Time value of money (TVM) is the idea that money that is 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. One of the most fundamental concepts in finance is that money has a time value
attached to it. In simpler terms, it would be safe to say that a dollar was worth more yesterday than today
and a dollar today is worth more than a dollar tomorrow.
SCOPE PF TVM
There are five (5) variables that you need to know:
1. Present value (PV) - This is your current starting amount. It is the money you have in your
hand at the present time, your initial investment for your future.
2. Future value (FV) - This is your ending amount at a point in time in the future. It should be
worth more than the present value, provided it is earning interest and growing over time.
3. The number of periods (N) - This is the timeline for your investment (or debts). It is usually
measured in years, but it could be any scale of time such as quarterly, monthly, or even daily.
4. Interest rate (I) - This is the growth rate of your money over the lifetime of the investment.
It is stated in a percentage value, such as 8% or .08.
5. Payment amount (PMT) - These are a series of equal, evenly-spaced cash flows.
TIME VALUE OF MONEY IN QUANTITAVIE TECHNIQUES
1. Interest rates as Required Rate of Return/ Discount Rate/ Opportunity cost:

Equilibrium interest rates/ market rates are the required rate of return (RRR) for an investor.

The RRR/ interest rates can be used as discount rates for calculation of present value of an
investment. RRR can also be interpreted as the opportunity cost of current consumption.
2. Interest rate as sum of real risk-free rate, expected inflation, and risk premiums:

Real risk free rate of interest is the theoretical rate on a single period investment that has no
expectation of inflation in it.

US T-bill rates are nominal risk free rates as they contain expected inflation premium.

Other securities in addition to inflation premium, also contain risk premiums associated with
specific types of risk i.e. default risk, liquidity risk, maturity risk etc.

Accordingly the RRR can be defined as RRR = Nominal Risk free rate+ default risk premium”
liquidity premium+ maturity risk premium+…(other risk premiums)
3. Effective annual rate (EAR):

The annual rate of interest that an investor actually realizes as a result of compounding over
periods is called as EAR. The EAR is adjusted over different compounding periods.

It is determined as EAR = (1+ periodic rate) m – 1
4. Time value of money problems for different frequencies of compounding:

The problems can include semiannual/ quarterly/ monthly/ daily compounding. Ceteris paribus
as the compounding period increases, the EAR increases.

The limit of shorter and shorter compounding is called continuous compounding. To convert
an annual stated rate to the EAR with continuous compounding,
5. Future value (FV) and present value (PV) calculation:

FV of a single cash flow is calculated as: FV = PV (1+ I/Y)N (Here I/Y is rate of return per
compounding year)

An annuity is a stream of equal cash flows that occurs at equal intervals over a given period.
Annuity can be of two types: a) Ordinary annuity- annuity payments occur at the end of each
compounding period and b) Annuity Due- annuity payments occur at the beginning of each
compounding period

Perpetuity is a financial instrument that pays a fixed amount of money at a defined set of
intervals over an infinite period of time. The PV of perpetuity is: PV= PMT/ (I/Y)

One crude way of calculating the PV of annuities is the sum of PVs of all the annuity payments.
The same can be easily calculated by using PV calculation function in financial calculator.
However, if it is not an annuity i.e. the cash flows are uneven then PV of each tranche of
cashflow will give the correct figure.

A critical concept here is PV of any series of CFs is equal to the sum of the PV of individual
CFs.
6. Use of a time line in modeling and solving time value of money:

Timeline comes in handy for solving problems related to uneven CFs and finding out value of
investment at an intermittent period.