 920,000*PVIF (15%, 6) -$ 5,700,000
PVAF (15%, 6) = 3.784 from PVAF table, PVIF (15%, 6) = 0.432 referring PVIF table
NPV= 1,700,000*3.784 + 920,000*0.432 - 5,700,000
NPV= 1,130,240
At 30000 units NPV= 1,210,000*PVAF (15%, 6) + 920,000*PVIF (15%, 6) -$ 5,700,000
= - 723,920
Sensitivity of NPV to change in units= [1130240-(-723920)]/ [40000-30000]
= $ 185.416
c) So for every quantity change NPV changes by $ 185.416, for minimum quantity we can divide total NPV of 40000 units with npv sensitivity to find out how many units can be reduced
Q=1130240/185.416= 6095.7 units
I.e. Minimum units to operate where NPV is 0 is 40000units- 6095.7 units
=33,904.3 units
Calculation Of Operating Cash flows
40000 Unit
30000 Unit
Particulars
Amount
Amount
Revenue 40,000Tonne * 370
$ 148,00,000.00
$ 111,00,000.00
Variable Cost per Tonne 40000*300
$ 120,00,000.00
$ 90,00,000.00
Contribution
$ 28,00,000.00
$ 21,00,000.00
(-) Annual fixed cost
$ 7,00,000.00
$ 7,00,000.00
(-)Depreciation
$ 7,66,666.67
$ 7,66,666.67
PBT
$ 13,33,333.33
$ 6,33,333.33
(-) Tax 30%
$ 4,00,000.00
$ 1,90,000.00
PAT
$ 9,33,333.33
$ 4,43,333.33
OCF = PAT+ Depreciation
$ 17,00,000.00
$ 12,10,000.00
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