3.4 Time Value of Money - Alternative Slides

8/20/2019 3.4 Time Value of Money - Alternative Slides

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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=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=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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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


7/44

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.


8/44

The time value of money the value of

money figuring in a given amount of interest

earned over a given amount of time.

Definition…


9/44

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


10/44

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:


11/44

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


12/44

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


13/44

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


14/44

Comparison of Simple and Compound Interest @ 12%


15/44

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


16/44

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


17/44

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


18/44

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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25/44

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

Documents

3.4 Time Value of Money - Alternative Slides