Calculating PV and FV of different cash flows:
Present Value
This is the current value of some future cash flow.
- The longer the time period till the future amount is received, the lower the present value.
- Higher the discount rate, the lower the present value.
Future Value
This is the value to which an investment will grow after one or more compounding periods.
- Longer the time period till which the investment is allowed to grow, higher the future value.
- Higher the interest rate, the higher the future value.
Single-Sum of Money
The future value and the present value of a single sum of money can be calculated by using the formulae given below or by using the TVM keys on a financial calculator (recommended approach for the exams).
Ordinary Annuity
An annuity is a series of equal cash flows that occur at regular intervals of time. In an ordinary annuity, the cash flows occur at the end of each compounding periods.
Annuity Due
An annuity is a series of equal cash flows that occur at regular intervals of time. In an annuity due the cash flows occur at the beginning of each compounding periods.
Perpetuity
Perpetuity is a series of equal cash flows at regular intervals occurring forever. The present value of perpetuity can be calculated as:
Series of unequal cash flows
The present (future) value of any series of cash flows is equal to the sum of the present (future) values of the individual cash flows.
Useful formulae:
FV = PV (1 + I/Y)N
PV = FV / (1 + I/Y)N
PV of a perpetuity = PMT / (I/Y)