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 financial break-even quantity assuming 10% as discount rate?

Answer 1

Financial break-even quantity:

The project has a ten-year life. The project has a zero NPV when the present value of the operating cash flows equals the $1,000,000 investment. Because the cash flow is the same each year, we can solve for the unknown amount by viewing it as an ordinary annuity.

So, The ten-year annuity factor at 10 % discount rate (aka, Interest rate) = [ 1 - {1 / (1+r)^n} ] / r

Annuity factor = 6.145

And the OCF (Operating cash flows) can be determined as follows:

Initial Investment = OCF * Annuity factor

or, $1,000,000 = OCF * 6.145

So, OCF = $ 162,734

Thus, the project needs an operating cash flow of $162,734 each year to break even. We can now plug this OCF into the equation for sales volume:

Financial Break even quantity (Q) = (Fixed cost + OCF) / (Selling price per quatity - variable cost per quantity)

= ( 350,000 + 162,734) / (1000 - 700)

= 512,734 / 300 = 1709.11 ~ 1710

Hence, the Financial break even Quantity is 1710.