In: Finance
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?
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 | |||||||||||