2. Time Value of Money
References:
- Gitman & Zutter: Chapter -5
- Class Notes
2
3. 3
Time Value of Money
Which would you rather have ?
◦ $100 today - or
◦ $100 after One month
◦ The sooner, the better
4. 4
Time Value of Money
The core concept of finance.
The time value of money refers to the
observation that it is better to receive
money sooner than later.
Money that you have in hand today can be
invested to earn a positive rate of return,
producing more money tomorrow.
5. 5
Time Value of Money ….Why?
Four underlying reasons:
1. Consumption: People like to consume today rather than
consuming in future.
2. Uncertainty: Future is always uncertain. For this uncertainty
people need some compensation.
3. Investment Opportunity: If one gets the money now, he can
invest the amount and after a certain period can get a return on
the invested capital
4. Inflation: The purchasing power of money decreases with the
passes of time because of the inflation.
6. 6
Time Value of Money
Time line
A horizontal line on which time zero appears at the leftmost end
and future periods are marked from left to right; can be used
to depict investment cash flows.
7. 7
Time Value of Money
Techniques of TVM:
Future Value Technique
Present Value Technique
8. 8
Time Value of Money
Future Value Technique
The future value technique uses compounding to find the future
value of each cash flow at the end of the investment’s life and
then sums these values to find the investment’s future value.
Present Value Technique
the present value technique uses discounting to find the present
value of each cash flow at time zero and then sums these
values to find the investment’s value today.
11. 11
Future Value of A Single Amount
Principal
The amount of money on which interest is
paid.
Compound Interest
Interest that is earned on a given deposit and has
become part of the principal at the end of a
specified period.
12. 12
The Equation for Future Value
FVn = PV x (1+ r)n
FVn = Future value at the end of period n
PV = Initial principal, or present value
r = Annual rate of interest paid.
n = Number of periods (typically years) that the money is left on
deposit
13. 13
Example -1
Jane Farber places $800 in a savings
account paying 6% interest compounded
annually. She wants to know how much
money will be in the account at the end of 5
years.
14. 14
Present Value Of A Single Amount
Present Value
The current dollar value of a future amount; the amount of
money that would have to be invested today at a given
interest rate over a specified period to equal the future
amount.
Discounting Cash Flows
The process of finding present values; the inverse of
compounding interest.
15. 15
The Equation for Present Value
PV = FVn / (1+ r)n
FVn = Future value at the end of period n
PV = Initial principal, or present value
r = Annual rate of interest paid.
n = Number of periods (typically years) that the money is left on
deposit
16. 16
Example - 2
Pam Valenti wishes to find the present value
of $1,700 that she will receive 8 years from
now. Pam’s opportunity cost is 8%.
17. 17
In practice, when making investment
decisions, managers usually adopt the
present value approach.
The higher the discount rate, the lower the
present value.
The longer the period of time, the lower the
present value.
18. 18
Home Task
1. Assume that a firm makes a $2,500 deposit into its money
market account. If this account is currently paying 0.7%,
what will the account balance be after 1 year?
2. If Bob and Judy combine their savings of $1,260 and $975,
respectively, and deposit this amount into an account that
pays 2% annual interest, what will the account balance be
after 4 years?
19. 19
Annuity
A stream of equal periodic cash flows over
a specified time period.
These cash flows can be inflows of returns
earned on investments or outflows of funds
invested to earn future returns.
20. 20
Types of Annuities
1. Ordinary Annuity – cash flow occurs at the
end of each period.
2. Annuity Due - cash flow occurs at the
beginning of each period.
21. 21
Types of Annuities
Personal Finance Example 5.6
“The value (present or future) of an annuity due is
always greater than the value of an otherwise
identical ordinary annuity.”
23. 23
Example-3
Fran Abrams wishes to determine how much money she
will have at the end of 5 years if she chooses the
ordinary annuity. She will deposit $1,000 annually, at
the end of each of the next 5 years, into a savings
account paying 7% annual interest.
25. 25
Example- 4
Braden Company, a small producer of plastic toys, wants to
determine the most it should pay to purchase a particular
ordinary annuity. 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%.
27. 27
Example - 5
Fran Abrams wishes to determine how much money
she will have at the end of 5 years if she chooses
the annuity due. She will deposit $1,000 annually,
at the beginning of each of the next 5 years, into a
savings account paying 7% annual interest.
29. 29
Example - 6
Braden Company, a small producer of plastic toys, wants to
determine the most it should pay to purchase a particular
annuity due. The annuity consists of cash flows of $700 at the
beginning of each year for 5 years. The firm requires the
annuity to provide a minimum return of 8%.
30. 30
Perpetuity
An annuity with an infinite life, providing
continual annual cash flow is called
perpetuity. [n= α]
Finding The Present Value of a Perpetuity
PV= CF / r
31. 31
Questions
What is the difference between an ordinary
annuity and an annuity due? Which is more
valuable? Why?
What is annuity? What is a perpetuity?
33. 33
Mixed Stream
A stream of unequal periodic cash flows
that reflect no particular pattern
Financial managers frequently need to
evaluate opportunities that are expected to
provide mixed streams of cash flows
34. 34
Future Value of A Mixed Stream
Determining the future value of each cash
flow at the specified future date and then
add all the individual future values to find
the total future value
35. 35
Future Value of A Mixed Stream
Example 5.12
Shrell Industries, a cabinet manufacturer, expects to receive the following mixed
stream of cash flows over the next 5 years from one of its small customers.
If Shrell expects to earn 8% on its investments, how much will it accumulate by
the end of year 5 if it immediately invests these cash flows when they are
received?
End of year Cash flow
1 $11,500
2 14,000
3 12,900
4 16,000
5 18,000
36. 36
Present Value of A Mixed Stream
Determining the present value of each future
amount and then add all the individual
present values together to find the total
present value
37. 37
Present Value of A Mixed Stream
Example 5.13
Frey Company, a shoe manufacturer, has been offered an
opportunity to receive the following mixed stream of cash
flows over the next 5 years.
If the firm must earn at least 9% on its investments, what is the
most it should pay for this opportunity?
End of year Cash flow
1 $400
2 800
3 500
4 400
5 300
38. 38
Compounding Interest More
Frequently than Annually
Semiannual compounding
Compounding of interest over two periods within the year.
Quarterly compounding
Compounding of interest over four periods within the year.
Continuous compounding
Compounding interest an infinite number of times per year.
39. 39
Compounding Interest More
Frequently than Annually
“The more frequently interest is compounded,
the greater the amount of money
accumulated”- Do you agree with this
statement?
40. 40
A General Equation for Compounding More
Frequently Than Annually
m = Number of time compounded
41. 41
Nominal vs. Effective Interest Rate
Nominal Annual Rate
Contractual annual rate of interest charged by a lender or
promised by a borrower. It’s the stated rate.
Effective Annual Rate (EAR)
The annual rate of interest actually paid or earned. It’s the true
or realized rate.
42. 42
Loan Amortization
Loan amortization
The determination of the equal periodic loan payments
necessary to provide a lender with a specified interest return
and to repay the loan principal over a specified period.
Loan amortization schedule
A schedule of equal payments to repay a loan. It shows the
allocation of each loan payment to interest and principal.
TABLE 5.6
![30
Perpetuity
An annuity with an infinite life, providing
continual annual cash flow is called
perpetuity. [n= α]
Finding The Present Value of a Perpetuity
PV= CF / r](https://image.slidesharecdn.com/ch-4timevalueofmoney-250423155952-a73f7570/85/Chapter-Four-Time-Value-of-Money-an-important-chapter-for-a-finance-student-30-320.jpg)
