Profit = Revenue - Cost

At break-even, Revenue = cost, and profit = 0

     Revenue = unit sales price * amount sold

     Cost = fixed cost + variable cost (pg.703)

                 Fixed cost: rent, depreciation, etc.

                Variable cost: material, manufacturing cost, etc.

Let x be the amount sold at break-even

  Revenue = unit sales price * x
  Cost = fixed cost + unit variable cost * x

  At break-even, Revenue = Cost

     unit sales price * x = fixed cost + unit variable cost * x

     x = fixed cost/(unit sales price - unit variable cost)
 

pg.171 Problem 6
a.  x = 300000/(23-8) = 20000
b.  higher
c.  lower

pg. 171 Problem 7
x = 150000/(45-25) = 7500

Make-or-Buy decision

An example

C&A can either make a part in house or buy it from a supplier. C&A needs 70,000 of this part each year. Consider the following cost data:

Source	Fixed cost	Unit variable cost
Make	10,125	12.50
Buy	0	14.75

1. Should C&A make or buy the part?

2. At what quantity will C&A be indifferent towards making or buying the part?

1.
Total purchase cost = $14.75*70000 = $1,032,500

Total manufacturing cost = $12.50*70000+10125 = $885,125

It is cheaper to make

2.
Let x be the quantity at which C&A will be indifferent

14.75x = 10125+12.5x

x = 10125/(14.75-12.5) = 4500
 

Exercise
pg.171 Problems 8, 9, 10