This problem concerns the effect of taxes on the various break-even measures. Co

Question

This problem concerns the effect of taxes on the various break-even measures. Consider a project to supply Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial S3,000,000 investment in threading equipment to get the project started; the project will last for three years. The accounting department estimates that annual fixed costs will be S800,000 and that variable costs should be $250 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the three-year project life. It also estimates a salvage value of $650,000 after dismantling costs The marketing department estimates that the automakers will let the contract at a selling price of $360 per ton. The engineering department estimates you will need an initial net working capital investment of $420,000. You require a return of 15 percent and face a marginal tax rate of 38 percent on this project. Calculate the accounting, cash, and financial break-even quantities. (Do not round intermediate calculations and round your final answers to the nearest whole number, e.g., 32.) Cash break-even Accounting break-even Financial break-even

Explanation / Answer

Total Supply required = 30,000 Tons/annum

Initial Investment =$3,000,000

Project Life = 3 years

Annual Depreciation using Straight Line =$3,000,000/3 =$1,000,000

Salavage Value of Equipment =$650,000

Selling Price =$360/Ton

Total Revenue =$360x30,000 =$10,800,000

Net Working Capital Required =$420,000

Annual Fixed Cost =$800,000

Variable Costs =$250x30,000 =$7,500,000

Marginal Tax Rate =35%

Required Return =15%

We know, Cash Breakeven = Fixed costs- Non-cash expenses/(Selling price - Variable cost)

Income Statement

Sales                       $10,800,000

Fixed Cost                $    800,000

Variable Cost            $ 7,500,000

Depreciation             $ 1,000,000

EBIT                      $ 1,500,000

Operating Cash Flow = EBITx(1-T) + D =$1,500,000x(1-0.35) + 1,000,000 =1,975,000

Accounting Break-Even, ABE = (Fixed Cost + Depreciation)/Contribution Margin

ABE = (800,000 + 1,000,000)/110

= 16,364 Tons

Hence, Accounting Break Even is at 16,364 Tons

Contribution Margin per unit =$360 - 250 =$110

Cash Break Even = Fixed Cost/Contribution Margin =800,000/110 =7,272 Tons

Hence, Cash Break Even is at 7,272 Tons

Financial Breakeven is at the sales at which NPV=0

Let n be the number of breakeven units,

Operating Cash Flow = (110n - 1,800,000)x0.65 + 1,000,000 = 71.50n - 1,170,000 + 1,000,000 =71.50n - 170,000

=> -3,000,000 + (71.50n - 170,000)x{(1-(1+0.15)-3)/0.15} + 650,000/1.153 =0

=> (71.50n - 170,000)x2.2832 + 427,386 = 3,000,000

=> 71.50n - 170,000 = 1,126,746

=> 71.50n = 1,296,746

=> n = 18,136.31

Hence, Financial Breakeven units are 18,136.31 Tons

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