Question

Arktec Manufacturing must choose between the following two capacity options:

	Fixed Cost (per year)	Variable Cost (per unit)
Option 1	$500,000	$3 per unit
Option 2	$100,000	$10 per unit

a. What would the cost be for each option if the demand level is 30,000 units per year? If it is 80,000 units per year?

b. In general, which option do you think would be better as volume levels increase? As they decrease? Why?

c. What is the indifference point?

Answer 1

a.

Let us assume the following:

X = Number of units

So,

Total Cost for Option 1 = 500,000 + 3X

Total Cost for Option 2 = 100,000 + 10X

When demand level or X = 30,000

Total cost for Option 1 = 500,000 + ( 3 x 30,000) = 500,000 + 90,000 = $ 590,000

Total cost for Option 2 = 100,000 + ( 10 x 30,000) = 100,000 + 300,000 = $ 400,000

When demand level or X = 80,000

Total cost for Option 1 = 500,000 + ( 3 x 80,000) = 500,000 + 240,000 = $ 740,000

Total cost for Option 2 = 100,000 + ( 10 x 80,000) = 100,000 + 800,000 = $ 900,000

b.

The Total cost for both options can be plotted on a graph as follows:

1200000 1100000 1000000 900000 800000 700000 Total Cost 600000 Option 1 500000 Option 2 400000 300000 200000 100000 0 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 Demand (Number of Units)

From the graph, it can be seen that Option 1 is better when the volume levels increase and Option 2 is better when the volume levels decrease.

This is because the Fixed cost for Option 2 is lower, and so the total costs are lower when the volume is lower.

Fixed cost for Option 1 is higher, and so the total cost is higher when the volume is lower. The total cost for Option 1 is lower than that of Option 2 after the Indifference point ie, the point where the two lines intersect. Since the variable cost for Option 1 is lower, the total cost for Option 1 after the Indifference point stays lower than the total cost for Option 2.

c.

The indifference point is the point where the total cost for both the options is the same.

So,

500000 + 3X = 100000 + 10X

500000 - 100000 = 10X - 3X

400000 = 7X

X = 400000 / 7 = 57142.86 units = 57143 units (Rounding off)

Below X value, Option 2 is cheaper

Above X value, Option 1 is cheaper.

At X value, Total cost for both options is the same.