You are considering buying a car from a local auto dealer. The dealer offers you

Question

You are considering buying a car from a local auto dealer. The dealer offers you one of two options:

Option1: You can pay $30,000 cash.

Option2 (The deferred payment plan): You can pay the dealer $5,000 cash today and a payment of $1,050 at the end of each of the next 30 months. As an alternative to the dealer financing, you have approached a local bank, which is willing to give you a car loan of $25,000 at the rate of 1.24 percent per month.

a. Assuming that 1.25 percent is the opportunity cost, calculate the present value of all the payments on the dealer’s deferred payment plan.

b. What is the effective interest rate being charged by the dealer?

Explanation / Answer

Part A)

The present value of deferred payment plan can be calculated with the use of Present Value (PV) function/formula of EXCEL/Financial Calculator. The function/formula for calculating PV is PV(Rate,Nper,PMT,FV) where Rate = Opportunity Cost, Nper = Period, PMT = Monthly Payment and FV = Future Value (if any)

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Here, Rate = 1.25%, Nper = 30, PMT = $1,050 and FV = 0

Using these values in the above function/formula for PV, we get,

Present Value of Monthly Payments = PV(1.25%,30,1050,0) = $26,133.35

Present Value of Deferred Payment Plan = Present Value of Monthly Payments + Down Payment = 26,133.35 + 5,000 = $31,133.35

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Part A)

To determine the effective rate of interest, we need to calculate the IRR. The IRR can be calculated with the use of IRR function/formula of EXCEL as follows:

IRR = Effective Rate of Interest = 1.56%

Month Cash Payment (Option 1) Payment under Deferred Payment Plan (Option 2) Difference (Option 1 - Option 2) 0 30,000 5,000 25,000 1 0 1,050 -1,050 2 0 1,050 -1,050 3 0 1,050 -1,050 4 0 1,050 -1,050 5 0 1,050 -1,050 6 0 1,050 -1,050 7 0 1,050 -1,050 8 0 1,050 -1,050 9 0 1,050 -1,050 10 0 1,050 -1,050 11 0 1,050 -1,050 12 0 1,050 -1,050 13 0 1,050 -1,050 14 0 1,050 -1,050 15 0 1,050 -1,050 16 0 1,050 -1,050 17 0 1,050 -1,050 18 0 1,050 -1,050 19 0 1,050 -1,050 20 0 1,050 -1,050 21 0 1,050 -1,050 22 0 1,050 -1,050 23 0 1,050 -1,050 24 0 1,050 -1,050 25 0 1,050 -1,050 26 0 1,050 -1,050 27 0 1,050 -1,050 28 0 1,050 -1,050 29 0 1,050 -1,050 30 0 1,050 -1,050 IRR =IRR(25000,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050,1050)=1.56%

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