Question

Consider a project to supply Detroit with 27,000 tons of machine screws annually for automobile production. You will need an initial $5,700,000 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 $1,375,000 and that variable costs should be $260 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 $750,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $374 per ton. The engineering department estimates you will need an initial net working capital investment of $550,000. You require a return of 13 percent and face a tax rate of 24 percent on this project. Calculate the accounting, cash, and financial break-even quantities. (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) Answer is complete but not entirely correct. Cash break-even Accounting break-even Financial break-even 9,430 20,395 25,483 %

Answer 1

financial break even is a level where NPV is ZERO

suppose the break even units are Y

NPV = 0 = Present value of cash outflow- present value of cash inflow

(1) present value of cash inflow = [(((374-260)y-1,375,000)(1-0.24)) + depreciation tax shield (950000*24%) ] * P/A(6years,13%)

=[(114y-1375000)(0.76) + 228000]*3.9975

=86.64y -1045000+228000]*3.9975

=346.3434y - 3265957.5

depreciation =5700000/6year = 950000

(2) present value of cash outflow

=initial investment -present value of salvage net of tax+initial cash outflow in form of working capital- cash inflow in form of working capital received at the end of project

= 5,700,000- (750000-24%)(1/1.13)⁶ +550000 - 550000(1/1.13)⁶

=5700000-273781.560629+550000-264175.190081

=5712043.2493

(3) 0 = 346.3434y-3265957.5-5712043.2493

346.343y = 8978000.7493

y = 25922units (rounded to nearest whole unit)