What is the concept of "Time Value of Money"?
Time Value of Money: The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.
- Everyone knows that money deposited in a savings account will earn interest. Because of this universal fact, we would prefer to receive money today rather than the same amount in the future.
- For example, assuming a 5% interest rate, $100 invested today will be worth $105 in one year ($100 multiplied by 1.05). Conversely, $100 received one year from now is only worth $95.24 today ($100 divided by 1.05), assuming a 5% interest rate.
What is the PV of a Single Amount or "PV of $1"?
PV of $1: Value now (at present) of a single amount to be received in the future.
- Amount to be received in the future is discounted using an interest rate to get the PV of that amount.
The amount that must be invested now at a specific interest rate so that $1 can be paid or received in the future.
- PV= Future Amount x PVF (Present Value Factor)
What is the FV of a Single Amount or "FV of $1"?
FV of $1: Value at some future date if a single amount invested now.
- Amount that will accumulate as a result of compounding of interest on the single amount invested at the present.
The amount that would accumulate at a future point in time (w compound interest) if $1 were invested now.
- FV= PV (Present amount) x FVF
Define an Annuity:
Annuity: A series of equal amounts paid or received at equal intervals.
Define: Compound Interest:
Compound Interest: Interest computed not only on the principal but also on any accumulated unpaid interest (i.e., interest is paid on interest).
Distinguish between an "ordinary annuity (also called an annuity in arrears)" and an "annuity due (also called an annuity in advance)."
Ordinary annuity: Series of equal amounts received or paid at the end of each equal period.
Annuity due: Series of equal amounts received or paid at the beginning of each equal period.
Define the "Present Value" of an Ordinary Annuity:
PV of Ordinary Annuity:
Value now of a series of equal amounts to be received at the end of equal intervals over some future period
Equal amounts to be received at the end of a number of equal periods are discounted using an interest rate to get the present value of those amounts.
Define "Future Value" of an Ordinary Annuity.
FV of Ordinary Annuity:
Value at some future date of a series of equal amounts to be invested at the end of equal intervals over some period of time.
Amount that will accumulate as a result of the amounts invested at the end of each period and the compounding of interest on those amounts.
Define "PV of Annuity Due":
PV of Annuity Due:
Determines value now of a series of equal amounts to be paid at equal intervals with payments at the beginning of each period.
Define FV of Annuity Due:
FV of Annuity Due:
Determines the value at some future date of a series of equal payments to be paid at equal intervals with payments at the beginning of each period.
True or False:
The interest rate used to determine the present value of a future amount is called the discount rate.
True or False:
In computing the present value of an annuity due that has 10 payments, only 9 payments have to be discounted.
Since an an annuity due involves the 1st payment or receipt occurring at the present, that pymt does not have to be discounted. Therefore, the # of pymts discounted is one less than # of pymts in annuity and # of periods in one less.
True of False:
An annuity due will result in a higher future value (or present value) than an ordinary annuity of the same amount.
For PV: It will result in higher PV than ord annuity because the firm amount does not have to discounted (given at present)
For FV: Because 1st amount is paid (or received) at start of annuity, the amount of interest earned and amount of end annuity will be greater than FV or ord annuity (because that pymt earns an additional period of interest).
True or False:
In computing present value, for a given number of periods, the higher the discount (interest) rate, the higher the discount factor.
In PV: The higher the discount rate, the lower the factor:
- The lower the PV
In FV: The higher the discount rate, the higher the factor:
- FV will be greater