Time Value of Money

[1] The time value of money means that a dollar received today is worth more than a dollar received in the future because of the effect of compounding.
- Compounding and discounting are the major concept involved in time value of money calculations.
- Compounding is the process of finding future value while discounting is the process of finding present value.

[2] Future value (FV) is the value at the end of a time period from a sum of money today.
[3] Present value (PV) is the current value of a future sum of money.

FV = PV x (1+i)^n, e.g. i = the annual interest rate, n = the no. of years.

[4] NPV is employed to make investment decisions.
- NPV = PV of future net cash inflows - initial outlay.
- If an investment's NPV >0, a firm or an individual should invest in it.
- If its NPV < 0, one should not invest in it.
- If its NPV = 0, a firm or an individual should invest in it.

E.g. NPV = (PVs of all annual net case inflows from using the machine + PV of the machines's market value in Year 10) - Initial cost of the machine.

[5.1] The difference between nominal & effective rates of return is due to differences in the frequency of compounding.
[5.2] When comparing different investment plans, we should use the effective rate of return (ERR) if the frequency of compounding differs.

ERR = (1-i/m)^m - 1. Nominal annual interest rate of i and the interest is compounded at a rate of m times per year.

E.g. ERR = (1+0.1/4)^4 - 1 = 10.38%. where i = 10% and is compounded 4 time a year.