Question

In: Finance

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

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?

Solutions

Expert Solution

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


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