Time Value of Money

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.

A ringgit received today is worth more than a Ringgit received tomorrow

This is because a Ringgit received today can be invested to earn interest

The amount of interest earned depends on the rate of return that can be earned on the investment

Time value of money quantifies the value of a Ringgit through time

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

Using Formula FVn = PV (1+i)n

Using Future Value Table FVn = PV (FVIF i%,n)

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)

Using your Formula PVn = FV [1 / (1+i)n ]

Using Future Value Table PVn = FV (PVIF i%,n)

Future Value of a Multiple Cash Flow

FVn = PV (1+i) n-1 + PV (1+i) n-2 + PV (1+i) n-3 + PV (1+i) n-4

FV = PV(FVIF i%,n-1)+PV(FVIF i%,n-2)+PV(FVIF i%,n-3)+ PV(FVIF i%,n-4)

Present Value of a Multiple Cash Flow

PV = FV1/(1+i)1 + FV2/ (1+i)2 + FV3/(1+i) + FV4/ (1+i)

PVn = FV (PVIF 10%,1)+ FV (PVIF 10%,2)+ FV (PVIF 10%,3)+ FV (PVIF 10%,4)

Annuities

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

Annuity Due - cash flow occur at the beginning of the periods.

FVA = PMT (1 + i )n - 1 / i

FVA = PMT (FVIFA i%, n)

PVA Ordinary Annuity

PVA = PMT (PVIFA i%, n)

PVA - Annuity Due