Question

Consider a project to supply Tacoma 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 Tacoma’s actual machine screw requirements.

a. What is the sensitivity of the project OCF to changes in the quantity supplied?

b. 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?

Answer 1

CF0=-Cost of equipment-working capital
CF1, CF2, CF3, CF4, CF5=((number of cartons*(price per carton-variable cost per carton)-fixed costs per year-depreciation)*(1-tax rate)+depreciation)
Additional cash flow in year 6=Salvage value*(1-tax rate)+working capital
Depreciation=Initial cost of equipment/5
NPV=CF0+CF1/(1+r)+CF2/(1+r)^2+CF3/(1+r)^3+CF4/(1+r)^4+CF5/(1+r)^5+CF6/(1+r)^6+Additional cash flow in year 6/(1+r)^6

a. What is the sensitivity of the project OCF to changes in the quantity supplied?
=(340-250)*(1-24%)
=68.4

b. What about the sensitivity of NPV to changes in quantity supplied?
=(340-250)*(1-24%)/13%*(1-1/1.13^6)
=273.4324056

c. Given the sensitivity number you calculated, is there some minimum level of output below which you wouldn’t want to operate?
-5600000-560000+560000/1.13^6+450000*(1-24%)/1.13^6+((Q*(340-250)-600000-5600000/6)*(1-24%)+5600000/6)/13%*(1-1/1.13^6)>=0
=>Q>=24335.755762