A project has the following estimated data: price = $68 per unit; variable costs
ID: 2709180 • Letter: A
Question
A project has the following estimated data: price = $68 per unit; variable costs = $44 per unit; fixed costs = $18,000; required return = 10 percent; initial investment = $40,000; life = five years.
Ignoring the effect of taxes, what is the accounting break-even quantity? (Round your answer to 2 decimal places. (e.g., 32.16))
What is the financial break-even quantity? (Round your answer to 2 decimal places. (e.g., 32.16))
What is the degree of operating leverage at the financial break-even level of output? (Round your answer to 3 decimal places. (e.g., 32.161))
A project has the following estimated data: price = $68 per unit; variable costs = $44 per unit; fixed costs = $18,000; required return = 10 percent; initial investment = $40,000; life = five years.
Explanation / Answer
price = $68 per unit; variable costs = $44 per unit; fixed costs = $18,000; required return = 10 percent; initial investment = $40,000; life = five years.
depreciation=40,000/5=8000 per year using straight line depreciation.(its not mentioned how are you depreciating the asset so i am assuming SL method)
Let n be the accounting break-even quantity
at this break-even quantity,Total Revenue=n*68 =68n
Total variable costs=44n
Total accounting cost=Total variable costs+Total fixed costs + depreciation
Total accounting cost=44n+18,000 + 8000 =44n+26000
At break even, accounting profit=0 or Total Revenue=Total accounting cost =>68n=44n+26000=>68n-44n=26000=>n=26000/24=1083.33 units
Thus 1083.33 units is the accounting break-even quantity.
In cash break-even quantity we exclude non cash operating expense as depreciation,
at cash break-even quantity n,
Total Revenue=n*68 =68n
Total cost=Total variable costs+Total fixed costs=44n+18,000
=>Total Revenue=Total cost =>68n=44n+18,000=>24n=18,000 =>n=18000/24=750
Thus 750 units is the cash break-even quantity.
At financial break-even quantity n,
Total costs=Total variable costs+Total fixed costs+ Interest cost+depreciation
Interest cost=10%*40000=4000
Total costs=44n+18,000+ 4000+8000=44n+30000
Total Revenue=Total cost =>68n=44n+30000=> n=30000/24=1250
Thus 1250 units is the financial break-even quantity.
degree of operating leverage at the financial break-even level of output,
DOL=contribution margin/operating income
at financial break-even quantity n=1250 ,
Total Revenue=n*68 =68*1250 =85000
Total variable costs=44n=44*1250 =55000
Contribution Margin=85000-55000=30000
Total operating cost=Total variable costs+Total fixed costs + depreciation=55000+18,000+8000=81000
operating income=Total Revenue-Total operating cost=85000-81000=4000
DOL=Contribution Margin/operating income=30000/4000=7.5
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