In: Finance
Do the Math 8-4
Rebate Versus Low Interest Rate
Kyle Parker of Concord, New Hampshire, has been shopping for a new car for several weeks. He has negotiated a price of $31,000 on a model that carries a choice of a $2,500 rebate or dealer financing at 2 percent APR. The dealer loan would require a $1,000 down payment and a monthly payment of $526 for 60 months. Kyle has also arranged for a loan from his bank with a 6 percent APR. Use the Run the Numbers worksheet to advise Kyle about whether he should use the dealer financing or take the rebate and use the financing from the bank. Round your answer to two decimal places.
Given the price is $31000
Price after rebate = $31000 - 2500 = 28500
Let us calculate the NPV and IRR under both the models .
Under model -1 where loan is financed by bank
Let us calculate the equalised monthly installments.
Given annual interest is 6% per annum
Hence monthly installment is 6/12 = 0.5% per annum.
Loan Amount required = 31000 - 2500 = 28500
The formula for calculating the monthly equalised installments is.
[P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month
= (28500 * 0.005 * (1.005)60)/((1.005)60-1) = 550.9848 per month
Total Amount of monthly payments = 550.9848 * 60 = 33059.09
Hence principal amount = 28500 and interest amount is 33059.09 - 28500 = 4559
Here the IRR of the loan will also be 0.5%
Under model -2 where loan is financed by Dealer-
Here we get no rebate for prepayment moreover we have to make a down payment of 1000
Hence the total loan value = 31000
Given monthly repayment amount is 526 for 60 months
Hence the total amount repaid = 526*60 = 31560 +1000 = 32560
Hence the amount of interest is 1560
IRR for Model -2 will be 0.16773%
Please note that IRR here is calculated excluding the initial down payment of 1000.
In model 1 the total payments over 5 Years is 33059 including principal and in model 2 it is 32560.
Hence we have to select Model -2 as this have lower IRR and Lower cost of interest