Question

You are trying to decide between two mobile phone carriers. Carrier A requires you

to pay $200 for the phone and monthly charges of $60 for 24 months. Carrier B wants

you to pay $100 for the phone and monthly charges of $70 for 12 months. Assume you

will keep replacing the phone after your contract expires. Your cost of capital is 4%.

Based on cost alone, which carrier should you choose?

Answer 1

Let us find the equated annual cost for the initial payment made and add to the monthly payments to get the effective EAC

Carrier A
Let the equated annual cost for $200 be P
Number of months = n = 24
Monthly Interest Rate = r = 0.04/12
Present Value of annual cost should be equal to PV = $200
=> PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r
=> 200 = P[1- (1+0.04/12)^-24]/(0.04/12)
=> P = 200*(0.04/12)/[1- (1+0.04/12)^-24] = $8.68
Hence, effective annual cost = $60 + $8.68 = $68.68

Carrier B
Let the equated annual cost for $100 be P
Number of months = n = 12
Monthly Interest Rate = r = 0.04/12
Present Value of annual cost should be equal to PV = $100
=> PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r
=> 100 = P[1- (1+0.04/12)^-12]/(0.04/12)
=> P = 100*(0.04/12)/[1- (1+0.04/12)^-12] = $8.51
Hence, effective annual cost = $70 + $8.51 = $78.51

Since the effective equated annual cost for Carrier A is lower, we should choose Carrier A