Asmall firm intends to increase the capacity of a bottleneck operation by adding a new machine. two alternatives, a and b, have been identified, and the associated costs and revenues have been estimated. annual fixed costs would be $40,000 for a and $30,000 for b; variable costs per unit would be $10 for a and $11 for b; and revenue per unit would be $15.a. determine each alternatives break-even point in units.
b. at what volume of output would the two alternatives yield the same profit?
c. if expected annual demand is 12,000 units, which alternative would yield the higher profit?

a. Alternative A Break-even point is 8,000 units Alternative B Break-even point is 7,500 units

b. Same profit with both alternatives at 10,000 units

c. Alternative A would have higher profit with a demmand of 12,000 units

Explanation:

a. FC/CMGu=BP

being:

FC= fixed costs

CMGu=contribution margin per unit

BP= Break even point

CMGu is the difference between price of sale and variable cost (per unit)

Alt. A Break-even point is $40,000/$5=8,000 UNITS

Alt. B Break-even point is $30,000/$4=7,500 UNITS

b. At 10,000 units both alternatives have the same profit

Alt. a.

Revenues= $150,000

Variable cost= $-100,000

Fixes Costs= $-40,000

profit $10,000

Alt. b.

Revenues= $150,000

Variable cost= $-110,000

Fixes Costs= $-30,000

profit $10,000

c. sales for 12,000 units

Alt. a.

Revenues= $180,000

Variable cost= $-120,000

Fixes Costs= $-40,000

profit $20,000

Alt. b.

Revenues= $180,000

Variable cost= $-132,000

Fixes Costs= $-30,000

profit $18,000

A) BEP (Units): Product A = 8000 Units

                        Product B = 7500 Units

B) 10000 Units

C) Alternative A

Explanation:

A) BEP (Units) = Fixed Cost/Contribution margin per unit

Contribution margin per unit = Revenue per unit - Variable cost per unit

For Product A -

Revenue per unit = $15

VC per unit = $10

FC = $40,000

CM per unit = 15 - 10 = $5

∴ BEP (unit) = 40000/5 = 8,000 units

For Product B -

Revenue per unit = $15

VC per unit = $11

FC = $30,000

CM per unit = 15 - 11 = $4

∴ BEP (unit) = 30000/4 = 7,500 units

B) Let the level at which the 2 alternatives yield same profit = Y

Equation: Profit = Y*CM per unit - Fixed Cost

Profit A = Y*5 - 40,000 (1)

Profit B = Y*4 - 30,000 (2)

putting the 2 equations together

5Y - 40000 =  4Y - 30000

5Y - 4Y = 40000 - 30000

Y = 10000 units

C) Profit when annual demand is 12000 units

Using equation from B

Profit = Y*CM per unit - Fixed Cost

Y = 12000

Alternative A = 12000 * 5 - 40000

= 60000 - 40000 = $20,000

Alternative B = 12000 * 4 - 30000

= 48000 - 30000 = $18,000

∴Alternative A should be chosen as it yields the highest profit