Question

Imagine that you are the manager of a gym with 2000 members. Each member pays $600 and the operational costs are $300 per member. A competitor will open a new unit next to yours and that will reduce the number of members in your gym, unless you expand your facilities. You need to decide whether to expand your facilities to maintain or increase the number of members. For this decision-making, forecasts for the next three years were considered.

Option 1: Do not invest in expansion but reduce the monthly fee to $500 and keep costs at $300/member. With that it is expected that in the next three years: probability of 70% that the number of members drops to 1500, or probability of 30% that the number drops to 1200 members.

Option 2: Invest in the upgrade with an expected cost of $500K. There are two expected scenarios for this option. Scenario 1: 60% probability that the number of members remains at 2000; Scenario 2: 40% probability that the number of members increases to 2200. However, with the expansion, operational costs will be affected with a 50-50 percent chance that it will increase to either $350 or $400.

Use decision tree to decide which option maximizes the expected monetary value.

Answer 1

After performing decision tree analysis, the best financial option for the gym is to invest in expanding facilities, as it has a higher expected monetary value of $1,160,000 compared to not investing which has an EMV of $282,000.

Step-by-step explanation:

Decision Tree Analysis for Gym Membership Expansion

To choose the best course of action for the gym, we can calculate the expected monetary value (EMV) for each option. The EMV is the sum of all possible values each outcome can take, weighted by its probability of occurrence.

Option 1: Do not expand.

• 70% chance members drop to 1500: (1500 members * $500 revenue - 1500 members * $300 cost) = $300,000 EMV
• 30% chance members drop to 1200: (1200 members * $500 revenue - 1200 members * $300 cost) = $240,000 EMV

So, EMV = 0.7 * $300,000 + 0.3 * $240,000 = $210,000 + $72,000 =

$282,000

.

Option 2: Invest in expansion.

• 60% chance members stay at 2000 with $350 operational cost: (2000 members * $600 revenue - (2000 * $350 cost + $500,000 expansion)) = $1,000,000 EMV
• 40% chance members increase to 2200 with $400 operational cost: (2200 members * $600 revenue - (2200 * $400 cost + $500,000 expansion)) = $1,320,000 EMV

For both scenarios, we consider the average of increased operational costs: (($1,000,000 + $1,320,000) / 2) = $1,160,000 EMV

Then, final EMV for expansion is 0.6 * $1,160,000 + 0.4 * $1,160,000 = $1,160,000.

Comparing both options, investing in expansion has a higher EMV of $1,160,000 versus not investing with an EMV of $282,000. Therefore, expanding the gym facilities maximizes the expected monetary value and is the best choice financially for the gym.