Opportunity cost

CFA Level I
#1

You are interested in purchasing a car that costs 14.000 dollars. You have the following options: you can purchase it in cash or you can take a car loan (here we assume that you have enough money to purchase the car without a loan). The loan would require you to put 20% down. The annual interest rate on the loan is 12% (compounded monthly), for four years.

A)Find the monthly payment on the car loan.

B) If your opportunity cost of capital is 1.2% monthly, find the net present values of each of the two options. Which option would you prefer?

The first part wasn’t hard, we use the PV formula and we get the result which is around 294 dollars per month.

Could someone be so kind to explain me how to work on the second problem ?

Thanks a lot !

#2

The NPV of the cash purchase is easy: it’s −$14,000.

For the NPV of the credit purchase, you need to discount all of the payments at 1.2% monthly and tot them up.

However, to decide which option is better, you don’t need to compute the NPV for the credit purchase. Because the interest rate on the loan is less than the opportunity cost, that approach will give a lower NPV and is, therefore, preferable.

(For whatever it’s worth, the NPV of the credit purchase is −$13,514.)