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Welcome to:
Petroleum Economics
Courses
• Time Value of Money
•
Economic Indicators
To get the “Money”:
Make sure you are present (sign in the attendance sheet)
Listen carefully and full concentration
Do assignments and quiz
Successful in the Final Exam
“Its all about Money”
http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=D0NTTKs9z7I5gM&tbnid=JufN5UGo8IZbLM:&ved=0CAgQjRwwAA&url=http://borderlessnewsandviews.com/2013/04/money/&ei=v3jaUfPqNsa_rgenvYFQ&psig=AFQjCNFguEOBVOF05pL4qmNf9dUzeseTFg&ust=1373358656025535http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=D0NTTKs9z7I5gM&tbnid=JufN5UGo8IZbLM:&ved=0CAgQjRwwAA&url=http://borderlessnewsandviews.com/2013/04/money/&ei=v3jaUfPqNsa_rgenvYFQ&psig=AFQjCNFguEOBVOF05pL4qmNf9dUzeseTFg&ust=1373358656025535
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WHY?
In 1980’s, oil industries realize that the strategic company
decisions were made by a non petroleum background which
has little knowledge on the technical petroleum point of view.
Petroleum man just takes a role only in a Field or as an Engineer
not in the management position.
Such that, the company policies regarding petroleum
development should be treated by Petroleum man with additional
knowledge in Economic and management.
Eventually “Petroleum Economics” was born.
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TIME VALUE
OF MONEY P E T R
OL E U M E
C O N O M I C
S Dr. Ridha
http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557
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Obviously,
$1,000 today.
Money received soonerrather than later allowsone to use the funds forinvestment orconsumption purposes.This concept is referred to
as the
TIME VALUE OF
MONEY !!
Which would you
rather have --
$1,000 today or
$1,000 in 5 years?
http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url=http://ebarah.com/power-point-design-template/powerpoint-design-template-free/&ei=cWHaUbjiK8PorAeq94G4Dg&psig=AFQjCNGZeJ0ffr6TmRhNT_ceSscgM6WeJw&ust=1373352689838557http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=jnPwoEg5WfluEM&tbnid=VmOMMsE88k_oIM:&ved=0CAgQjRwwADgM&url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TIME allows one the opportunity to
postpone consumption and earn
INTEREST.
NOT having the opportunity to earn
interest on money is called OPPORTUNITYCOST.
Why TIME?
http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=fcMQGtA-BpS6cM&tbnid=NVKs0G62-vwMyM:&ved=0CAgQjRwwADjmAQ&url=http://www.wallm.com/powerpoint-backgrounds-getcliparts-visual-communication-design/&ei=lGHaUafVKI7RrQeJkoDYDw&psig=AFQjCNFcglO662VfpGtiNaVnryvNLFsE-w&ust=1373352724764850
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How can one compare amounts in
different time periods?
• One can adjust values from different time
periods using an interest rate.
• One CANNOT compare numbers in different
time periods without first adjusting themusing an interest rate.
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The time value of money the value of
money figuring in a given amount of interest
earned over a given amount of time.
Definition…
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Sooner or Later?
A productive life of petroleum project may take more than 40
years
In such circumstances, it is clearly necessary to consider how
the value of money changes over time
Under most circumstances, early receipt carries logicalbenefits, including:
a. Investment opportunity
b. Purchasing power
c. Riskd. Security and flexibility
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a. Investment opportunity the sooner one receive the
money, the sooner it may be invested and the sooner it may
start to grow
b. Purchasing powermoney spent sooner can buy more
goods and services
c. Risk the further into the future, the greater the
opportunity for something to fail or to be broken
d. Security and flexibility Early access to funds reduces riskof problems associated with cash shortage, including
bankruptcy.
Early receipt benefits:
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Interest [ i ]
Fundamentals of time value of money This is a cost of having money available for use
Interest is a basis for investment analysis
It is the income, which grows to the owner of money or
capital as a routine payment
Conversely, interest is the cost, which grows to one who
borrow.
There types of Interest in the cash flow
analysis:
1. Fixed Interest
2. Simple Interest3. Compound Interest
4. Nominal Annual Interest
5. Continuous Compounding
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1. Fixed Interest
Defined as a proportion of the amount invested (or borrowed) and
independent of the investment time
P Fn
timeRM 1000
i = fix
RM 1200
2. Simple Interest
Defined as a constant proportion of the initial amount per period of time
P = Present Amount [time zero]
Fn = Future Amount [after n period]
i = interest rate [per period]
Fn = P * [ 1 + ( n * i ) ]
Example: P = RM 100i = 12%
n = 10 years
The future value of simple interest?
Fn = 100 * [ 1 + ( 10 * 0.12 ) ]
= RM 220
RM 1300Could be
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3. Compound Interest
Defined as a proportion of the accumulated debt or investment. The
interest charged or paid in the current year includes a proportion ofinterest incurred or awarded in previous years.
Fn = P * [ 1 + i ]n
Example: RM 100 is invested for 10 years at 12 % interest per year, what is
the future value?
Fn = 100 * [ 1 + 0.12 ]10
Fn = 100 * 3.106
= RM 310.6
Comparisons:
Simple interest = RM 220
Compound interest = RM 310.6Different growth
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Comparison of Simple and Compound Interest @ 12%
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4. Nominal Annual Interest
An interest rate is called nominal if the frequency of compounding
(e.g. a month) is not identical to the basic time unit (normally a year).
By that, two further definitions of interest can be recognized:
Period interest the proportional interest which is added after each
compounding period
Nominal interest the period interest times the number of periods
in a year. j = Nominal interest, p = Compounding periods per year
j/p = Period interestLet
Fn = P * [ 1 + (j/p) ]p*n
Example: RM 100 is invested for 10 years at 12 % nominal interest per year,
with monthly compounding. What is the future value?
Fn = P * [ 1 + (0.12/12) ]12*10
Fn = 100 * [1.01] 120
= RM 330
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5. Continuous Compounding
Defined as a compounding scheme based on infinite number of compounding
periods in the year.
Fn = P * e j*n
RM 100 is invested for 10 years at 12 % nominal interest, with
compounding first per year then 12 and 365 times per year.
For continuous compounding, the number of compounding
periods becomes infinitely large.
Example:
Fn
= P * e j*n
= 100 * [ e ] 0.12 * 10
= 100 * 3.320
= RM 332
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Short Exercises Its all about Money
1. You deposit RM 345 into a bank account paying 7% simple
interest per year. How much interest would you earn after
5 years?
2. You take out a loan of RM 800 and the bank charges you
15% compound interest per year. If you don't pay off anyof the loan in 4 years, how much would you owe the bank?
3. How much money would you need to deposit today at 9%
annual interest compounded monthly to have RM 12000 in
the account after 6 years?
4. What will the future value if RM 200 is invested for 10
years at 12 % nominal interest, with compounding first per
year then 12 and 365 times per year?
Simple Interest
Compound Interest
Continuous
Compounding
Nominal Annual
Interest
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1. P = RM 345, i = 7% (0.07), n = 5 years, F = ???
F = 345 * [ 1+(5*0.07)]
F = 345 * 1.35
F = 465.75
So the interest earned after 5 years which
will be (465.75 – 345) = RM120.75
2. This time we are dealing with compound interest so the interest
earned gets added to the original amount each year.
P = RM800, i = 15% (0.15), n = 4 years, F = ???
F = 800 * [1 + 0.15]4
F = 800 * 1.749
F = 1399.2 (you owe the bank)
Fn = P * [ 1 + ( n * i ) ]
Fn = P * [ 1 + i ]n
Solutions
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F = 200 * [ e ] 0.12 * 10
F = 200 * 3.320
F = RM 664
Fn = P * [ 1 + (j/p) ]p*n
12000 = P * [ 1 + (0.09/12) ] 12*6
12000= P * [ 1.7125527]
P = 7007.08 [RM]
3. Define a Present value?…., with monthly compounded for 6 years.
We use Nominal Annual Interest
P = RM 12000, I = 9% (0.009), p = 12 months, n = 6 years
4. Define a Future value?...., with compounding first per year then 12
and 365 times per year Continuous Compounding
Fn = P * e j*n
P = RM 200, j = 12% (0.12), n = contunious
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Application of Compounding
a. Compute terminal value of a single investment.
b. Time shifting of cash flows for addition and
comparison.
c. Prices escalations.
d. Ranking of investments on basis of terminal
values.
Compounding Interest Compounding
Define as : The ability of an asset to
generate earnings, from previous
earnings.
The process of determining thefuture value of a payment
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a. Terminal Value
Defined as the present value to future point in time
Recall: Fn = P * [ 1 + i ]n [compounding equation]
It enables the terminal value (Fn) to be calculated when the initial
amount (P), the rate of interest (i), and the investment period (n) are
known.Example:
If RM 100 is invested for 10 years at 12% interest per year, what is the terminal
value at year 10.
F10 = P * [ 1 + i ]n
= 100 * [1 + 0.12 ]10
= 100 * 3.106
= RM 310.6 [terminal value]
P = RM 100, i = 0.12, n = 10 years
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b. Time Shifting of Cash Flows
Cash flows associated with an investment commonly occur at different
points in time
In order to compare these cash flows at different points in time, the cashflows must be brought to a common point in time.
[time shift]
1. Cumulative method
CashFlow [C] is compounded forwarded by one time step
{ C4 + C3 [ 1 + i ] + C2 [ 1 + i ]2
+ C1 [ 1 + i ]3
}In general form:
Cn + Cn-1 [ 1 + i ] + . . . + C2 [ 1 + i ]n-2 + C1 [ 1 + i ]
n-1
2. Direct method
Each CashFlow [C] is taken separately and is compounded
directly forward to an appropriate time period
C1 = C1 * [ 1 + I ]3
C2 = C2 * [ 1 + I ]2
C3 = C3 * [ 1 + I ]1
C4 = C4
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c. Price Escalations
Interest rate
Compound factor
Price projection as a
function of time and
interest rate
Supply
Demand
Inflation
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Note:1 US gallon = 3.78 Liter
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d. Ranking of Investments
By Compounding
Applied as a basis for comparing investment opportunities.
Compare terminal values at the same point in time.
Rank the values.
http://www.google.com/url?sa=i&rct=j&q=investment+ranking&source=images&cd=&cad=rja&docid=v4_0ATqwK3VbSM&tbnid=-lUQWnB5rc42uM:&ved=0CAUQjRw&url=http://blueandgreentomorrow.com/2012/12/08/fairpensions-publishes-ethical-investment-responsibility-ranking/&ei=_BDeUeK2Den9iAeo6oDYCQ&bvm=bv.48705608,d.aGc&psig=AFQjCNHwyMU0EKsD6x9z-B1O5f4jE3Wolg&ust=1373593957064211http://www.google.com/url?sa=i&rct=j&q=investment+ranking&source=images&cd=&cad=rja&docid=v4_0ATqwK3VbSM&tbnid=-lUQWnB5rc42uM:&ved=0CAUQjRw&url=http://blueandgreentomorrow.com/2012/12/08/fairpensions-publishes-ethical-investment-responsibility-ranking/&ei=_BDeUeK2Den9iAeo6oDYCQ&bvm=bv.48705608,d.aGc&psig=AFQjCNHwyMU0EKsD6x9z-B1O5f4jE3Wolg&ust=1373593957064211
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Case study….
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Option 2
(1)
(2)
(3)
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Discounting Interest Discounting
• The process of determining the present value of a
payment.• Mathematically, discounting is the inverse of
compounding.
Recall, compounding equation: F = P * (1 + i ]n
Then,
Discounting equation would be:
P = F * (1 + i ]-n F = future valueP = present value
i = interest
(1+i)n = compound factor
(1+i)-n = discount factor
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Application of Discounting
a. Computation of present value of a single futurecash flow.
b. Computation of present value of a series of
future cash flows.
c. Ranking of investments on the basis of present
value.
d. Comparison of production profiles.
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a. Present value of a single future cash flow
P = F * (1 + i ]-nRecall Discounting equation
b. Present value of a series of future cash flows
a. Cumulative method
b. Direct method
Each cash flow is taken separately and
discounted directly backward in time
C1 = C1C2 = C2 * [ 1 + I ]
-1
C3 = C3 * [ 1 + I ]-2
C4 = C4 * [ 1 + I ]-3
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c. Ranking of investments
By Discounting
Present value can be computed for any cash flows.
It has intrinsic an advantage over compounding for
ranking of investments.
The time origin is similar with other project compared to
that of compounding.
http://www.google.com/url?sa=i&rct=j&q=investment+ranking&source=images&cd=&cad=rja&docid=v4_0ATqwK3VbSM&tbnid=-lUQWnB5rc42uM:&ved=0CAUQjRw&url=http://blueandgreentomorrow.com/2012/12/08/fairpensions-publishes-ethical-investment-responsibility-ranking/&ei=_BDeUeK2Den9iAeo6oDYCQ&bvm=bv.48705608,d.aGc&psig=AFQjCNHwyMU0EKsD6x9z-B1O5f4jE3Wolg&ust=1373593957064211http://www.google.com/url?sa=i&rct=j&q=investment+ranking&source=images&cd=&cad=rja&docid=v4_0ATqwK3VbSM&tbnid=-lUQWnB5rc42uM:&ved=0CAUQjRw&url=http://blueandgreentomorrow.com/2012/12/08/fairpensions-publishes-ethical-investment-responsibility-ranking/&ei=_BDeUeK2Den9iAeo6oDYCQ&bvm=bv.48705608,d.aGc&psig=AFQjCNHwyMU0EKsD6x9z-B1O5f4jE3Wolg&ust=1373593957064211
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Similar data
as it used for
Terminal
Value
Case study….
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Option 1: £1250 is placed on deposit for 10 years at 5%.
Regardless of when this investment is withdrawn, it will have a
discounted of present value of £1250.
Option 3: The direct payment of £3500 would be received after 10 years.
The present value is derived by discounting at 5% over 10
years:
P = 3500 * [1 + 0.05)-10
P = 3500 * 0.614P = £2148.7
Option 2: This is more complex calculation as the investment returns 10
years payments of £250, each of which must be discounted
back to the present value by the appropriate number of years.
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(1)
(2)
(3)
Case 2
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Another Issues…..?
How if we change the Interest Rate? Lets say we change to 12%
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Rank by Present value @ variation of Interest rate
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d. Comparison of Production Profiles
Example of
HUTTON Field
in North Sea
Why decline?
3 reasons..
* Discount rate
* Reservoir pressure* Taxation
[oil price]
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ANNUITY
Annuity is a series of payments made at fixed intervals of time
The present value of an annuity is the value of a stream of payments,
discounted by the interest rate to account for the fact that payments are
being made at various moments in the future.
(Annuity equation)
P = Present value of annuity
A = present value for payment
I = discount rate
N = number of cash flow
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During years one and two, a company is spending RM 5000
each year on a new oil field. The company expects to save
(positive cash flow) RM 8000 each year for years 3, 4, 5, & 6. Is
the project worthy of consideration if the company expects a
15% interest on its investments?
Example:
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Solution:
PV of -RM5000 Annuity, 2 years, 15% = 1.62571 x -RM5000 = -RM8128.54
PV of RM8000 Annuity, 4 years, 15% = 2.85498 x RM8000 = RM22839.84
(The RM22839.84 is lands at the end of year 2 and must be treated as a lump sum)
PV of RM22839.84, end of year 2, 15% = 0.75614 x RM22839.84 = RM17270.12
Add up the results inside the boxes for the final total = RM9141.57
Since the end result is positive (greater than zero) the project passes the NPV test
and might be worthy of further consideration.
Present Value Calculation
1 2 3 4 5 6 7
-RM5000 -RM5000 RM8000 RM8000 RM8000 RM8000
15%The following are the cash flows:
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THANK YOU
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