Question

A project requires an initial investment of $1,000,000 and is depreciated straight-line to zero salvage over its 10-year life.

The project produces items that sell for $1,000 each, with variable costs of $700 per unit. Fixed costs are $350,000 per year.

 What is the accounting break-even quantity? o Q = (FC + D)/(P – v)

 What is the operating cash flow at accounting break-even? o OCF= [PQ - vQ – FC – D] + D

•  What is the cash break-even?
  o Q = (FC + OCF)/(P – v); where OCF=0

•  What is the financial break-even? I = 10%

o Find OCF where NPV = 0, Q = (OCF + FC) / (P – v)

Show all work as follows:

Identify:

•  FC = Fixed Cost

•  D = Depreciation

•  P = Price

•  v = variable cost per unit

•  OCF = operating cash flow (if needed)

  Then compute the break-even quantities.

Answer 1

depreciation per year = cost of asset / life of asset = $1,000,000 / 10 = $100,000

1) Account break enen quantity :-

Account break enen quantity = (Fixed cost + depreciation) / (selling price - variable cost per unit)

= (350,000+100,000) / (1000-700) =

Account break enen quantity = 1500 units

2) Operating cash flows at accounting break even point :-

Operating cash flows at account break even point :-

Sale value(1500*1000)	1,500,000
less-Variable cost	1,050,000
less-Fixed cost	350,000
less-Depreciation	100,000
PBT	0
profit after tax	0
Add-Depreciation	100,000
Operating cash flows at account break even point	100,000

3) Cash break even quantity :-

Here depreciation is non cash expense.So depreciation is not taken on calculation of the cash break even quantity

Cash break even quantity = Fixed cost /(selling price - variable cost per unit)

= 350,000 / ( 1000- 700)

Cash break even quantity = 1166.6667 units

4) Financial break even quantity :-

We need to find where OCF, where NPV = 0.

NPV = 0

Present value of cash inflows - initial investment = 0

Present value of cash inflows = initial investment

OCF * PVAF(10%,10years) = 1,000,000

OCF * 6.14456710570469 = 1,000,000

OCF = 162,745.394882512

Financial break even quantity = (OCF + fixed cost ) / (Selling price - variable cost) = (162,745.394882512 + 350,000) / (1000 - 700)

= 512,745.394882512 / 300

Financial break even quantity = 1709.151316 units