Albuquerque Radiology Group plans to invest in a new CT scanner. The group estim
ID: 2617904 • Letter: A
Question
Albuquerque Radiology Group plans to invest in a new CT scanner. The group estimates $1,500 net revenue per scan. Preliminary market assessments indicate that demand will be less than 5,000 scans per year. The group has the choice between two different types of scanner 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 $1,000,000 per year and would yield a profit of $500,000 if the volume is 5,000 scans. Scanner B would result in total fixed costs of $800,000 per year and would yield a profit of $450,000 if the volume is 5,000 scans. At what number of scans are the scanners equally profitable? Show all work and rationale.
Explanation / Answer
Scanner A
Total fixed cost = $1,000,000
Volume = 5,000 scans
Profit = $500,000
Revenue per scan = $1,500
Total revenue = 5,000 x 1,500
= $7,500,000
Profit = Total revenue - Total Variable cost - Total fixed cost
500,000 = 7,500,000 - Total variable cost - 1,000,000
Total variable cost = $6,000,000
Hence, variable cost per scan = 6,000,000/5,000
= $1,200
Scanner B
Total fixed cost = $800,000
Volume = 5,000 scans
Profit = $450,000
Revenue per scan = $1,500
Total revenue = 5,000 x 1,500
= $7,500,000
Profit = Total revenue - Total Variable cost - Total fixed cost
450,000 = 7,500,000 - Total variable cost - 800,000
Total variable cost = $6,250,000
Hence, variable cost per scan = 6,250,000/5,000
= $1,250
Let Z be the number of scans where total profits of the two scanners are same.
Profit from scanner A = Total revenue - Total Variable cost - Total fixed cost
= 1,500 x Z - 1,200 x Z - 1,000,000
= 1,500Z - 1,200Z - 1,000,000
= 300Z - 1,000,000
Profit from scanner B = Total revenue - Total Variable cost - Total fixed cost
= 1,500 x Z - 1,250 x Z - 800,000
= 1,500Z - 1,250Z - 800,000
= 250Z - 800,000
Hence, 300Z - 1,000,0000 = 250Z - 800,000
50Z = 200,000
Z = 4,000
Hence when 4,000 scans are done, total profits of the two scanners would be same
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