chapter : the time value of money - ca sri lanka · chapter 3: the time value of money . 2 time...
TRANSCRIPT
![Page 1: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/1.jpg)
Investments: An Introduction
10e
Herbert B. Mayo
Chapter 3: The Time Value of Money
![Page 2: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/2.jpg)
2
Time Value
• The process of expressing
– the future value of cash flows
(compounding)
– the present value of future flows
(discounting)
![Page 3: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/3.jpg)
3
Time Value
• Payments are either
–a single payment
–a series of equal payments
(an annuity)
![Page 4: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/4.jpg)
4
Future Value
• The future value of $1 takes a single
payment in the present into the future
• The general equation for the future
value of $1:
P0(1 + i)n = Pn
![Page 5: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/5.jpg)
5
Greater Terminal Values
• Higher interest rates
• Longer time periods
• Result in greater terminal values
![Page 6: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/6.jpg)
6
Greater Terminal Values
![Page 7: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/7.jpg)
7
Present Value
• The present value of $1 brings a single payment in the future back to the present.
• The general equation for the present value of $1:
P0 = Pn (1+i)n
![Page 8: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/8.jpg)
8
Lower Present Values
• Higher interest rates
• Longer time periods
• Result in lower present values
![Page 9: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/9.jpg)
9
Lower Present Values
![Page 10: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/10.jpg)
10
Annuities - Future Sum
• The future sum of annuity takes a series of payments into the future.
• Payments may be made:
– at the end of each time period (ordinary annuity), or
– at the beginning of each time period (annuity due).
![Page 11: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/11.jpg)
11
Greater Terminal Values
• Higher interest rates
• Longer time periods
• Result in greater terminal values
![Page 12: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/12.jpg)
12
Greater Terminal Values
![Page 13: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/13.jpg)
13
Annuities - Present Value
• The present value of an annuity
brings a series of payments in the
future back to the present.
![Page 14: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/14.jpg)
14
Annuities - Present Value
• Higher interest rates result in lower
present values.
• But longer time periods increase
the present value (because more
payments are received).
![Page 15: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/15.jpg)
15
Annuities - Present Value
![Page 16: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/16.jpg)
16
Time Value Problems
• Time value of money problems may
be solved by using:
–algebraic formulas
– interest tables
– financial calculators
–software
![Page 17: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/17.jpg)
17
Variables for Time Value of
Money Problems
• PV = present value
• FV = future value
• PMT = annual payment
• N = number of time periods
• I = interest rate per period
![Page 18: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/18.jpg)
18
Financial Calculators
• Express the cash inputs (PV, FV, and PMT) as cash inflows and cash outflows
• At least one of the cash variables must be
–an inflow (+)
–an outflow (-)
![Page 19: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/19.jpg)
19
Future Value of $1: Illustration
• What is the future value after ten
years of $1000 deposited in a
savings account that pays 4
percent annually?
![Page 20: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/20.jpg)
20
Future Value of $1
• The unknown: FV
• The givens:
– PV = -1000
– PMT = 0
– N = 10
– I = 4
The answer:
$1,480.24
![Page 21: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/21.jpg)
21
Interpretation
• Depositing $1,000 (a current cash outflow) in the saving account produces $1,480.24 after ten years.
• Of the $1,480.24,
–$1,000 is the initial principal, and
–$480.24 is the earned interest.
![Page 22: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/22.jpg)
22
Present Value of $1: Illustration
• What is the present value
$1,480.24 received after ten years
if the rate of interest is 4 percent
annually?
![Page 23: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/23.jpg)
23
Present Value of $1
• The unknown: PV
• The givens:
–FV = 1,480.24
–PMT = 0
–N = 10
– I = 4
The answer:
$1,000
![Page 24: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/24.jpg)
24
Interpretation
• $1,480.24 received after ten years
is worth $1,000 today if the interest
rate is 4 percent.
![Page 25: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/25.jpg)
25
Interpretation of Future and
Present Values
These two problems are the same:
• In the first case, the $1,000 is
compounded into its future value
($1,480.24).
• In the second case, the future value
($1,480.24) is discounted back to its
present value ($1,000).
![Page 26: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/26.jpg)
26
Future Value of an
Ordinary Annuity: Illustration
• You deposit $1,000 in an account
at the end of each year for ten
years. What is the total amount in
the account if you earn 8 percent
annually?
![Page 27: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/27.jpg)
27
Future Value of an
Ordinary Annuity
• The unknown: FV
• The givens:
–PV = 0
–PMT = -1,000
–N = 10
– I = 8
The answer:
$14,486.56
![Page 28: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/28.jpg)
28
Interpretation
• For an annual cash payment of $1,000,
you will have $14,486.56 after ten
years.
• Of the $14,486.56,
–$10,000 is the total cash outflow, and
–$4,486.56 is the earned interest.
![Page 29: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/29.jpg)
29
Present Value of an
Ordinary Annuity: Illustration
• What is the present value of (or
required cash outflow to purchase)
an ordinary annuity of $10,000 for
ten years, if the rate of interest is 8
percent?
![Page 30: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/30.jpg)
30
Present Value of an Annuity
• The unknown: PV
• The givens:
–FV = 0
–PMT = 10,0000
–N = 10
– I = 8
The answer:
$67,100.81
![Page 31: Chapter : The Time Value of Money - CA Sri Lanka · Chapter 3: The Time Value of Money . 2 Time Value •The process of expressing –the future value of cash flows (compounding)](https://reader031.vdocuments.us/reader031/viewer/2022022013/5b2f72637f8b9ac06e8d665a/html5/thumbnails/31.jpg)
31
Interpretation
• For a present payment of $67,100.81,
the individual will annually receive
$10,000 for the next ten years.
–The $67,100.81 is an immediate cash
outflow;
–The $10,000 annual payment is a cash
inflow.