Question

In: Finance

Adam has just graduated, and has a good job at a decent starting salary. He hopes...

Adam has just graduated, and has a good job at a decent starting salary. He hopes to purchase his first new car. The car that Adam is considering costs $39,000. The dealer has given him three payment options:

1. Zero percent financing. Make a $2,500 down payment from his savings and finance the remainder with a 0% APR loan for 48 months. Adam has more than enough cash for the down payment, thanks to generous graduation gifts.

2. Rebate with no money down. Receive a $3,400 rebate from the car dealer and finance the rest with a standard 48-month loan, with an 5% APR. He likes this option, as he could think of many other uses for the $2,500 of his saving.

3. Pay cash. Get the $3,400 rebate and pay the rest with cash. While Adam doesn’t have $39,000, he wants to evaluate this option. His parents always paid cash when they bought a family car; Adam wonders if this really was a good idea.

1. What are the cash flows associated with each of Adam’s three car financing options?

2. Suppose that, similar to his parents, Adam had plenty of cash in the bank so that he could easily afford to pay cash for the car without running into debt now or in the foreseeable future. If his cash earns interest at a 5.4% APR (based on monthly compounding) at the bank, what would be his best purchase option for the car?

Solutions

Expert Solution

1 CASH FLOWS
ZERO FINANCING
Monthly Payment $760.42 (39000-2500)/48
Month Cash Flow
Month 0 $2,500
Month 1-48 $760.42
REBATE WITH NO MONEY DOWN
Pv Car Cost =39000-3400 $35,600
Rate Monthly interest=(5/12)%= 0.4167%
Nper Number of months of payment 48
PMT Monthly Payment $819.84 (Using PMT function of excel with Rate=0.4167%,Nper=48, Pv=-35600, )
Month Cash Flow
Month 1-48 $819.84
PAY CASH
Month Cash Flow
0 $35,600 (39000-3400)
2 Discount Rate =Opportunity Cost 5.40% APR
Rate Monthly discount rate=(5.4/12)% 0.450%
ZERO FINANCING OPTION
PV Present Value of Monthly Payments $32,761.29 (Using PV function of excel with Rate=0.45%,Nper=48, Pmt=-760.42, )
Down payment $2,500
Net Present Value (NPV)of Costs $35,261.29
REBATE WITH NO MONEY DOWN OPTION
PV Present Value of Monthly Payments $35,321.29 (Using PV function of excel with Rate=0.45%,Nper=48, Pmt=-819.84, )
OPTION NPV of Cost
ZERO FINANCING OPTION $35,261.29
REBATE WITH NO MONEY DOWN OPTION $35,321.29
PAY CASH OPTION $35,600
ZERO FINANCING OPTION is the best
NPV of cost is lowest

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