Time Value of Money
CPA Ansbert Kishamba
Time value of money
Time value of money means that the value of a given
amount of money is different at different points in
time.
• The value of a particular amount of money received
today is more than its value if received in future.
• The worth of money that a person has today is more
than the expectation of receiving that money in the
future. Money in hand today can be invested and
returns can be earned on that investment.
Money has time value because of the following reasons:
i. Risk
ii. Consumption
iii. Investment opportunity
iv. Inflation
Perspectives of time value of money
There are two perspectives to converting the cash
flows to a common point in time:
i. Compounding technique (future value)
ii. Discounting technique (present value)
COMPOUNDING TECHNIQUE
Compounding is the technique of calculating
future value of cash flows when the present values
are stated. Future value represents the amount
that an investment made today will grow to at
some point of time in future if invested at a
specific rate of interest.
Formula to compute compound value:
Where:
𝑖 𝑛𝑚
𝐴 = 𝑃(1 + )
𝑚
A= amount at the end of the period
P= principal at the beginning of the period
i = rate of interest
n= number of years
m= number of times compounding is done in a
year
Annuity
An annuity is a level stream of regular
payments that lasts for a fixed number of
periods.
𝐹𝑉 = 𝐶
(1+𝑟)𝑛 −1
𝑟
Continuous Compounding
FV = 𝐶 × 𝑒
𝑟𝑡
Example:
Calculate the amount to be received by an
investors when they invest Tshs10,000 for 2 years
at an interest rate of 10% compounded:
i. Annually
ii. Semi annually
iii. Quarterly.
Present Value or Discounting
Technique
Present value is the current value of a future amount.
Present value of money that will be received in the
future will be less than the value of money in hand
today hence this technique is also called discounting
technique.
This technique determines the present value of a
future amount assuming that the investor has an
opportunity of earning a return on his money. This
return is known as the discount rate.
Present value equation is as follows:
𝐴
𝑃=
(1 + 𝑖)𝑛
WHERE:
P = present value of future sum to be
received
A = sum to be received in future
i = interest rate
n = number of years
Annuity
𝑃𝑉 = 𝐶
1−(1+𝑟)−𝑛
𝑟
Growing annuity
𝑃𝑉 = 𝐶
1+𝑔 𝑛
1−
1+𝑟
𝑟−𝑔
Perpetuity
A perpetuity is a constant stream of cash
flows without end.
𝐶
𝑃𝑉 = 𝑟
Growing perpetuity
𝐶
𝑃𝑉 = 𝑟−𝑔
Effective Annual Rate
R = (1 + )𝑚 −1
𝑟
𝑚
Use of Time Value of Money in
Financial Management
Time value of money is a very important concept in
financial management. It is of more significance in
the following decisions:
i. Investment decision
ii. Financing decision
INVESTMENT DECISION
The concept of time value of money is very
important for decisions pertaining to long-term
capital investments. A person intending to
invest in a business project needs to
understand the returns expected from the
business.
Since returns from a business accrue over a
number of years after the business is set up
while investment has to be made in the current
period, the cash inflows and outflows occur in
different periods and cannot be compared with
each other directly.
FINANCING DECISION
The time value of money concept is useful when comparing
costs of different sources of financing to determine the
minimum cost source. In case of borrowings, cash inflow
occurs immediately on disbursal of borrowings and cash
outflows occur over a number of years in the form of interest
payment and principal repayment.
Present value of costs of various alternatives of financing are
compared to decide the source of financing. For example,
when a company borrows funds from a bank or financial
institution to be repaid in equal annual instalments, it uses
the present value technique to find out the size of the
instalment.
Comprehensive example:
Ms. Mwang’onda will be retiring from her soon.
Her employer has offered her two options for
postretirement benefits:
a) Tshs3.5 million lump sum
b) Tshs0.4 million for 10 years
The rate of interest is 10%.
Required:
Which option should Ms. Mwang’onda choose?