Time value of Money

Basic Concept

Present values

Annuities

Future values

Future Value of a Multiple Cash Flow

Future value of lump sum

Present value of lump sum

Present Value of a Multiple Cash Flow

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Present value of Annuities Due

Present Value of Ordinary Annuities

Future value of Annuities Due

Future value of Ordinary Annuities

Future Value of a Lump Sum

Future value determines the amount that a sum of money invested today will grow to in a given period of time

Present Value of a Lump Sum

Present value calculations determine what the value of a cash flow received in the future would be worth today (time 0)

Future Value of a Multiple Cash Flow

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A cash flow stream is a finite set of payments that an investor will receive or invest over time.

The future value of a cash flow stream is equal to the sum of the future values of the individual cash flows.

The FV of a cash flow stream can also be found by taking the PV of that same stream and finding the FV of that lump sum using the appropriate rate of return for the appropriate number of periods.

Present Value of a Multiple Cash Flow


The PV of a cash flow stream can also be found by taking the FV of the cash flow stream and discounting the lump sum at the appropriate discount rate for the appropriate number of periods

The PV of the cash flow stream is equal to the sum of the present value of each of the individual cash flows in the stream.

Annuities

An annuity is a cash flow stream in which the cash flows are all equal and occur at regular intervals

Note that annuities can be a fixed amount, an amount that grows at a constant rate over time, or an amount that grows at various rates of growth over time

Ordinary annuities – cash flow occur at the end of the period


Annuity Due - cash flow occur at the beginning of the period

Interpolation

Process of determining the exact rate of interest (i) or the exact period of time (n)

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INTERPOLATION

= Interest (before) + (factor value (before) – calculated factor value) x

(factor value (before) – factor value (after))