5. A project has the following estimated data: price = $74 per unit; variable co

Question

5.

A project has the following estimated data: price = $74 per unit; variable costs = $47 per unit; fixed costs = $22,500; required return = 8 percent; initial investment = $24,000; life = three 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 = $74 per unit; variable costs = $47 per unit; fixed costs = $22,500; required return = 8 percent; initial investment = $24,000; life = three years.

Explanation / Answer

Requirement 1:

Accounting Break Even Quantity = (Fixed Cost + Depreciation)/(Selling Price - Variable Cost)

Depreciation= Initial Investment/Life = 24,000/3 = $8,000

Using the values provided in the questions, we get:

Accounting Break Even Quantity = (22,500 + 8,000)/(74 - 47) = 1129.63 units

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Requirement 2:

Cash Break Even Quantity = (Fixed Cost)/(Selling Price - Variable Cost) = (22,500)/(74 - 47) = 833.33 units

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Requirement 3:

Financial Break Even Quantity

We need to calculate operating cash flow to determine the financial break even quantity.

Step 1: Calculate Operating Cash Flow

Operating cash flow can be calculated with the use of financial calculator/excel. You need to take the values as follows:

N (period)= 3 years

PV (initial investment) = 24,000

R (required return) = 8%

FV (future value) = 0

PMT (operating cash flow)= To be calculated

The formula for calculating PMT in EXCEL = PMT(Rate,Nper,PV,FV)

Operating Cash Flow = PMT(8%,3,24,000,0) = $9312.80 (similar methodology for financial calculator)

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Step 2: Calculate Financial Break Even Quantity

Financial Break Even Quantity = (Operating Cash Flow - Depreciation*Taxes + Fixed Cost*(1-Taxes)/(Price - Variable Cost)*(1-Taxes)

Depreciation = Initial Investment/Life = 24,000/3 = $8,000

Financial Break Even Quantity = [(9312.80 - 8000*(0) + 22,500*(1-0)]/(74 - 47)*(1-0) = 1178.25 units

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Requirement 4:

Degree of Operating Leverage = Quantity*(Price - Variable Cost)/EBIT

EBIT = Quantity*(Price - Variable Cost) - Fixed Cost - Depreciation = 1178.25*(74 - 47) - 22500 - 8000 = 1312.75

Degree of Operating Leverage = 1178.25*(74 - 47)/1312.75 = 24.234

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