Seattle Grace Hospital plans to invest in a new piece of CT imaging equipment. T

Question

Seattle Grace Hospital plans to invest in a new piece of CT imaging equipment. The hospital estimates that it can bill $1,500 per scan. Preliminary market assessments indicate that demand will be fewer than 5,000 scans per year. The hospital has the choice between two different types of spiral CT that can fill its imaging needs. Each scanner has a capacity of 5,000 scans per year but involves a different mix of labor and capital. Scanner A would result in total fixed costs of $1 million per year and would yield a profit of $500,000 if the hospital produced and billed for 5,000 scans. Scanner B would result in total fixed costs of $800,000 per year and would yield a profit of $450,000 per year if the hospital produced and billed for 5,000 scans. At what number of scans are the scanners equally profitable?

Explanation / Answer

                                                      Scanner "A"                                         Scanner "B"

Fixed cost                                       $10,00000                                                  $800000

Profit                                              $5000000                                                    $400000

Per unit price                                     $1500                                                       $1500

Quantity Scannes                               5000                                                           5000

Computation of breakeven number of each scan

$500,000 = $5,000*(P-VC) $1,000,000 CM = $300                   $450,000 = $5,000*(P-VC) $800,000 CM = $250

At what number of scans are the scanners equally profitable

$300 * x $1,000,000 = $250 * x$800,000 X = 4,000

Answer = 4000 scannes

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