You are thinking of buying a used car thatcosts $8,000 and has an expected zero

Question

You are thinking of buying a used car thatcosts $8,000 and has an expected

zero resale value at the end of 4 years. Both Royal Bank (RY) and

Toronto-Dominion Bank (TD) are offeringspecial low-rate car loans to York

students. RY will loan you the $8,000and charge you a 5% EAR and wants the

loan repaid in 48 equal monthly payments,with the first payment due at the end

of the first month. TD will loan you thepurchase price of the car at a 6% APR, with the first payment alsodue at the end of the first month. The TD loan has also to be paidin full within 48 equal monthly payments. Your estimated costs ofoperating the car, including insurance, are $300 per month, payableat the beginning of each month. If you currently have $19,000 in aninvestment account which is earning interest at an 8% EAR, can youafford the car using either one of the special paymentplans?

a)    What is themonthly payment for the RY loan?

b)    What is themonthly payment for the TD loan?

c)  What is the total cost (present value) of buying and operating thecar over the four year period?

Explanation / Answer

Monthly payment PMT is calculated using Excel PMTfunction ie Instalment = PMT(rate,nper,pv) where Rate is monthly rate,nper = total no of instalments, pv = Loan amount
For your $19000 invested at 8% EAR, monthly Interest will be =PMT(rate,nper,pv) = PMT(8%/12,4*12,-19000) = $463.85
a) What is the monthly payment for the RYloan? ie Instalment = PMT(5%/12,4*12,-8000) = $184.23 Total Monthly expense = Running Cost + Loan Instalment =300+184.23 = 484.23
b) What is the monthly payment for the TDloan? ie Instalment = PMT(6%/12,4*12,-8000) = $187.88 Total Monthly expense = Running Cost + Loan Instalment =300+187.88 = 487.88
c) What is the total cost (present value) of buying andoperating the car over the four year period? Present value of Buying car = PV(Rate, nper, PMT) For RY Loan, PV of buying & operating car = PV(5%/12,4*48, -484.23) = $21,026.70
For TD Loan, PV of buying & operating car = PV(6%/12,4*48, -487.88) = $21,185.19
As Interest income from Investment income is only $463.85while monthly outgoing is $484.23 (RY Loan) & $487.88 (TDLoan), it is not advisable to Buy car unless you can bridgethe shortfall from other income.

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