The goal of every organization is to
grow and expand within its industry.In order to ensure that business endeavors
and projects are going to increase profits and the value of the organization,
financial managers look at the time value of money. This concept helps a manager
and/or investor comprehend the benefits and the future cash flow to make
decisions.
Money has a time value means
financial managers must take this time value of money into consideration when
making financial decisions. To make decisions they restating money values
through time with Time Value of Money Calculations. Time value of money
calculations are used to shift rupee values through time. They can be used to
state future cash flows in present value terms or to restate present value amounts
into future cash values. The calculations are the most powerful tool available
for making financial and business decisions. Once the methods of restating
money values through time is mastered, they can be used for restating cash
flows in such a way as to make them comparable in the financial decision making
process. The calculation of present values is the foundation for many financial
decisions facing both individuals and managers in all types of firm.
The time value of money is a tool to
understand the effective rates on business loans or the true return on an
investment by helping the manager determine the actual value of money now and
in the future based on interest rates, discount rates, expected costs, and
expected sales. Through targeted analysis, organizations are able to use this
information to decide whether projects, big or small, simple or complex, are
going to be beneficial to the company. By observing various tools and
indicators such as future value, present value, future value of an annuity, and
present value of an annuity, companies can determine the expected return on an
investment to ensure that it will result in increased profits.
There are several reasons that the
time value of money is important for businesses. One is obviously their ability
to invest the funds and earn interest. Another reason is making contract and
other expenditure decisions; such as the use of installment payments. The
consideration of issuing long-term and short-term debt is yet another reason
the time value of money is an important aspect to consider. The concept, time
value of money also important to take capital allocating decisions.
The decision to invest in new plant
and equipment or the introduction of a new product in the market requires using
capital allocating, capital budgeting techniques, and determining whether
future benefits are large enough to justify current spending. To make those
decisions, managers should fully understand the various financial applications
of the time value of money and the components of discount/interest rate.
The time value of money is
the value of money figuring in a given amount of interest earned over a given
amount of time.
Time value of money derived from 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, money available sooner give chance to consume or invest and
earn more money. Time value of money is also referred as present discounted
value.
TVM can calculate in two main ways,
· Simple interest
· Compound interest
Simple interest- when investing if
the return is only from the principle amount that invested that method of
investment called as simple interest.
Compound interest- when the
principle amount and the interest which earn from the principle amount also
earn the return investment called as compound interest.
Using simple and compound methods
can value present money’s future value and present values the future cash
flows.
Present value The current worth of a future sum of money or stream of cash flows given a
specified rate of return. Future cash flows are discounted at the discount
rate, and the higher the discount rate, the lower the present value of the
future cash flows. Determining the appropriate discount rate is the key to
properly valuing future cash flows, whether they are earnings or obligations.
Present value of an annuity
An annuity is a series of equal payments or receipts that occur at evenly
spaced intervals. Leases and rental payments are examples. The payments or
receipts occur at the end of each period for an ordinary annuity while they
occur at the beginning of each period for an annuity due.
Future value is the value of an asset or cash at a specified date in the
future that is equivalent in value to a specified sum today.
Future value of an annuity (FVA) is the future value of a stream of payments
(annuity), assuming the payments are invested at a given rate of interest.
Calculations
Money received sooner rather than
later allows one to use the funds for investment or consumption purposes. Rs
100 bill has the same value as an Rs100 bill one year from now, although the
bill is the same, person can do much more with the money if they have it now
because over time they can earn more interest on money.
Example- Suppose You has won a cash
prize of Rs 10000. You have two options:
1) Receive Rs10,000 now
OR
2) Receive Rs10,000 in after few years
1) Receive Rs10,000 now
OR
2) Receive Rs10,000 in after few years
If you are like most people, you
would choose to receive the Rs10, 000 now. It is because of the time value of
money.
Time value of money can be
calculated under the interest rate as well as under the present value and the
future value.
Simple
interest
Interest earned only on the original
investment, no interest is earned on interest.
Interest =Interest rate * Initial
investment
Future
value
Amount to which an investment will
grow after earning interest.
FV =P (1+ rt)
FV= Future Value
PV = Present value
r =Interest rate
t =Time period
Example-Suppose you have Rs1000
invested in a bank account and bank currently paying an interest rate of 6% per
year on deposits under simple interest. What will be future value of your
account after three years?
Interest rate * Initial investment
=Interest
1st year =0.06 * 1000= 60
or Fv= P (1+rt)
2nd year=0.06 * 1000= 60
= 1000 (1+0.06*3)
3rd year=0.06 * 1000= 60
=Rs 1180
Total interest = 180
Future value = 1000+180
=Rs1180
Present
value
The current value of future payment.
Fv = P (1+rt)
P (1+rt) =FV
P =FV
(1+rt)
FV= Future Value
P = Present value
r =Interest rate
t =Time period
Example-Suppose you have receive Rs
1180 after invested on a bank in three years. Interest rate is 6% under simple
interest. What is the value of money today?
P =FV
(1+rt)
= 1180
(1+0.06*3)
= Rs 1000
Compound
Interest
When interest paid on an investment
is added to the principal in each year or interest earned on interest.
Future
value
How much a sum will grow in a
certain number of years when compounded at a specific rate by using accumulated
factor= (1+r).
FVt=P (1+r) t
FV= Future Value
P = Present value
r =Interest rate
t =Time period
There are many other equations for
calculate future value under quarters, month, daily and semi-annually.
Semi annually = FV= PV (1+r2/2)2t
Quarter = FV= PV (1+r4/4)4t
Month = FV= PV (1+r12/12)12t
Daily = FV= PV (1+r365/365)365t
Example-Suppose you have Rs1000
invested in a bank account and bank currently paying an interest rate of 10%
per year on deposits under compound interest. What will be future value of your
account after ten years?
FVt=P (1+r) t
Fvt= 1000 (1+0.1)10
= Rs 2594
Present
value
The current value of a future cash
flow when compounded at a specific rate by using discounting rate= 1
(1+r) t
PV= FV
(1+r)t
FV= Future Value
P = Present value
r =Interest rate
t =Time period
Example-Suppose you have receive Rs
2594 after invested on a bank in ten years. Interest rate is 10% under compound
interest. What is the value of money today?
PV= FV
(1+r)t
= 2594
(1+0.1)10
=Rs 1000
Example-Saving to buy a new computer
· Suppose you need Rs 30000 after
two years to buy a new computer. The interest rate is 8% per year. How much
money should you set aside now in order to pay for the purchase?
PV= Rs 30000 / (1+0.08)2
=Rs 25720
· Suppose you have Rs 25720 in the
bank to buy a new computer after two years. The interest rate is 8% per year.
What will be the future value of your money after two years?
FV=Rs 25720 (1+0.08)2
=Rs 30000
Multiple
Cash Flows
Investments which are involve many
cash flows overtime.
Future value of multiple cash flows
Future value of a stream of cash
flows.
Example - Suppose you are going to
purchase a computer in 3 years. You plan to same amount of money each year. You
might be able to put Rs1200in today, and anther Rs1400 in 1year and Rs 1000in
next year. If you earn 8% rate of interest how much you able to spend on a
computer in 3 years?
Year 0 1 2 3
1200 1400 1000
1000*(1.08)=1080.00
1400* (1.08)2=1632.96
1200*(1.08)3=1511.65
Future value in 3 years =4224.61
Present
value of multiple cash flows
Present value of a stream of cash
flows.
Example - Suppose you are entering
to an installment plan to buy a new car where you pay Rs8000 today and make
payments of Rs 4000 each of next 3 years. Interest rate is 8% and you are going
to buy it in 3 years. What is the present value of that cash flow?
8000 4000 4000 4000
Year 0 1 2 3
8000
4000 = 3703.70
(1.08)
4000 = 3429.35
(1.08)2
4000 = 3175.32
(1.08)3
Present value =18308.37
Perpetuities
Stream of level cash payments that
never end.
Present value of perpetuity= C
= cash payment
r interest rate
Example-Suppose a worthy person
wishes to finance on your university. If the rate of interest is 10% and the
aim is to provide Rs100000 a year forever. What is the amount of that cash flow
in today?
PV of perpetuity = 100000
0.10
= Rs 1,000,000
Annuities
Equally spaced level of stream of
cash flows.
· Present value of annuities
Present value of t-year annuity=
Payment * Annuity factor
Present value of t-year annuity= C *
[1/r – 1/r (1+r) t]
Example- Suppose the Kangaroo offers
an “easy payment “scheme of Rs4000 a year at the end of each of the next 3
years. The interest rate is 10% and what is the present value of annuities?
4000 4000 4000
Year 0 1 2 3
4000 = 3636.36
(1.10)
4000 = 3305.78
(1.10)2
4000 = 3005.25
(1.10)3
Present value= 9947.39
Or otherwise it is easy to calculate
using formula.
Present value = 4000 * [1/0.10 –
1/0.10(1.10)3]
= 4000 * 2.487
= 9948
· Future value of annuities
FV of annuity= PV of annuity *(1+r)
t
= [1/r – 1/r (1+r) t] *
(1+r) t
= (1+r) t -1
r
Example-Suppose you are setting
aside Rs 3000 at the end of every year in order to buy a mountain bike. If your
saving earn interest 8% a year ,how much will they be worth at the end of 4
years ?
3000 3000 3000 3000
Year 0 1 2 3 4
3000
3240 = 3000*(1.08)
3499 = 3000*(1.08)2
3779 = 3000*(1.08)3
Future value of annuity = 13518
Or otherwise it is easy to calculate
using formula.
Future value of annuity = C *(1+r)
t -1
r
= 3000 * 4.506
= 13518
Conclusion
· Money has a time value means
financialmanagers must take this time value of money into consideration when
making financial decisions.
· The time value of money is a tool
to understand the effective rates on business loans or the true return on an
investment by helping the manager determine the actual value of money now and
in the future based on interest rates, discount rates, expected costs, and
expected sales.
· The concept, time value of
money is also important to take capital allocating decisions.
· Eventually calculation of time
value of money is playing a big role in business activities.
Money makes money. And the “money
that money makes” makes more money.
-Benjamin Franklin
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