Ohio Motor dealership has given you three options to purchase a new Ohio-OU. Eac

Question

Ohio Motor dealership has given you three options to purchase a new Ohio-OU. Each of these options is available through financing through the dealer. Banks are currently charging 8% for new vehicle loans. Which of the following is the best deal? Show all calculations.

1. Pay $40,000 in cash today

2. Pay interest only (on the amount due at the end of the contract) at the end of each of six years at 5% and then pay a lump sum of $51,000 at the end of the sixth year.

3. Pay three easy annual payments of $18,000, beginning a year from today, which includes interest at 4.5%.

Explanation / Answer

Amt $ 1 Option 1 Present value of loan          40,000 2 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Interest payment on 51000 @5%         2,550         2,550         2,550         2,550         2,550         2,550 Lump sum payment      51,000 Total Payment         2,550         2,550         2,550         2,550         2,550      53,550 Discount factor@8%                    1      0.9259      0.8573      0.7938      0.7350      0.6806      0.6302 PV of paymnets         2,361         2,186         2,024         1,874         1,735      33,746 Net PV of payments today          43,927 3 Formula for loan amortization = A= [i*P*(1+i)^n]/[(1+i)^n-1] Amt $ A = periodical installment          18,000 P=Loan amount = ? i= interest rate per period = 4.500% n=total no of payments                    3 Or ,18000=0.045*P*(1.045^3)/(1.045^3-1) 18000=0.045*1.141*P/0.141 18000=0.3641P P= 49430 So Loan amount =          49,430 Therefore the best deal is the cash payment which has the lowest Present value

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