Question

Scenario 1) Tim 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. His discount rate is between 2.5% - 5%.

Scenario 2) A home gym that costs $2,995. He also has to purchase equipment worth $495 and pay for installation ($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

Calculate NPV, IRR, MIRR, EAC, and Payback Period (Show work and formulas used for credit).

Answer 1

Case A : Discount rate is 2.5%

Scenario 1) Gym membership option

Using a PV in excel or financial calculator

PV(0.025/12,120,-130)

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

rate = 0.025/12 ( Since each period is a month)

PMT = 130 (Monthly membership fee)

We get PV = -$13,790.19

EAC =

r is the periodic discount rate = 0.025/12

n is number of period per year = 120

EAC = NPV * [(0.025/12)/(1-(1+(0.025/12))^(-120))]

EAC = NPV * 0.009427

EAC = -$130

Scenario 2)

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(0.025/12,120,49)

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

NPV = -$9402.64

EAC =

EAC = NPV * 0.009427

EAC = -$88.64

Case B : Discount rate is 5%

Scenario 1) Gym membership option

Using a PV in excel or financial calculator

PV(0.05/12,120,-130)

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

rate = 0.05/12 (Since each period is a month)

PMT = 130

We get PV = -$12256.58

EAC =

EAC = NPV*0.010607

EAC =-12256.58*0.010607

EAC = -$130.005

Scenario 2)

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(0.05/12,120,49)

NPV = -4204.8 + PV(0.5/12,120,-49)

NPV = -$8824.59

EAC =

EAC = NPV*0.010607

EAC =-8824.59*0.010607

EAC = -$93.60

In this question, IRR, MIRR, and the payback period cannot be obtained, as all the cash-flow pertains to investments ( or rather cash-outflows) rather than cash-inflows.