Question

Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,600,000 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 $600,000 and that variable costs should be $250 per ton. Further, the accounting department will depreciate the initial fixed asset investment straight-line to zero over the 6-year project life and estimate 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 $340 per ton. The engineering department estimates you will need an initial net working capital investment of $560,000. You require a return of 13 percent and face a marginal tax rate of 24 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? What about the sensitivity of NPV to changes in quantity supplied? c. Given the sensitivity number you calculated, is there some minimum level of output below which you wouldn’t want to operate? Show step by step

Answer 1

Answer (a):

Sensitivity of the project OCF to changes in the quantity supplied:

Changes in OCF due to increase in quantity by 1 ton = (Sales price - Variable cost) * (1 - Tax rate)

= (340 -250) * (1-24%)

= $68.40

Hence:

Changes in OCF due to change in quantity per unit = $68.40

Answer (b):

The cash flows and NPV is calculated based on 40000 units as follows:

Sensitivity of NPV to changes in quantity supplied

Sensitivity of NPV to increase quantity supplied per unit = Change in OCF * PV of $1 annuity for 6 yrs at 13% rate

= 68.40 * 3.99755

= $273.43242

Sensitivity of NPV to increase quantity supplied per unit = $273.43

Answer (c):

As calculated in answer above, Initial investment = $6,160,000

PV of terminal cash flows = $433247.31

You would operate if NPV of the project is positive meaning NPV at least should be = $1

Hence:

Minimum quantity required = (Initial investment + PV of Fixed cost of net of tax - PV of Depreciation tax shield - PV of terminal cash flow + NPV required) / Sensitivity of NPV to change quantity supplied per unit

= (6160000 + 600000 * (1- 24%) * 3.99755 - 933333 * 24% * 3.99755 - 433247.31 + 1) /273.43242

= 24336 tons

Hence:

Minimum level of output below which you wouldn’t want to operate = 24,336 tons