Question

Suppose you are a health fitness consultant. Your clients come to you for advice ranging from diet and nutrition to exercise. One of your clients is Dustin Winthrop. He is relatively healthy but has an underlying health condition that puts him in the vulnerable category for COVID-19. He is worried about going back to the gym to workout if Monterey County lifts the shelter-in-place order by May 1. He wants you to help him evaluate two options:

Option A: Go back to the gym. He is currently paying $130 per month for a gym membership. He assumes that this price will likely remain the same for the next 10 years. If he goes back to the gym, he will make sure to observe social distancing, wear gloves and a face mask, and make sure each equipment that he uses is wiped down and sanitized.

Option B: Purchase Tonal. A home gym that costs $2,995. He also has to purchase equipment worth $495 and pay for installation (assume this is $350) and taxes (assume the sales tax is 9.5% and will be applied to the total price). He also has to pay a $49 per month membership fee. He assumes this monthly membership fee will likely remain the same for the next 10 years. Dustin plans to stay on his workout regimen for the next five to ten years. His opportunity cost, i.e., discount rate is between 2.5% - 5%. Your job is to make a recommendation about which option will be more cost-effective.

Answer 1

We use the NPV analysis to taking a cost-effective decision. The decision with the highest NPV should be taken

Case A : Discount rate is 2.5%

Go back to the gym option

Using a PV in excel or financial calculator

PV(0.025,120,-130)

nper = 10*12 = 120 ( 10 years or 120 months)

rate = 0.025

PMT = 130

We get PV = -$4931.38

Purchase tonal option

Initial investment excluding sales tax = -2995-495-350 = -$3840

Sales tax =-3840*0.095 = -364.8

Total initial investment = -$4204.8

Since $49 is the membership fee,

Using PV(0.025,120,49)

NPV = -4204.8 + PV(0.025,120,-49)

NPV = -$6063.55

Since the NPV of 'Go back to the gym' option is higher, 'Go back to the gym' is the more cost-effective solution

We recheck if the decision changes if the discount rate changes to 5%

Case A : Discount rate is 5%

Go back to the gym option

Using a PV in excel or financial calculator

PV(0.05,120,-130)

nper = 10*12 = 120 ( 10 years or 120 months)

rate = 0.05

PMT = 130

We get PV = -$2592.55

Purchase tonal option

Initial investment excluding sales tax = -2995-495-350 = -$3840

Sales tax =-3840*0.095 = -364.8

Total initial investment = -$4204.8

Since $49 is the membership fee,

Using PV(0.05,120,49)

NPV = -4204.8 + PV(0.025,120,-49)

NPV = -$5181.99

Since the NPV of 'Go back to the gym' option is higher, we can conclude that 'Go back to the gym' is the more cost-effective solution