Time Value of Mokkkkkkkkkkkkkkkkkkkkney.PPT

..............................

1. Time Value of Money
“The value of money varies in terms
of time.”

2. Why you need to study?
Accounting: To understand time-value-of-money (T-V-M) calculations in
order to account for certain transactions such as loan amortization, lease
payments, and bond interest rates.
Information systems: To design systems that optimize the firm’s cash flows.
Management: To make plan of cash collections and disbursements in a way
that will enable the firm to get the greatest value from its money.
Marketing: To ensure funding for new programs and products must be
justified financially using time-value-of-money techniques.
Operations: To identify the optimum ways of investments in new equipment,
in inventory, and in production quantities will be affected by TVM
techniques.

3. Basic Chapter Contents…..
Concept of Time Value of Money,
Significance of Time value of money.
Present Value, Future Value.
Concept & Types of Annuity,
Present Value of an Annuity.
Future Value of an Annuity, Perpetual annuity.
Loan Amortization & Sinking Fund.
Problems and Solutions

4. 10/09/254
Concept of Time Value of Money
The idea that today’s a specific sum of money is
worth more than the same amount in the future
because time allows us the opportunity to postpone
consumption and earn return.

5. Significance of Time value of money
This chapter introduces the topic of financial
mathematics also known as the time value of money.
To avoid Inflationary effect in assets
To secure the assets’ return both in short and long-run
by creating proper working capital Management and
capital budgeting decisions
To calculate the cost of capital when a firm is going to
raise capital.
To determine pricing a bond issuance
To find out whether lease financing is applicable or not.

6. 10/09/256
Simple vs Compound Interest Rate
Simple Interest Rate: Interest is applicable only on the
principal amount.
Compound Interest Rate: Interest is applicable on both
the principal amount and cumulative interest earned.

7. 10/09/257
Nominal vs Effective Annual Interest Rates
i.Nominal Interest Rate: The contractual interest rate
for a year which is not adjusted for frequency of
compounding.
ii.Effective Annual Interest Rate: The rate of interest for
a year which is adjusted for frequency of
compounding.

8. 10/09/258
Present Value vs Future Value
Present Value: It is the current value of a future
amount of money, or a series of payments, evaluated
at a given interest rate.
Future Value: It is the value at some future time of a
present amount of money, or a series of payments,
evaluated at a given interest rate.

9. Future Value of a Lump Sum
The future value in 2 years of $1,000 earning
5% annually is an example of computing the
future value of a lump sum. We can compute
this in any one of three ways:
Using a calculator programmed for financial math
Solve the mathematical equation
Using financial math tables

10. Solve for the Future Value
The general equation for future value is:
FV
n
= PV x (1+i)
n
Computing the future value in the example:
FV
2
= $1,000 x (1+5%)
2
= $1,102.50

11. Present Value of a Lump Sum
How much do you need to invest today so
you can make a single payment of $30,000
in 18 years if the interest rate is 8%? This is
an example of the present value of a lump
sum.

12. The general equation for present value is:
Computing the present value in the example:
Solve for the Present Value

n
n
i1
FV
PV


 
47.507,7$
8%1
$30,000
PV
18




13. 
n
n
i1
FV
PV


FV
n = PV x (1+i)
n
Future Vs Present Value

14. Annuities

15. 10/09/2515
Types of Annuity
i.i.Ordinary AnnuityOrdinary Annuity: Payments or receipts occur at the
end of each period.
ii.ii.Annuity DueAnnuity Due: Payments or receipts occur at the
beginning of each period.
iii.Perpetual Annuity: It is expected to be continued
forever.

16. Future Value of an Annuity
Suppose you plan to deposit $1,000
annually into an account at the end of each
of the next 5 years. If the account pays
12% annually, what is the value of the
account at the end of 5 years? This is a
future value of an annuity example.

17. Solve for the Future Value of an Annuity
The general equation for a FV of an annuity is:
The FV of the annuity in the example is:






 

i
1i1
x PMTFVA
n
n
 
85.352,6$
12%
112%1
x 000,1$FVA
5
5





 


18. Present Value of an Annuity
You plan to withdraw $1,000 annually from
an account at the end of each of the next 5
years. If the account pays 12% annually,
what must you deposit in the account today?
This is an example of a present value of an
annuity.

19. Solve for the Present Value of an Annuity
The general equation for PV of an annuity is:
The PV of the annuity in the example is:















i
i1
1
-1
x PMTPVA
n
n
 
78.604,3$
12%
12%1
1
-1
x 000,1$PVA
5
5 















20. 





 

i
1i1
x PMTFVA
n
n















i
i1
1
-1
x PMTPVA
n
n
The general equation for PV of an annuity is
The general equation for a FV of an annuity is:
Future Vs Present Value of an Annuity

21. Perpetuity—An Infinite Annuity
A perpetuity is essentially an infinite annuity.
An example is an investment which costs you
$1,000 today and promises to return to you $100
at the end of each forever!
What is your rate of return or the interest rate?
%10
$1,000
$100

PV
PMT
i 

22. The Present Value of a Perpetuity
Another investment pays $90 at the end of
each year forever. If 10% is the relevant
interest rate, what is the value of this
investment to you today? We need to solve
for the present value of the perpetuity.
900$
10%
$90
i
PMT
PV 

23. Compounding Periods Other Than Annual
Future value of a lump sum.
–i
nom
= nominal annual interest rate
–m = number of compounding periods per year
–n = number of years
n x m
nom
n
m
i
1 x PVFV 







24. Compounding Periods Other Than Annual
A $1,000 investment earns 6% annually
compounded monthly for 2 years.
2 x 12
2
12
6%
1 x 000,1$FV 






  16.127,1$0.5% 1 x 000,1$FV
24
2 

25. Compounding Periods Other Than Annual
PV of a lump sum uses a similar adjustment to the basic
equation for non-annual compounding.
–
i
nom
= nominal annual interest rate
–m = number of compounding periods per year
–n = number of years
n x m
nom
n
m
i
1
FV
PV









26. n x m
nom
n
m
i
1
FV
PV








n x m
nom
n
m
i
1 x PVFV 






Future Vs Present Value of an Annuity
Compounding Periods

27. Effective Annual Rate
An effective annual rate is an annual
compounding rate. When compounding periods
are not annual, the rate can still be expressed as
an effective annual rate using the following:
–i
nom = nominal annual rate
–m = number of compounding periods in 1 year
1
m
i
1 Rate Annual Effective
m
nom








28. Effective Annual Rate
A bank offers a certificate of deposit rate of 6%
annually compounded monthly. What is the
equivalent effective annual rate?
  6.17% 1 - 0.5%11
12
6%
1
12
12








29. SINKING FUND
Vs
AMORTIZATION
SINKING FUND: With the sinking fund we begin with a fund of
zero and make periodic deposits into the fund which, along with
the interest earned on these deposits, accumulate to the total
amount of a savings goal.
Where, S= Amount (Future value of annuity) Sinking fund after
n payment.








1)1(
x SR
n
i
i

30. SINKING FUND
Vs
AMORTIZATION
AMORTIZATION: With the amortization of a debt, we begin with a
debt balance of ‘X’ taka and make periodic payments toward the
debt and the interest on the unpaid balance, eventually reducing
the debt balance to zero taka.
Where, A= Amount of Debt (Present value of annuity)














n-
i1
1
-1
A x R
i

31. 1. Calculate the payment per period.
2. Determine the interest in Period t.
(Loan Balance at t-1) x (i% / m)
3. Compute principal payment principal payment in Period t.
(Payment - Interest from Step 2)
4. Determine ending balance in Period t.
(Balance - principal payment principal payment from Step 3)
5. Start again at Step 2 and repeat.
Steps to Amortizing a Loan

32. Julie Miller is borrowing $10,000 $10,000 at a compound
annual interest rate of 12%. Amortize the loan if
annual payments are made for 5 years.
Step 1:Payment
PVPV
00
= R (PVIFA
i%,n
)
$10,000 $10,000 = R (PVIFA
12%,5
)
$10,000$10,000 = R (3.605)
RR = $10,000$10,000 / 3.605 = $2,774$2,774
Amortizing a Loan Example

33. Usefulness of Amortization
2.2.Calculate Debt Outstanding Calculate Debt Outstanding -- The quantity
of outstanding debt may be used in
financing the day-to-day activities of the
firm.
1.1. Determine Interest Expense Determine Interest Expense --
Interest expenses may reduce taxable
income of the firm.

34. Reference:
Gitman, L.J. (2007) Principles of Managerial Finance (Twelfth Edition).
Boston, MA: Pearson Education, Inc.
Besley, S., & Brigham, E. F. (2008). Essentials of managerial finance.
Thomson South-Western.
Brigham, E. F., & Houston, J. F. (2012). Fundamentals of financial
management. Cengage Learning.
Hoque, Md. Jahirul (2007), Fundamentals of Managerial Finance,
Open University.