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Do the Math 8-4 Rebate Versus Low Interest Rate Kyle Parker of Concord, New Hampshire, has...

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.

Solutions

Expert Solution

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


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