2. Main Idea about Time Value
of Money
Money that the firm or an individual has
in its possession today is more valuable
than future payments because the
money it now can be invested and earn
positive returns.
“A bird in hand worth more than two in
the bush”
3. Why Money has Time Value?
The existence of interest rates in the
economy results in money with its time
value.
Sacrificing present ownership requires
possibility of having more future ownership.
Inflation in economy is one of the major
cause.
Risk or uncertainty of favorable outcome.
4. Major Importance of Time Value
of Money
It is required for accounting accuracy for certain
transactions such as loan amortization, lease
payments, and bond interest.
In order to design systems that optimize the
firm’s cash flows.
For better planning about cash collections and
disbursements in a way that will enable the firm
to get the greatest value from its money.
5. Major Importance of Time
Value of Money
Funding for new programs, products, and
projects can be justified financially using
time –value-of-money techniques.
Investments in new equipment, in
inventory, and in production quantities are
affected by time-value-of-money
techniques.
6. Major Concepts Here
Simple Interest:
Interest paid (or earned) on the original
amount, or principal borrowed (or lent).
Example-1:
Assume that you deposit $100 in a savings
account paying 8% simple interest and keep it
there for 10 years. What is your total interest
at the end of ten years?
7. Major Concepts Here (Cont.)
o Compound Interest:
Interest paid or earned on any previous interest
earned as well as on the principal amount.
Future Value:
The value of a present amount at a future date,
found by applying compound interest over a
specified time period.
Compounding:
The process of going from present values to
future values is called compounding.
8. Major Concepts Here (Cont.)
Computational tools for compounding: Financial
tables, financial calculators and computer
spreadsheets are used for computations of both
the future and present values. The following
formula is used to calculate the future value of
an amount.
FVn = PV x (1+i)n
The later portion of the equation (1+i)n
is called
the FVIFi,n, or the Future Value Interest Factor.
Thus, when one uses financial table the
equation becomes :
FVn = PV x (FVIFi,n)
9. Major Concepts Here (Cont.)
Example-2
Mr. Tushar deposits Tk. 1000 in a savings account
paying 12% interest compounded annually. What is
the future value of his fund at the end of 5th
year?
FVn = PV x (1+i)n
= PV x (FVIF12%,5)
= Tk. 1000 x 1.762
= Tk. 1762
10. Major Concepts Here (Cont.)
Example -3 The Rule of 70: You can find
approximately how long (no. of years) does it
take your fixed deposit to becomes double by
just simply dividing 70 with the rate of interest
Example:
If the compound interest rate is 7%, how many
years does it take your savings to become
double?
70 years
7
= 10 years
11. Major Concepts Here (cont.)
Present Value:
The current value of a future amount of
money or a series of payments.
Formula to Calculate Present Value:
PV = FVn x 1/(1+i)n
The term 1/(1+i)n
is called (PVIFi,n), Present
Value Interest Factor. Its value is always
less than one as it is a discounting factor.
12. Major Concepts Here (cont.)
Discounting Process: The process of finding the
present value of a payment or a series of future
cash flows, which is reverse of compounding.
Example-3:
Mr. Arman has an opportunity to receive
Tk.5000 five years from now. If he can earn
9% on his investments in the normal course
of events, what is the most he should pay
now for this opportunity?
13. Self-Test Problem
Practice Q 1:
Suppose you will receive $2000 after
10 years and now the interest rate is
8%, calculate the present value of this
amount.
Practice Q 2:
You have $1500 to invest today at 9%
interest compounded semi-annually. Find
how much you will have accumulated in the
account at the end of 6 years.
14. Self Test Problems:
Solving for interest rate (i) & period (n)
Practice Q.3
Suppose you can buy a security at a price of
Tk78.35 that will pay you Tk100 after five years.
What will be the rate of return, if you purchase
the security?
Practice Q.4
Suppose you know that a security will provide a
10% return per year, its price is Tk68.30 and you
will receive Tk.100 at maturity. How many years
does the security take to mature?
15. Major Concepts Here (cont.)
Annuity:
A series of equal payments or receipts of
money at fixed intervals for a specified number
of periods.
Types of Annuity:
1) Ordinary (deferred) annuity: Payment or
receipts occurring at the end of each period.
Installment payment on a loan.
2) Annuity Due: Payment or receipts occur at the
beginning of each period. Example, insurance
payment.
16. Example for Annuity:
Example-4:
Mr. Hamid is choosing which of two
annuities to receive. Both are 5-year, $1000
annuities; annuity A is an ordinary annuity,
and annuity B is an annuity due. Which is
the better option for him if he considered
the future value? (The market interest rate
is 7%).
Note: FV & PV of annuity due are always
greater than those of an ordinary annuity.
17. Example for Annuity (cont.)
Solution:
For ordinary annuity
FVAn = PMT [{(1+i)n
-1}/i]
= Tk 1000 x [{(1+0.07)5
-1}/0.07]
= Tk 5750.74
For annuity due
FVAn = PMT [{(1+i)n
-1}/i x (1+i)]
= Tk 1000 x [{(1+0.07)5
-1}/0.07 X (1+0.07)]
= Tk 6153.29
18. Example for Annuity (cont.)
Example-5: (P. 166)
Cute Baby Company, a small producer of plastic
toys, wants to determine the most it should pay to
purchase a particular ordinary annuity. Find the
present value if the annuity consists of cash flows
of $700 at the end of each year for 5 years. The
firm requires the annuity to provide a minimum
return of 8%.
For an ordinary annuity, PVAn = PMT x [1-(1+i)-n
]/i
Using the table PVA is PVAn = PMT x (PVIFAi,n)
and the FVA is FVAn = PMT x (FVIFAi,n)
For annuity due, PVAn = PMT x [{1-(1+i)-n
]/I}(1+i)]
19. Perpetuity
# A stream of equal payments expected to continue
forever.
Formula:
Payment PMT
PV (Perpetuity) = =
Interest Rate i
The present value of this special type of annuity
will be required when we value perpetual bonds
and preferred stock.
20. Effective Annual Interest Rate
The effective annual interest rate is the interest
rate compounded annually that provides the same
annual interest as the nominal rate does when
compounded m times per year.
EAR = (1+ isimple/m)m
– 1
where, m is the number of compounding period per
year.
Example-6
Nominal (annual) interest rate = 8%, compounded
quarterly on a one-year investment. Calculate the
effective rate.
21. Example-7
Mr. Mahin has Tk.10000 that he can deposit
any of three savings accounts for 3-year
period. Bank A compounds interest on an
annual basis, bank B twice each year, and
bank C each quarter. All 3 banks have a stated
annual interest rate of 4%.
a. What amount would Mr. Mahin have at the end
of the third year in each bank?
b. What effective annual rate (EAR) would he
earn in each of the banks?
c. On the basis of your findings in a and b, which
bank should Mr. Mahin deal with? Why?
22. Example-8
A municipal savings bond can be
converted to $100 at maturity 6 years
from purchase. If this state bonds are
to be competitive with B.D Government
savings bonds, which pay 8% annual
interest (compounded annually), at
what price must the state sell its bonds?
Assume no cash payments on savings
bond prior to redemption.
