Question

Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,800,000 investment in threading equipment to get the project started; the project will last for 6 years. The accounting department estimates that annual fixed costs will be $700,000 and that variable costs should be $210 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the 6-year project life. It also estimates a salvage value of $680,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $300 per ton. The engineering department estimates you will need an initial net working capital investment of $580,000. You require a return of 14 percent and face a marginal tax rate of 25 percent on this project.

  

Suppose you’re confident about your own projections, but you’re a little unsure about Detroit’s actual machine screw requirements.

   

a.	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 about 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, is there some minimum level of output below which you wouldn’t want to operate? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

(All amounts in $)

Initial Investment = 5,800,000 ...(1)

Investment in Net Working Capital (NWC) = 580,000 ...(2)

Total Project Cost = (1) + (2) = 6,380,000 ...(3)

Sale Price per unit = 300

Variable Cost = 210

Contribution/Gross Profit per unit = 90

Number of Units sold = 40,000

Total Contribution/Gross Profit = 40000 X 90 = 3,600,000 ...(4)

Annual Fixed Costs = 700,000

Earnings before Interest, Tax and Depreciation& Amortization (EBITDA) = 2,900,000 ...(5)

Depreciation of machinery:

Cost of Equipment = 5,800,000 (a)

Salvage Value = 680,000 (b)

Useful Life = 6 years (c)

Depreciation per annum = (a-b)/(c) = 853,333.33 ...(6)

Earnings before Interest and Tax (EBIT) = (5) - (6) = 2,046,666.67 ...(7)

Tax rate @ 25% on EBIT = 25% x (7) = 511,666.67

Earnings after Tax (EAT) = 1,535,000....(8)

Operating Cash Flow per year = EAT + Non cash expenses ie depreciation = (8) + (6) = 2,383,333 ... (9) = OCF

Operating Cash Flows per unit = (9)/number of units = 2,383,333/40,000 = 232.19... (10)

Answer (a): For every unit change in quantity, the present value of Operating Cash flows will change by $232.19

Present Value of Cash Flows:

Annuity Factor (r)= 14%

Present Value of cash flows = OCF per year/r x [1-(1/(1+r)^n)]

Substituting for the above formula, we get = PV of cash flows = 9,287,434.25 .... (11)

To the above, we add back investment in NWC at present value and salvage value:

Overall Cash Flows = (10) + (b) + Present value of NWC in year 6

= 9,287,434.25 + 680,000 + (580,000 * 1.14^-6 ) = 10,231,674.25... (12)

Net Present Value = (12) - (1) = 10,231,674.25 - 5,800,000 = 44,31,674.25... (13)

Net Present Value per unit = (13) / 40,000 = $110.79

Answer (b): For every unit change in quantity, the net present value will change by $110.79

Answer (c): Minimum Output Quantity at which NPV approximates to zero = ~ 26,000 UNITS based on above workings