Option Car Loan Solution
(Handout problem)
There will be a little rounding error in the answers below and in your answers. If your answers are reasonably close to the ones given below, you should not try to get them to match exactly.
PLAN A is to take the cash rebate and not apply it as a down payment.
PLAN A' is to use the rebate as a down payment and finance $22,500 at 10%.
PLAN B is as stated in the problem.
PLAN A will have a monthly payment of $520.55 and a payoff balance after three years of $11,280.82.
PLAN A' will have a payment of $478.05 and a payoff balance of $10,359.94.
PLAN B will have a payment of $457.96 and a payoff balance of $5,320.98
Compare A to A':
The benefit of A' over A is a lower payment (by $42.50)for 36 months and a lower payoff balance (by $920.88) after three years. It costs $2,000 to get these benefits since you must give up the rebate to do it.
PMT = 42.5
FV = 920.88
n = 36
i = 8/12
Compute PV = 2081.22 which is the value of the savings to you in today's dollars.
Since it costs $2,000 to get these savings, the net present value of the decision to take A' over A is $81.22. Since this amount is positive, it means you prefer A' over A.
Compare A to B:
The benefit of B over A is a lower payment (by $62.59)for 36 months and a lower payoff balance (by $5,959.84) after three years. It costs $7,000 to get these benefits since you must give up the $2,000 rebate and put up a $5,000 down payment to do it.
PMT = 62.59
FV = 5959.84
n = 36
i = 8/12
Compute PV = 6689.27 which is the value of the savings to you in today's dollars.
Since it costs $7,000 to get these savings, the net present value of the decision to take B over A is NEGATIVE $310.73. This means that you prefer A over B.
Compare A' to B:
The benefit of B over A' is a lower payment (by $20.09)for 36 months and a lower payoff balance (by $5,038.96) after three years. It costs $5,000 to get these benefits since you must give up the $5,000 down payment to do it.
PMT = 20.09
FV = 5038.96
n = 36
i = 8/12
Compute PV = 4608.52 which is the value of the savings to you in today's dollars.
Since it costs $5,000 to get these savings, the net present value of the decision to take B over A' is NEGATIVE $391.48. This means that you prefer A' over B.
Now you know that A' is better than A, A' is better than B, and A is better than B. So the order of your preferences must be A', A, B. The value of your first choice over your second choice is $81.22. (Note that there is a little rounding error in this answer, and yours may vary a bit from this exact answer.)
Remember that you can check your calculations by adding the results from A' vs. A and B vs. A' which should equal the result of B vs. A' (with a small allowance for rounding error.
