Question

Consider a project with the following data: accounting break-even quantity = 5,400 units; cash break-even quantity = 5,000 units; life = five years; fixed costs = $200,000; variable costs = $38 per unit; required return = 10 percent. Ignoring the effect of taxes, find the financial break-even quantity.

(Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

Answer 1

Cash Breakeven = Fixed Cost/(Sales Price - Variable Cost)
5000 = 200000/(SP - 38)
5000 SP - 190000 = 200000
SP =(200000+190000)/5000 = 78

Accounting Breakeven = (Fixed Cost+ depreciation)/(sales Price - Variable Cost)
5400 =( 200000+ Depreciation)/(78-38)
5400*40 = 200000 + Depreciation
Depreciation = 216000 - 200000 = 16000

Hence Initial Investment = Depreciation * Life if machine = 16000* 5 = 80000

Equivalent annual cost of Investment = 80000/(1-(1+10%)^-5)/10% = 21103.7985

For Financial Break even quantity ( since no taxes hence no use of depreciation)
(Sales Price - Variable Cost) * Quantity - Fixed Cost - Equivalent annual cost of Investment =0
Quantity = (21103.7985+200000)/(78-38) = 5527.59

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