Consider a project with the following data: accounting break even quantity = 16,700 units., cash break even quantity = 15,000 units., life = four years., fixed costs = $150,000 variable cost = $ 32 per unit., required return = 15 percent. Ignoring the effect of taxes. Required:
Find the financial break-even quantity.

The financial break-even quantity is 17,385.97

Explanation:

Cash Break even = Fixed Cost / (Price- variable Cost)

15,000 = $150,000 / (P-$32)

15,000 (P) -15,000*32 = $150,000

15,000 (P) - $480,000 = $150,000

15,000 (P) = $150,000 + $480,000

15,000 (P) = $630,000

P = $630,000/15,000

P = $42 per unit

From accounting break even quantity = 16,700 units, = QA

QA= (FC + D)/(P –v)

16,700 = ($150,000 + D)/($42 - $32)

16,700 = ($150,000 + D)/$10

16,700*$10 = ($150,000 + D)

$167,000 = ($150,000 + D)

$167,000 - $150,000 = D

D = $17,000

Therefore, the depreciated value is = $17,000

To find the annual depreciation amount we assume straight-line depreciation Initial investment = 4($17,000) = $68,000

The PV of the OCF must be equal to this value at the financial break even since the NPV is 0:

$68,000 = OCF (PVIFA15%, 4)

$68,000 = OCF * [ 1 - ( 1+ r)^-n ] / r

$68,000 = OCF * [ 1 - ( 1+ 0.15)^-4] / 0.15

$68,000 = OCF * 2.85

OCF = $68,000/2.85

OCF = $23,859.65

Therefore, Break-even level of OCF = $23,859.65

Then,

QF= ($150,000 + $23,859.65)/($42 – $32)

QF= 17,385.97

Therefore, financial break-even quantity is 17,385.97

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