Question

Consider a project to supply Detroit with 27,000 tons of machine screws annually for automobile production. You will need an initial $4,600,000 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 $1,100,000 and that variable costs should be $205 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 $475,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $308 per ton. The engineering department estimates you will need an initial networking capital investment of $440,000. You require a return of 12 percent and face a tax rate of 23 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.) b. What is the sensitivity of NPV to changes in quantity supplied? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) 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 answer to the nearest whole number, e.g., 32) AOCFIAQ b. ANPVIAQ Minimum level of output

Answer 1

a) Change in OCF/Change in Q

This ratio measures the Change in Operating Cash flow for every unit change in Quantity.

Based on 27000 tons of screws to be manufactured, the operating cash flow will be worked out as below:

Operating Cash Flow = (Quantity(Price-Variable Costs) - Annual FIxed Costs)*(1-tax rate) + Tax rate (Initial Investment/Useful life i.e tax benefit on Depreciation)

= ((27,000*(308-205)-1,100,000))*(1-0.23)+(0.23*(4,600,000/5))

= ((27000*(103)-1,100,000))*(0.77))+0.23*(920,000)

= (2,781,000 - 1,100,000)*0.77+0.23*(920,000)

=(1,681,000)*0.77+0.23*(920,000)

= (1,294,370+211,600)

= 1,505,970

Assuming that instead of 27000 tons of screws, 26000 tons of screws are to be manufactured, the operating cash flow would be

((26,000*(308-205)-1,100,000))*(1-0.23)+(0.23*(4,600,000/5))

= ((26000*(103)-1,100,000))*(0.77))+0.23*(920,000)

= (2,678,000 - 1,100,000)*0.77+0.23*(920,000)

=(1,578,000)*0.77+0.23*(920,000)

= (1,215,060+211,600)

= 1,426,660

Change in OCF/Change in Quantity = (1,505,970-1,426,660)/(27,000-26,000) = 79,310/1000 =79.31

2) Sensitivity of NPV to Change in Quantity

Based on 27000 tons of Screws to be manufactured, the NPV would be as below

NPV = - Initial Investment cost - Net Working Capital + PV of all Operating Cash flows till year 5+ PV of Salvage Value at end of year 5+ PV of Net Working capital at end of year 5

= -4,600,000- 440,000 + 1,505,970(1-((1+12%)^-5/0.12))+475,000/1.12^5+440,000/1.12^5

= -5,040,000+5,428,685+2,69,527.76+249,667.82

= 907,880.58.

Assuming that instead of 27000 tons of screw, 26000 tons of screw is manufactured the NPV would be

=-4,600,000- 440,000 + 1,426,660(1-((1+12%)^-5/0.12))+475,000/1.12^5+440,000/1.12^5

= -5,040,000+5,142,790+2,69,527.76+249,667.82

= 621,985.59

Change in NPV/Change in Quantity = (907,880.58-621,985.59)/(27,000-26,000) = 285,895/1000 = 285.90

c) Minimum output

The minimum level of output below which i would not operate is worked out as below:

The NPV of the project for 27000 tons of screws is 907,880.58. Dividing this by the Change in NPV/Change in Quantity factor will give the number of tons of screws required to make this NPV.

i.e 907,880.58 / 285.90 = 3175.52

This means 3176 tons are required to make this NPV. Reducing this from 27000 tons will give the quantity at which NPV will be zero.

i,e 27000-3176 = 23,824 tons of screws, below which I would not operate.