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Homework answers / question archive / Consider a project with the following data: accounting break even quantity = 16,000 units; cash break even quantity = 12,500 units; life = three years; fixed costs = $120,000; variable costs = $20 per unit; required return = 15%
Consider a project with the following data: accounting break even quantity = 16,000 units; cash break even quantity = 12,500 units; life = three years; fixed costs = $120,000; variable costs = $20 per unit; required return = 15%. Ignoring the effect of taxes, find the financial break-even quantity
Financial break-even can be caclulated by calculing OCF and for this we'll use accounting break-even and cash break even equations;
As we don't know the price, so we'll use cash break-even equation to find it;
Cash break-even equation:
Cash break even quantity = Fixed Cost / ( Price - Variable cost)
12,500 = 120,000 / ( Price - 20)
12,500 * ( Price - 20) = 120,000
Price - 20 = 120,000 / 12,500
Price - 20 = 9.6
Price = 9.6 + 20
Price = $29.6
Now,
Acconting Break even quantity;
Accounting break-even quantity = (Fixed cost + Depreciation) / ( Price - variable cost)
16,000 = ( 120,000 + Depreciation) / ( 29.6 - 20)
16,000 * ( 9.6 ) = 120,000 + Depreciation
153,600 = 120,000 + Depreciation
153,600 - 120,000 = Depreciation
33,600 = Depreciation
Assuming Depreciation as Straight line method, and having life of asset as 3 years , Cost of asset can be calculated;
Depreciation = Cost of Asset / Life of asset
; 33,600 =Cost of asset / 3
; 33,600 * 3 = cost of asset
; 100,800 = cost of asset
And we know that at Financial break-even NPV is zero,
So, Present value of cash outflows (Cost of Asset) = Present value of inflows
so, OCF(present value of inflows) will be
PV of outflows = OCF * PVIFA (at 15%, 3 years)
100,800 = OCF * 2.2832
$ 44,148.56 = OCF
Now,
Financial Break-even quantity;
Financial break - even quantity = (OCF + Fixed cost) / ( Price - variable cost)
= ( 44,148.56 + 120,000) / ( 29.6 - 20)
= 164,148.56 / 9.6
= 17,098.808
so,
Financial break-even quantity = 17,098.808 units