Question

Problem 2-21B Effects of operating leverage on profitability

CFEs R Us conducts CFE review courses. Public universities that permit free use of a classroom support the classes. The only major expense incurred by CFEs R Us is the salary of instructors, which is $5,000 per course taught. The company recently planned to offer a review course in Boston for $400 per candidate; it estimated that 50 candidates would attend the course.

Complete these requirements based on the preceding information.

Part 1:

Required

Relative to the number of CFE candidates in a single course, is the cost of instruction a fixed or a variable cost?

Page 103Determine the profit, assuming that 50 candidates attend the course.

Determine the profit, assuming a 10 percent increase in enrollment (i.e., enrollment increases to 55 students). What is the percentage change in profitability?

Determine the profit, assuming a 10 percent decrease in enrollment (i.e., enrollment decreases to 45 students). What is the percentage change in profitability?

Explain why a 10 percent shift in enrollment produces more than a 10 percent shift in profitability. Use the term that identifies this phenomenon.

Part 2:

The instructor has offered to teach the course for a percentage of tuition fees. Specifically, he wants $100 per candidate attending the class. Assume that the tuition fee remains at $400 per candidate.

Required

Is the cost of instruction a fixed or a variable cost?

Determine the profit, assuming that 50 candidates take the course.

Determine the profit, assuming a 10 percent increase in enrollment (i.e., enrollment increases to 55 students). What is the percentage change in profitability?

Determine the profit, assuming a 10 percent decrease in enrollment (i.e., enrollment decreases to 45 students). What is the percentage change in profitability?

Explain why a 10 percent shift in enrollment produces a proportional 10 percent shift in ­profitability.

Part 3:

CFEs R Us sells a workbook to each student who attends the course. The workbook contains printed material unique to each course. Workbooks that are not sold must be destroyed. Prior to the first class, CFEs R Us printed 50 copies of the books based on the estimated number of people who would attend the course. Each workbook costs $32 and is sold for $50. This cost includes a royalty fee paid to the author and the cost of duplication.

Problem 2-21B (Continued)

Required

Calculate the total cost and the cost per candidate of the workbooks, assuming that 45, 50, or 55 candidates attempt to attend the course. Round your figures to two decimal points.

Classify the cost of workbooks as fixed or variable relative to the number of candidates attending the course.

Discuss the risk of holding inventory as it applies to the workbooks.

Explain how a just-in-time inventory system can reduce the cost and risk of holding inventory.

Answer 1

Part 1:

i) Relative to the number of CFE candidates in a single course, the cost of instructors is fixed cost as cost of instructor is $5,000 per course and it is independent of the facts that how many candidates are studying in one course. Therefore, relative to the number of CFE candidated in a single course, the cost of instructor is to be considered as Fixed cost.

ii) If 50 candidates attend the class, then the profit will be:-

Tuition fees = 50 candidates*$400 per candidate = $20,000

Cost of instructor = $5,000

Profit = Tuition fees revenue - Cost of instructor = $20,000 - $5,000 = $15,000

iii)  If 55 candidates attend the class, then the profit will be:-

Tuition fees = 55 candidates*$400 per candidate = $22,000

Cost of instructor = $5,000

Profit = Tuition fees revenue - Cost of instructor = $22,000 - $5,000 = $17,000

Percentage change in profitability = [(profit if 55 candidates-profit if 50 candidates)/profit if 50 candidates]*100

= ($17,000 - $15,000)/$15,000*100 = 13.33%

iv) If 45 candidates attend the class, then the profit will be:-

Tuition fees = 45 candidates*$400 per candidate = $18,000

Cost of instructor = $5,000

Profit = Tuition fees revenue - Cost of instructor = $18,000 - $5,000 = $13,000

Percentage change in profitability = [(profit if 45 candidates-profit if 50 candidates)/profit if 50 candidates]*100

= ($13,000 - $15,000)/$15,000*100 = -13.33%

v) The cost of instructor is the only cost in this case and that is fixed cost and not change with increase or decrease in number of candidates, therefore 10% change in number of candidates produces more than 10% shift in profitability.

Part 2 :

i) In this case the cost of instructor is $100 per candidate and varies with the number of candidates. Therefore it is a variable cost.

ii)  If 50 candidates attend the class, then the profit will be:-

Tuition fees = 50 candidates*$400 per candidate = $20,000

Cost of instructor = $100*50 candidates = $5,000

Profit = Tuition fees revenue - Cost of instructor = $20,000 - $5,000 = $15,000

iii)  If 55 candidates attend the class, then the profit will be:-

Tuition fees = 55 candidates*$400 per candidate = $22,000

Cost of instructor = $100 per candidate*55 candidates = $5,500

Profit = Tuition fees revenue - Cost of instructor = $22,000 - $5,500 = $16,500

Percentage change in profitability = [(profit if 55 candidates-profit if 50 candidates)/profit if 50 candidates]*100

= ($16,500 - $15,000)/$15,000*100 = 10%

iv) If 45 candidates attend the class, then the profit will be:-

Tuition fees = 45 candidates*$400 per candidate = $18,000

Cost of instructor = $100 per candidate*45 candidates = $4,500

Profit = Tuition fees revenue - Cost of instructor = $18,000 - $4,500 = $13,500

Percentage change in profitability = [(profit if 45 candidates-profit if 50 candidates)/profit if 50 candidates]*100

= ($13,500 - $15,000)/$15,000*100 = -10%

v) The cost of instructor is the only cost in this case and that is variable cost and change with increase or decrease in number of candidates, therefore 10% change in number of candidates produces a proportional 10% shift in profitability.