Question

1. A manufacturing organization is looking at the following two locations:
Birmingham
Manchester
Variable costs
$14/unit
$16/unit
Annual fixed costs
$12000 000
$15 000 000
Initial fixed cost
$165000 000
$145 000 000
a. Draw a cost-volume graph for both locations over a 10-year period at a volume of 750,000 units per year.
b. Which location has the lowest cost at the end of the 10-year period?
c. At what volume do these locations have equal costs?

Answer 1

(a): Here the cost at time period 0 will be 165,000,000 for Birmingham and 145,000,000 for Manchester. This will be at volume of o units. Then in each year the cost equation will be: For Birmingham it will be: 12,000,000 + 14x and for Manchester it will be 15,000,000+16x where x = 750,000 units

180,000,000 160,000,000 140,000,000 120,000,000 100,000,000 80,000,000 Series1 -Series2 60,000,000 40,000,000 20,000,000 200,000 400,000 600,000 800,000 1,000,000

In the above graph production volume is shown on the x axis and costs on the y axis. Series 1 is the line for Birmingham and series 2 is the line for Manchester.

(b): Total cost at the end of 10 year period for Birmingham = 165,000,000 + [(12,000,000 + (14*750,000))*10]

= $390,000,000

Total cost at the end of 10 year period for Manchester = 145,000,000 + [(15,000,000+(16*750,000))*10]

= $415,000,000

Thus at the end of 10 year period Birmingham has the lowest cost.

(c): Let the volume be "x". Thus no. of years = x/750,000. So total cost for Birmingham = 165,000,000 + (12,000,000*x/750,000) + 14x

Total cost for Manchester = 145,000,000 + (15,000,000*x/750,000) + 16x

Now as both costs are equal we get: 165,000,000 + (12,000,000*x/750,000) + 14x = 145,000,000 + (15,000,000*x/750,000) + 16x

or 165,000,000 + 30x = 145,000,000 + 36x

or 20,000,000 = 16x

or x = 1,250,000 cumulative units