Question

# the quorum company has a prospective 6 year project that requires initial fixed assets of \$963,000,...

the quorum company has a prospective 6 year project that requires initial fixed assets of \$963,000, annual fixed \$403,400, variable costs \$123.60 per unit, sales price of \$249, discount rate 14%, tax rate 21%. asset straight line depreciated to zero over life of project.

compute accounting break even sales
compute financial break even quantity

Annual depreciation = \$ 963,000 / 6 = \$ 160,500

Total fixed costs = \$ ( 403,400 + 160,500) = \$ 563,900

Contribution margin per unit = \$ ( 249 - 123.60) = \$ 125.40

Accounting break even quantity = \$ 563,900 / \$ 125.40 = 4,496.81 units

Let the financial break-even quantity be Q.

Annual operating cash flows after taxes = EBITDA x ( 1 - t ) + Depreciation x t = ( 125.40Q - 403,400 ) x 0.79 + \$ 160,500 x 0.21= 99.066 Q - 318,686 + 33,705 = 99.066 Q - 284,981

PVIFA 14%, n=6 = [ { 1 - ( 1 / 1.14 ) 6 } / 0.14 ] = 3.88867

At financial break even, NPV = 0

or ( 99.066 Q - 284,981) x 3.88867 - 963,000 = 0

or 385.2349Q - 1,108,197.07 = 963,000

or Q = 5,376.45 units

Therefore, financial break even quantity is 5,376.45 units

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