Finance| Finance |
Time Value of Money
Newspapers today are full of car ads enticing buyers by offering low or even 0% interest rates to finance a purchase. To compare two alternative offers you need to be able to take all the elements (like down payment, trade-in, principal, interest, and term) and synthesize them into a common measure of value.
A commonly accepted single measure of value is the Net Present Value (NPV) associated with a set of cash flows. A down payment is a cash flow item made at the beginning of a finance period. Monthly payments on a loan or a mortgage are cash flow items pegged throughout time. To calculate NPV you need to convert each cash flow item to its present value, and then add them all up. To convert any item you have to use a "discount factor" which expresses how much less a dollar in the future is worth relative to one today.
Suppose you have money in various investments and expect to earn about 6% per year on average. Then a dollar today should be worth $1.00*(1.06)= $1.06 a year from now. And it should be worth $1.00*(1.06)*(1.06)= $1.1236 in two years. By the same token, if you need to pay someone a dollar in 24 months, you only have to plan to set aside $1.00/(1.06*1.06) = $0.89 today. This is the present value of a dollar paid 24 months out. The factor 1/1.06 is the discount factor and it is applied for every period (in this case, for each of 2 years). Someone else with better or worse earning investments would have a different discount factor from yours.
Using a spreadsheet tool like Excel makes it easy for you to compute the NPV of a series of cash flows.
It should be easy to see that a lender can realize the same NPV from your cash flows
by making the interest rate zero, but upping the down payment or monthly payment
-or-
by making the down payment zero, but changing the interest rate or monthly payments
-or-
by simply controlling any one of the three!
Final notes:
© 2003 Michael E. Doherty