Sam is considering starting a healthy life style this year and is looking to joi

Question

Sam is considering starting a healthy life style this year and is looking to join the local gym for the coming 10 months. He can choose between two plans A or B. In Plan A, the gym charges a sign-up fee of $120 and $30 per month, while in Plan B, there is no sign-up fee but the monthly fee is $45. Answer the following and show your analyses

a) Help Sam make a decision on which plan to choose? Show your work

b) After how many months would both plans become indifferent? Show your work

c) Suppose Sam saw a coupon that costs $10 and will give him a discount of $5/month for the first 6 months of being enrolled in Plan B. Should he purchase the coupon? Justify your answer and show your work

Explanation / Answer

Question a)

Plan A

Fixed Cost = Joining Fee =$120

Variable Cost =$ 30

Membership Period = 10 months

Total Cost Incurred = $120 + $ 30 * 10 = $ (120 +300) = $ 420

Plan B

Fixed Cost = Joining Fee =$ 0

Variable Cost =$ 45

Membership Period = 10 months

Total Cost Incurred = $0 + $ 45 * 10 = $ 450

The above calculation clearly shows that for the given tenure, it is best for Sam to choose Plan A as it would cost him $ 30 less as compared to Plan B.

Question b)

Let the number of months after which both the plans become indifferent is X.

In that case the cost of Plan A would be: - $120 + $ 30* X

The cost of Plan B would be: - $ 45* X

A user should become indifferent when both the plans have the same price, so equations both the equations we get,

$120 + $ 30* X = $ 45* X

So, the point of indifference is 8 months.

Question b)

Plan A

Fixed Cost = Joining Fee =$120

Variable Cost =$ 30

Membership Period = 10 months

Total Cost Incurred = $120 + $ 30 * 10 = $ (120 +300) = $ 420

If Sam Purchases a Coupon for $ 10 for Plan B, the new cost incurred for that would be

Plan B

Fixed Cost = Coupon Fee =$ 10

Variable Cost for the first 5 months=$ 45 – 5 = $ 40

Variable Cost for the next 5 months=$ 45

Membership Period = 10 months

Total Cost Incurred = $10 + $ 40 * 5 + $45 * 5 = $10+ $ 85 * 5 =$ 435

The above calculation clearly shows that for the given tenure and with the discount coupon, it is still best for Sam to choose Plan A as it would cost him $ 15 less as compared to Plan B.

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