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 25,000 tons of machine screws annually for automobile production. You will need an initial $2,600,000 investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be $650,000 and that variable costs should be $200 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the fve-year project life. It also estimates a salvage value of $600,000 after dismantling costs The marketing department estimates that the automakers will let the contract at a selling price of $290 per ton. The engineering department estimates you will need an initial net working capital investment of $260,000. You require a return of 12 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 13000

Explanation / Answer

Total Supply required = 25,000 Tons/annum

Initial Investment =$2,600,000

Project Life = 5 years

Annual Depreciation using Straight Line =$2,600,000/5 =$520,000

Salavage Value of Equipment =$600,000

Selling Price =$290/Ton

Total Revenue =$290x25,000 =$7,250,000

Net Working Capital Required =$260,000

Annual Fixed Cost =$650,000

Variable Costs =$200x25,000 =$5,000,000

Marginal Tax Rate =38%

Required Return =12%

Income Statement

Sales                       $ 7,250,000

Fixed Cost                $    650,000

Variable Cost            $ 5,000,000

Depreciation             $     520,000

EBIT                        $ 1,080,000

Operating Cash Flow = EBITx(1-T) + D =$1,080,000x(1-0.38) + 520,000 =$1,189,600

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

ABE = (650,000 + 520,000)/90

= 13,000 Tons

Hence, Accounting Break Even is at 13,000 Tons

Contribution Margin per unit =$290 - 200 =$90

Cash Break Even = Fixed Cost/Contribution Margin =650,000/90 =7,222.22 Tons

Hence, Cash Break Even is at 7,222.22 Tons

Financial Breakeven is at the sales at which NPV=0

Let n be the number of breakeven units,

Operating Cash Flow = (90n - 1,170,000)x0.62 + 520,000 =55.8n - 725,400 + 520,000 =55.8n - 205,400

=> -2,600,000 + (55.8n - 205,400)x{(1-(1+0.12)-5)/0.12} + 600,000/1.125 =0

=> (55.8n - 205,400)x3.6048 + 340,456 = 2,600,000

=> 55.8n - 205,400 = 626,815

=> 55.8n = 832,215

=> n = 14,914.25

Hence, Financial Breakeven units are 14,914.25 Tons

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