Question

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A project has the following estimated data: price = $79 per unit; variable costs = $41.87...

A project has the following estimated data: price = $79 per unit; variable costs = $41.87 per unit; fixed costs = $6,900; required return = 9 percent; initial investment = $10,000; life = six years. Ignore the effect of taxes.

  

a. What is the accounting break-even quantity?

  

b. What is the cash break-even quantity?

  

c. What is the financial break-even quantity?

  

d. What is the degree of operating leverage at the financial break-even level of output?

Solutions

Expert Solution

  1. Accounting BEP:
    • (SP-VC) x BEP units = Fixed Cost
    • (79-41.87) x BEP units = 6900
    • BEP Units = 185.8335578
    • As there cant be partial units, we should assume it to be 186 units, the next highest integer
  2. Cash BEP:
    • We reduce the Fixed cost by depreciation as it is a non cash expense
    • (SP-VC) x BEP units = Fixed Cost - Depreciation
    • Depreciation = initial investment/life
    • Depreciation = 10000/6 = 1666.666667
    • (79-41.87) x BEP units = 6900 - 1666.666667
    • BEP Units = 140.946225
    • As there cant be partial units, we should assume it to be 141 units, the next highest integer
  3. FInancial BEP is when the NPV = 0
    • Depreciation is added back as it is a non cash expense
      • Year 0 1 2 3 4 5 6
        Units Calculated 200.983872 200.983872 200.983872 200.983872 200.983872 200.983872
        SP Given 79 79 79 79 79 79
        Sale SP x BEP units 15877.72589 15877.72589 15877.72589 15877.72589 15877.72589 15877.72589
        VC per unit Given 41.87 41.87 41.87 41.87 41.87 41.87
        Total VC VC per unit x BEP units 8415.194719 8415.194719 8415.194719 8415.194719 8415.194719 8415.194719
        Fixed cost Given 6900 6900 6900 6900 6900 6900
        Depreciation Calculated above 1666.666667 1666.666667 1666.666667 1666.666667 1666.666667 1666.666667
        EAT Sale-VC-FC+Depreciation 2229.197833 2229.197833 2229.197833 2229.197833 2229.197833 2229.197833
        FCINV Given -10000
        FCF -10000 2229.197833 2229.197833 2229.197833 2229.197833 2229.197833 2229.197833
        Discount rate factor 1/1.09^0 1/1.09^1 1/1.09^2 1/1.09^3 1/1.09^4 1/1.09^5 1/1.09^6
        Discount factor 1 0.917431193 0.841679993 0.77218348 0.708425211 0.649931386 0.596267327
        DCF FCF x Discount factor -10000 2045.135627 1876.271217 1721.34974 1579.219945 1448.825638 1329.197833
        NPV Sum of all DCF 0
    • BEP Units = 200.983872
    • As there cant be partial units, we should assume it to be 201 units, the next highest integer


jeff jeffy answered 9 months ago
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