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The Quorum Company has a prospective 6-year project that requires initial fixed assets costing $962,000, annual...

The Quorum Company has a prospective 6-year project that requires initial fixed assets costing $962,000, annual fixed costs of $403,400, variable costs per unit of $123.60, a sales price per unit of $249, a discount rate of 14 percent, and a tax rate of 21 percent. What is the present value break-even point in units per year?

A. 4,995

B. 5,852

C. 6,144

D. 5,375

E. 6,081

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Homework Answers

Answer #1

Fixed cost per year = 403400

Contribution per unit = 249 - 123.6 = 125.4

The present value BEP is the level of sales at which NPV gets 0

Let that sales level be = m

I.e. PV of inflows - PV of outflows =NPV

Inflows =( m ×Contribution per unit - fixed cost)(1-tax rate) + depreciation tax shield

= (m ×125.4 -403400)(1 -.21) + depreciation × tax rate

=(125.4m -403400)×.79 + (cost of fixed asset/life) × .21

=(125.4m -403400) ×.79 +(962000/6) ×.21

=(125.4m -403400) ×.79 +33670

PV of inflows = inflows × PV factor for 6 years at 14%

= inflows × (1-(1.14)^-6)/.14

= inflows ×3.8887

=((125.4m -403400)×.79 + 33670)×3.8887

PV of outflows = 962000$

Therefore

((125.4m - 403400) ×.79 +33670) ×3.8887 - 962000 =0

Solving this for m we get m = 5374.19 i.e. option d 5375 is the answer.

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