Question

Arktec Manufacturing is considering two options for making Product A. The cost structures for the two options are shown below:

	Fixed Cost (Per Year)	Variable Cost (Per Unit)
Option 1	$500,000	$2 per unit
Option 2	$100,000	$10 per unit

Furthermore, ArkTec has identified two possible demand scenarios for Product A.

Demand (Units Per Year)	Probability
50,000	40%
100,000	60%

At what volume level do the two capacity options have identical costs?

What is the expected value in cost for Option 1 only?

Suppose Product A sells for $12. What is the break-even point for Option 2 only?

Answer 1

Let the required volume level at which both options have equal cost = N

Cost under option 1 for volume of N = $ 500,000 + $2.N

Cost under option 2 for volume of N = $100,000 $10.N

Therefore ,

500,000 + 2.N = 100,000 + 10.N

Or, 8.N = 400,000

Or, N = 50,000

REQUIRED VOLUME LEVEL AT WHICH TWO CAPACITY OPTIONS HAVE THE SAME COST = 50,000

Expected value of demand under option 1

= 40 % of 50,000 + 60% of 100,000

= 20000 + 60000

= 80,000

Expected value in cost for option 1

= Fixed cost + Variable cost / unit x expected demand

= $500,000 + $ 2 x 80,000

= $500,000 + $160,000

= $660,000

EXPECTED VALUE IN COST FOR OPTION 1 = $660,000

Break even point for option 2

= Fixed cost for option 2 / ( selling price/ unit – Variable cost / unit )

= 100,000 / ( 12 – 10 )

= 100,000/ 2

= 50,000

BREAKEVEN POINT FOR OPTION 2 = 50,000