Question

Seattle 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?

	a.	3,200
	b.	3,334
	c.	5,000
	d.	4,000
	e.	None of these answers is correct.

Answer 1

Profit = Revenue – Variable costs – Fixed costs

For Scanner A,

500,000 = (1500-Variable cost per unit)*5000 – 1,000,000

Hence, variable cost per unit of Scanner A = $1,200

Scanner B

450,000 = (1500-Variable cost)*5000- 800,000

Variable cost per unit = $1,250

Let the number of scanners for Equal profit be x

(1500-1200)*x – 1,000,000 = (1500-1250)*x – 800,000

300x -250x = -800,000+1,000,000

X = 4,000 scanners

Hence, the answer is d.