Time Value of Money

time value of money

measurement and recording of liabilities are based on the concept of the time value of money

• time value of money = compound interest

simple interest

earns interest on the principal invested

simple interest equation

principal x rate x time

4 time value of money cases

1. future value of a lump sum

2. present value of a lump sum

3. future value of an annuity

4. present value of an annuity

n

number of periods

i

interest rate

future value of a lump sum

we know the value of some amount today and want to know the value at some point in the future

FV of a lump sum equation

future value = present value x future value factor

compounding

the frequency with which interest is added to the principal

necessary adjustments to i and n

i / # of compounds per year

n x # of compounds per year

present value of a lump sum

we know the value of some amount in the future and we want to know the value today

PV of a lump sum equation

present value = future value x present value factor

discounting

figuring out how much a future value is worth today

Key point of FV & PV of a lump sum

present value of a lump sum and future value of a lump sum are reciprocal of each other, they can be used interchangeably to solve problems

lump sum

single payment

annuity

a series of equal payments (to be received or paid) with each payment having the same time interval between them

ordinary annuity

an annuity with payments occurring at the end of each period

annuity due

an annuity with payments occurring at the beginning of each period

FV of an ordinary annuity

we want to know the value of a series of equal cash flows occurring at the end of each period at some point in the future

FV of an ordinary annuity equation

future value of an ordinary annuity = payment amount x future value annuity factor

future value of an annuity due

we want to know the value of a series of equal cash flows occurring at the beginning of each period at some point in the future

FV of an annuity due equation

future value of an annuity due = payment amount x future value annuity factor (1 + i )

present value of an ordinary annuity

we want to know the value today of a series of equal payments to be made or received in the future

PV of an ordinary annuity equation

present value of an ordinary annuity = payment amount x present value annuity factor

present value of an annuity due

we want to know the value today of a series of equal payments to be made or received in the future

PV of an annuity due equation

present value of an ordinary annuity = payment amount x present value annuity factor (1 + i)

key point of FV & PV annuity

• ‘payment’ is the amount of each individual, equal payment

• FV and PV of annuities are NOT reciprocals