Question

Gibson’s Gym is a fitness and aerobic center located in Austin, TX. With over 25,000 square feet of space, Gibson’s offers its customers an unparalleled fitness experience, including the finest equipment for cardiovascular training, resistance training, and free-weight training. Gibson’s also features state-of-the-art aerobics, spinning, yoga, and tai chi classes taught by nationally certified instructors. And, when not working out, patrons can enjoy other amenities such as Gibson’s tanning salon, hot tub, sauna, and juice bar. The owners of Gibson’s Gym currently are working on their operating plan for the coming year, and they have provided you with the following average membership and cost data for the previous year:

Annual membership fee $500 per member Number of members 5,000 Variable cost (supplies, instructors, etc.) $200 per member Fixed costs (equipment, salaries, etc.) $1,200,000 The owners anticipate that, for the coming year, both total fixed costs and the variable cost per member will remain unchanged from the previous year.

-- In addition to lowering the regular membership fee by 10%, the owners are considering offering an additional type of membership. Customers under the current membership plan are limited to a certain set number of classes, services, etc. Market research indicates that some potential members may be willing to pay more for unlimited access to all gym amenities. To add this option, the owners would need to hire a director of premium membership, at an annual salary of $70,000 per year. The premium annual membership fee would be $1000, and the annual cost per premium member will be $300 more than the regular member cost. Preliminary market research suggests 10% of members would be interested in this upgrade. How many premium and regular memberships must be sold in order to meet a desired after-tax profit of $315,000 (still assuming 30% tax rate, and assuming regular membership fee will be reduced by 10% from prior year)?

--The owner’s believe premium membership sales are low due to lack of awareness. They also are not currently seeing as many total sales as they need to meet their desired level of income. They met with an advertising firm and now believe an aggressive advertising campaign could boost premium membership sales up to 15% of overall sales, and that the maximum total sales they can expect to see for the year will be 6,250 members. What is the maximum amount that the owners should pay for the advertising campaign to hit the expected profit $315000? What is the maximum the owners should spend on this advertising campaign if they want to meet a desired after-tax target profit of $315,000 (still assuming 30% tax rate, and assuming regular membership fee will be reduced by 10% from prior year)?

Answer 1

Selling piece under regular member ship (500-(500*10%))	450
Selling price under premium member ship	1000
Variable cost under regular	200
Variable cost under premium (200+300)	500
Revised fixed cost per year (1200000+70000 director salary)	1270000

Contribution per membership	Regular	Premium
Annual membership fee per member	450	1000
Less: variable cost per member	200	500
Contribution per membership	250	500
Let’s assume total member is X
Out of total member, Premium member is 10% it means 0.10X
Remaining regular member is X-0.10X=0.90X
	Regular	Premium	Total
Contribution per membership	250	500
No of membership	0.90X	0.10X
Total contribution (multiply of above both)	225X	50X	275X
Target profit after tax			315000
Target profit before tax (Tax rate 30% and remaining 70%= 0.70 considered as profit after tax) (315000/0.70)			450000
Target profit before tax			450000
Add: revised fixed cost			1270000
Total contribution required to earn			1720000
Total contribution Margin			275X
Value of X (1720000/275)			6254.55
Membership cannot be in fraction			6255
Premium membership (6255*10%)			625
Regular membership (6255*90%)			5630

Proof of answer
Membership	Regular	Premium	Total
No. Of membership	5630	625	6255
Membership fees per member	450	1000
Total member ship fees (No. Of membership*membership fees per member)	2533500	625000	3158500
Less:
Variable cost per member	200	500
Total variable cost (No. Of membership*Variable cost per member)	1126000	312500	1438500
Total Contribution			1720000
Less: Fixed cost (with director salary)			1270000
Profit before tax			450000
Less: Income tax @ 30% of 450000			135000
Target profit after tax			315000

Answer

Maximum membership			6250
Premium member (6250*15%) (Round down) (Member cannot be in fraction.)			937
Regular member (6250*85%)			5313
Membership	Regular	Premium	Total
No. Of membership	5313	937	6250
Membership fees per member	450	1000
Total member ship fees (No. Of membership*membership fees per member)	2390850	937000	3327850
Less:
Variable cost per member	200	500
Total variable cost (No. Of membership*Variable cost per member)	1062600	468500	1531100
Total Contribution			1796750
Less: Fixed cost (with director salary)			1270000
Profit before tax			526750
Target profit before tax (if after tax profit is 315000, it means profit before tax 450000 if tax rate 30% (already calculated.)			450000
Maximum amount paid for advertising			76750

Proof of answer
Membership	Regular	Premium	Total
No. Of membership	5313	937	6250
Membership fees per member	450	1000
Total member ship fees (No. Of membership*membership fees per member)	2390850	937000	3327850
Less:
Variable cost per member	200	500
Total variable cost (No. Of membership*Variable cost per member)	1062600	468500	1531100
Total Contribution			1796750
Less: Fixed cost (with director salary and advertising expense) (1270000+76750)			1346750
Profit before tax			450000
Less: Income tax @ 30% of 450000			135000
Target profit after tax			315000