Question

This question tests your understanding of the various form of "breakevens". A proposed project has the following facts:

o Investment required today, t=0, $10M (cash outflow)

o Length of project, 8 years o Forecast unit sales per year, 600,000

o Sales price per unit, $80

o Variable cost, $36 per unit

o Fixed costs, $20M per year - (includes $5M of depreciation)

o Taxes, 20%

o Net working capital which consists of, inventory +A/R -A/P, requires an investment of $500K today, t0, which is INCLUDED in the above "Investment required today, t=0, $10M"

The NWC investment of $500K noted in the last bullet point will reverse at the end of the project, in other words, cash flows will be higher by $500K at t=8

a) What is the contribution per unit?

b) How many units must the company sell PER YEAR to breakeven on a net income (or net earnings) basis?

c) How many units must the company sell PER YEAR to breakeven on a free cash flow basis in years 1 through 7 (they are identical so only one calculation needs to be shown)?

d) How many units must the company sell to breakeven on an NPV basis?

Answer 1

a. Contribution per unit = Sales price per unit - variable cost per unit = $80-$36 =$44

b. Breakeven point on net earnings = Fixed cost / contribution per unit = $20,000,000/$44 = 454,545 units

c. Free cash flow every year :

Contribution ( 44 * 600000)	$26,400,000
Less: Fixed Cost	$20,000,000
Profit before tax	$6,400,000
Less: Taxes (20% * 6,400,000)	$1,280,000
Add : Depreciation	$5,000,000
Free Cash Flow	$ 10,120,000

Thus, breakeven on a free cash flow basis = $10,120,000 / $44 = 230,000 units

d. Assuming discounting rate to be NIL,

Total Inflow = ($10,120,000 * 7) + $10,120,000 + $ 500,000 = $81,460,000

Total outflow = $ 10,000,000

NPV = $81,460,000 - $ 10,000,000 = $71,460,000

Units company must sell to breakeven on an NPV basis = $71,460,000 / $44 = 1,624,091 units over 8 years.