Business Math & TVM Concepts for Financial Analysis
1.
2. Business
mathematics is mathematics used
by commercial enterprises to record and
manage business operations.
Commercial organizations use
mathematics in accounting, inventory
management, marketing,
sales forecasting, and financial analysis.
3. TVM MEANS VALUE OF MONEY IS
DIFFERENT IN DIFFERENT TIME PERIODS
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.
Provided money can earn interest, any
amount of money is worth more the
sooner it is received.
4. VALUE OF INVESTMENT BASED ON
TIME
FUTURE
VALUE
SINGLE
AMOUNT
ANNUITY
PRESENT
VALUE
SINGLE
AMOUNT
ANNUITY
5. The value in the future of a payment stream with
the effect of interest included and expressed as a
single value
Future value is the value of an asset at a specific
date. It measures the nominal future sum of
money that a given sum of money is "worth" at a
specified time in the future assuming a
certain interest rate, or more generally, rate of
return
6. T
rPFV )1(
Solve for any variable, given the other three
•FV: How much will I have in the future?
•P: How much do I need to invest now?
•r: What rate of return do I need to earn?
•T: How long will it take me to reach my goal?
7. There are two ways of calculating future value
SIMPLE ANNUAL INTEREST:
Simple interest is the amount of money paid on a loan.
It is the easiest type of interest to calculate and
understand.
COMPOUNDED ANNUAL INTEREST:
Compound interest can be thought of as “interest on
interest,” and will make a deposit or loan grow at a
faster rate than simple interest, which is interest
calculated only on the principal amount
8. Future Value = Present Value x [1 + (Interest
Rate x Number of Years)
FV= PV[1+(R * T)]
EXAMPLE:
Mr.A invests 1,000 for five years with an
interest rate of 10%. What would be the future
value?
Future Value = 1,000 x [1 + (0.1 x 5)]
Future Value =1,000 x 1.5
Future Value = 1,500
9. Future Value = Present Value x [(1 + Interest
Rate) Number of Years
EXAMPLE:-
John invests Rs1,000 for five years with
an interest rate of 10%, compounded
annually. What would be the future
value of John's investment ?
Future Value = Rs1,000 x [(1 + 0.1)5]
Future Value = Rs1,000 x 1.61051
Future Value = Rs1,610.51
10. The value today of a payment stream with the
effect of interest removed and expressed as a
single value
Present value describes how much a
future sum of money is worth today.
“A dollar tomorrow is worth less
than a dollar today”
11. Where:
CF = cash flow in future period
r = the periodic rate of return or interest (also
called the discount rate or the required rate
of return)
n = number of periods
T
r
FV
P
)1(
12. Assume that you would like to put money in an
account today to make sure your child has enough
money in 10 years to buy a car.
If you would like to give your child Rs10,000 in 10
years, and you know you can get 5% interest
per year from a savings account during that time,
how much should you put in the account now?
The present value formula tells us:
PV = Rs10,000/ (1 + .05)10 = Rs6,139.13
Thus, Rs6,139.13 will be worth Rs10,000 in 10 years
if you can earn 5% each year. In other words, the
present value of Rs10,000 in this scenario is
Rs6,139.13.
13. An Annuity is a recurring amount for
specified number of periods.
Future value is the total amount which is
supposed to be received from the investment
in future at a given period of time and rate of
interest.
The future value of an annuity is how much
you would received in the future at a given
specified rate of return or discount rate.
14. FVA = A [(1+R)T – 1]
R
WHERE
A= ANNUITY
R=RATE OF INTEREST
T=TIME IN YEARS
15. FIVE EQUAL INSTALLMENTS(ANNUAL) OF RS. 10000 ARE MADE
INTO A DEPOSITE A/C OF SBI WITH 8% INTEREST P.A .WHAT IS
THE FUTURE VALUE OF THIS ANNUITY AT THE END OF FIVE
YEARS
Solution:- FVA = A [(1+R)T – 1]
R
=10000[(1.08)5 -1]
0.08
=10000*5.86625
=58662.5
16. An Annuity is a recurring amount for
specified number of periods
Present value is also known as “discounted
value”
The sum of present which is equivalent to the
total value of annuity to be paid in future is
called as “present value annuity”
17. PVA= A [(1+R)T -1]
R(1+R)T
HERE
A=ANNUITY
R=RATE OF INTEREST
T=TIME
18. WHAT IS THE PRESENT VALUE OF 5 YEARS
ANNUITY OF 10000 AT 12% INTEREST P.A.?
Solution:- PVA = A [(1+R)T -1]
R(1+R)T
=10000[(1.12)5-1]
0.12(1.12)5
= 10000*3.6048
=36.048
