Talk

Present Value of Money

It ofcourse makes sense that money in hand today is more valuable to money available at a later date. The value of money available in the future decreases its present value relative to the interest rate and the period of time you have to wait for the money. In this entry we'll look at the calculations behind calculating the present value of money.

PV = future amount / (1 + rate)^term

For example say you'd like to purchase a $30,000 car in 3 years. The interest rate is 6%. Then the present value of the $30,000 amount in 3 years is:

PV = 30,000 x 1/(1.06)³ = $25,188.57

So your $25,200 will become $30,000 in 3 years. The simplifying assumptions presume interest rates to remain constant. (you could lock down the rates in a CD I suppose). The expression 1/(1+r)^t is called the discount factor. Lets look at this problem a different way. Every so often furniture stores offer a promotion. No payments, no interest until 2004. So lets assume you buy a $1000 sofa (the current interest rate is still 6%). You have 24 months to pay off the sofa and incur no interest charges. What is the Present Value of your purchase?

PV = 1000 x 1/(1.06)² = 1000 x 0.88996 = $889.96

So if a competing store is offering you $150 off the same sofa you are better off taking that deal. Otherwise you are better off taking the no payment deal.

The final permutation of this equation is to calculate the interest rate from the present value of an asset. Suppose you are given a promisory note for $750 that promises to pay $1000 in two years what is your effective interest rate?

PV = amount/(1+rate)^term = (1+rate)^t = amount/PV = rate = (amount/PV)^1/t - 1
rate = (1000/750)^1/2 -1 = 1.154 -1 = .15 = 15%

Thats a pretty decent interest rate. I suggest you take up the offer!

To add: perpetuities, annuities, PV = C/r (for annuities) and PV = C[1/r - 1/(r(1+r)^t)], amortization, net present value. Opportunity cost of capital

Posted at May 6, 2002 07:07 PM