Garnet’s Gym is a fitness and aerobic center located in Atlanta, Georgia. With over 25,000 square feet of space, Garnet’s offers its customers an unparalleled fitness experience, including the finest equipment for cardiovascular training, resistance training, and free-weight training. Garnet’s also features state-of-the-art aerobics, spinning, yoga, and tai chi classes taught by nationally certified instructors.

Finally, when not working out, patrons can enjoy other amenities such as Garnet’s tanning salon, hot tub, sauna, and juice bar.

The owners of Garnet’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:

Membership fee .............................................. $500 per member

Number of members ..................................... 5,000

Variable costs (supplies, 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.

Required:

a. Write down the expression for Garnet’s annual profit.

b. How many members must Garnet’s Gym have to break even?

c. Assuming the same number of members as last year, what is Garnet’s expected profit for the coming year?

d. The owners of Garnet’s Gym are considering reducing the membership fee by 10%.

They believe that this action will increase membership to 6,500 for the coming year.

What will profit be if the owners adopt this alternative? Does this seem like a good option?

e. As an alternative to reducing the membership fee by 10%, the owners of Garnet’s Gym could increase membership to 6,500 by adopting a special advertising campaign.

What is the maximum amount that the owners should pay for the advertising campaign?

f. The owners of Garnet’s Gym noticed that you used the unit contribution margin approach in arriving at your answers. They wonder if your answers would change if you used a contribution margin ratio approach. Briefly explain to the owners why your answers would, or would not, change.