Question

1. Consider a project with the following data:

Accounting break-even quantity = 13,800 units;

Cash break-even quantity = 10,500 units;

Life = 5 years;

Fixed costs = $125,000;

Variable costs = $32 per unit;

Required return = 14 percent.

Ignoring the effect of taxes, find the financial break-even quantity. (HINT: Use the appropriate break even formulas to identify the unknown variables in the financial breakeven calculation).

Answer 1

Cash break even = fixed costs / contribution

contribution = selling price - variable cost

10500 = 125,000 / (selling price - 32)

selling price = 43.90

Accounting break even = (fixed cost + depreciaiton) / contribution

13800 = (125000 + depreciation) / (43.90 - 32)

depreciation = 39285.71

assuming straightline depreciation

depreciation = cost / life

39285.71 = cost / 5

so initial cost = 39285.71 x 5

= 196428.6

at financial break even NPV = 0

NPV = present value of future cash flows - initial investment

since NPV = 0

present value of future cash flows = initial investment

OCF x PVIFA( n = 5 ; r = 14%) = 196428.6

OCF x 3.4331 = 196428.6

OCF = 57,216.41

financial break even quantity = (OCF + Fixedcost) / contribution

= (57,216.41 + 125000) / (43.90 - 32)

= 15,306.18 units