The time value of money is a basic financial concept that holds that money in the present is worth more than the same sum of money to be received in the future. This is true because money that you have right now can be invested and earn a return, thus creating a larger amount of money in the future.

A simple example can be used to show the time value of money. Assume that someone offers to pay you one of two ways for some work you are doing for them: They will either pay you $1,000 now or $1,100 one year from now.

Which pay option should you take? It depends on what kind of investment return you can earn on the money at the present time. Since $1,100 is 110% of $1,000, then if you believe you can make more than a 10% return on the money by investing it over the next year, you should opt to take the $1,000 now.

On the other hand, if you don’t think you could earn more than 9% in the next year by investing the money, then you should take the future payment of $1,100 – as long as you trust the person to pay you then.

The time value of money is also related to the concepts of inflation and purchasing power. Both factors need to be taken into consideration along with whatever rate of return may be realized by investing the money.

Why is this important? Because inflation constantly erodes the value, and therefore the purchasing power, of money. It is best exemplified by the prices of commodities such as gas or food. If, for example, you were given a certificate for $100 of free gasoline in 1990, you could have bought a lot more gallons of gas than you could have if you were given $100 of free gas a decade later.

Inflation and purchasing power must be factored in when you invest money because to calculate your real return on an investment, you must subtract the rate of inflation from whatever percentage return you earn on your money.

If the rate of inflation is actually higher than the rate of your investment return, then even though your investment shows a nominal positive return, you are actually losing money in terms of purchasing power. For example, if you earn 10% on investments, but the rate of inflation is 15%, you’re actually losing 5% in purchasing power each year (10% – 15% = -5%).

Perpetuity is defined as an annuity wherein the cash payments or cash receipts start on a determined date and continue on a periodic basis indefinitely or perpetually. Some examples include fixed interest payments on permanently deposited money which is irredeemable. While computing the present value of perpetuity, the following points must be considered:

1. The value of the perpetuity is definite since payments or receipts which are likely to be expected too far in the future entail very minimal present value.

   
   

2. As the principal amount is not to be redeemed, the principal carries no present value.

FV = PV *(1 + i) ^n

FV = Future value of money
PV = Present value of money
i = Interest rate per payment period
r = Annual interest rate
k = number of payment periods per year
n = number of years

FVAn = R*[(1+i)^n - 1] / i

FVAn = Future value of an annuity
R = Each periodic receipt or payment
n = Length of the annuity

PVA(infinite) = R / (i-g)