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Understanding pricing theory is all fine and good. But you also have to be able to "crank the numbers". IMPORTANT NOTE: for the following case, assume that any change in costs, once made, continues from that point and then throughout the rest of the problem unless otherwise noted.
Calculate the breakeven point for a private, upscale K-8 (Kindergarten through 8th grade) academy with the cost structure listed below. Assume that tuition (i.e., the price) is $5500 per student. Note: be sure to round up to the nearest whole number -- we generally don't have 2/3rds of a student!
***Important hint: make sure you carefully think through which of the costs listed below will fall into Fixed Costs and which will fall into Variable Costs. You may want to re-read the Lecture to refresh your memory on this one. ·
administrator salaries $400,000 ·
faculty salaries $850,000 ·
coaches salaries $80,000 ·
medical,...benefits $600,000 ·
insurance $60,000 ·
mortgage/debt $40,000
· materials cost for each student $500
a. Breakeven point (number of enrolled students needed) for this Academy, given this cost structure is: ____________students. (Be sure to show an outline of your calculations.) Now assume that because enrollment has tapered off, your Board of Trustees has approved a $50,000 marketing budget to develop promotional materials and to hire a part-time recruiter. (Remember to include this cost from now on.) (Again, show an outline of your calculations.)
b. Your new B/E point is _________ students.
c. In other words, to cover this increase in promotion, you’ll need another ______ students in order to breakeven.
Faculty salaries have been frozen for the past 4 years. They now indicate that they will strike if they are not given an immediate 3% pay increase. You believe that this should also be extended to the coaching staff, to head-off potential problems in that area. (Again, remember to include this cost from now on.) (Also again, show an outline of your calculations).
d. Rounding up to the nearest whole number, your new B/E point is _________ students.
e. Enrollment turns out to be 422 students. Therefore your academy has made profits of $__________.
To help defray the new marketing costs, you decide to raise your tuition from $5500 to $6000.
f. Rounding up to the nearest whole number, your new B/E point is _________ students. (Show an outline of your calculations).
g. Another question… what would you say if the academy chose to use an odd pricing strategy, pricing tuition at $5,999? Your enrollment of 422 students (from part "d" above) drops 1 percentage point more than your tuition was raised (e.g., if tuition is raised 5%, enrollment drops 6%). Regrettably, school tuition appears to be far more elastic than expected.
h. Tuition was raised _____%.
i. Enrollment declines _____%.
j. Rounding up to the nearest whole number, enrollment is now ________ students.
Explanation / Answer
administrator salaries $400,000 Fixed faculty salaries $850,000 Fixed coaches salaries $80,000 Fixed medical benefits $600,000 Fixed insurance $60,000 Fixed mortgage/debt $40,000 Fixed materials cost for each student $500 Variable a Total Fixed Cost (a) $2,030,000 Revenue per Student (b) $5,500 Variable Cost per student ( c) $500 Contribution per student (d =b-c) $5,000 BreakEven Point (e = a/d) 406 (Fixed Cost/Contribution per unit) b New Fixed Cost (a) (2030000 + 50000) $2,080,000 Revenue per Student (b) $5,500 Variable Cost per student ( c) $500 Contribution per student (d =b-c) $5,000 BreakEven Point (e = a/d) 416 (Fixed Cost/Contribution per unit) c In other words, to cover this increase in promotion, you’ll need another 10 students in order to breakeven. d Fixed Cost $2,080,000 Increase in Faculty Salary (3% * 850000) $25,500 Increase in Coach Salary (3% * 80000) $2,400 Total Fixed Cost (a) $2,107,900 Revenue per Student (b) $5,500 Variable Cost per student ( c) $500 Contribution per student (d =b-c) $5,000 BreakEven Point (e = a/d) 422 (Fixed Cost/Contribution per unit) e Contribution from 422 students (422 * 5000) $2,110,000 Less: Fixed Cost $2,107,900 Profit $2,100 f Fixed Cost (a) $2,107,900 Revenue per Student (b) $6,000 Variable Cost per student ( c) $500 Contribution per student (d =b-c) $5,500 BreakEven Point (e = a/d) 384 (Fixed Cost/Contribution per unit) g Tuition Fee Raised (a) $5,999 Old Tuition Fee (b) $5,500 Raise Amount (c = a-b) $499 h Increase in Tuition Fee (499/5500) 9% i Enrollment Decline (9% + 1%) 10% j. Old Enrollment (a) 422 Decline (10% * 422) (b) 42 New Erollment (c = a-b) 380
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