Peter Billington Stereo, Inc., supplies car radios to auto manufacturers and is

ID: 351018 • Letter: P

Question

Peter Billington Stereo, Inc., supplies car radios to auto manufacturers and is going to open a new plant. The company is undecided between Detroit and Dallas as the site. The fixed costs in Dallas are lower due to cheaper land costs, but the variable costs in Dallas are higher because shipping distances would increase. Dallas Detroit Fixed costs $ 560 comma 000 $ 780 comma 000 Variable costs $ 28/radio $ 22/radio a) Based on the analysis of the volume, after rounding the numbers to the nearest whole number, Dallas is best below and Detroit is best above radios. b) Dallas's fixed costs have increased by 10%. Based on the analysis of the volume, after rounding the numbers to the nearest whole number, Dallas is best below and Detroit is best above radios.

Explanation / Answer

Cost

Dallas

Detroit

Fixed Cost

$560000

$780000

Variable Cost

$28/radio

$22/radio

a) We need to formulate the total cost equation for both the sites and find a crossover point between them.

Total Cost Dallas: 560000 + 28x

Total Cost Detroit: 780000 + 22x

Crossover point can be found by equalizing both the above total cost equations:

560000 + 28x = 780000 + 22x

6x = 220000

x= 36667

Dallas has lower costs for the production volume up to 36667 and Detroit would have, above this level.

b) If Dallas fixed cost increases by 10%:

new Fixed Cost = 616000

new Total Cost= 616000 + 28x

Finding the new crossover point:

616000 + 28x = 780000 + 22x

6x = 164000

x = 27334

In this scenario, Dallas has lower costs for the production volume up to 27334 and Detroit would have, above this level.