time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
Investment Decision — Capital Budgeting Techniques — Pay Back Method — Accounting Rate Of Return — NPV — IRR — Discounted Pay Back Method — Capital Rationing — Risk Adjusted Techniques Of Capital Budgeting. — Capital Budgeting Practices
The Cash Flow Statement translates earnings in the Income Statement into cash inflows. Explained in detail above as a part of the topic “Financial accounting”, is brought to you by Welingkar’s Distance Learning Division.
For more such innovative content on management studies, join WeSchool PGDM-DLP Program: http://bit.ly/SlideshareFaccounting
Join us on Facebook: http://www.facebook.com/welearnindia
Follow us on Twitter: https://twitter.com/WeLearnIndia
Read our latest blog at: http://welearnindia.wordpress.com
Subscribe to our Slideshare Channel: http://www.slideshare.net/welingkarDLP
risk and return. Defining Return, Return Example, Defining Risk,Determining Expected Return , How to Determine the Expected Return and Standard Deviation, Determining Standard Deviation (Risk Measure), Portfolio Risk and Expected Return Example, Determining Portfolio Expected Return, Determining Portfolio Standard Deviation, Summary of the Portfolio Return and Risk Calculation, Total Risk = Systematic Risk + Unsystematic Risk,
Describes in detail the steps involved in the calculation of Internal Rate of Return. Useful to students of Under graduate, post graduate and professional course students pursuing course in finance
This is the third presentation for the University of New England Graduate School of Business unit GSB711 - Managerial Finance. It explores the time value of money, using examples to help students clarify this concept.
Investment Decision — Capital Budgeting Techniques — Pay Back Method — Accounting Rate Of Return — NPV — IRR — Discounted Pay Back Method — Capital Rationing — Risk Adjusted Techniques Of Capital Budgeting. — Capital Budgeting Practices
The Cash Flow Statement translates earnings in the Income Statement into cash inflows. Explained in detail above as a part of the topic “Financial accounting”, is brought to you by Welingkar’s Distance Learning Division.
For more such innovative content on management studies, join WeSchool PGDM-DLP Program: http://bit.ly/SlideshareFaccounting
Join us on Facebook: http://www.facebook.com/welearnindia
Follow us on Twitter: https://twitter.com/WeLearnIndia
Read our latest blog at: http://welearnindia.wordpress.com
Subscribe to our Slideshare Channel: http://www.slideshare.net/welingkarDLP
risk and return. Defining Return, Return Example, Defining Risk,Determining Expected Return , How to Determine the Expected Return and Standard Deviation, Determining Standard Deviation (Risk Measure), Portfolio Risk and Expected Return Example, Determining Portfolio Expected Return, Determining Portfolio Standard Deviation, Summary of the Portfolio Return and Risk Calculation, Total Risk = Systematic Risk + Unsystematic Risk,
Describes in detail the steps involved in the calculation of Internal Rate of Return. Useful to students of Under graduate, post graduate and professional course students pursuing course in finance
This is the third presentation for the University of New England Graduate School of Business unit GSB711 - Managerial Finance. It explores the time value of money, using examples to help students clarify this concept.
Time Preference for Money, Required Rate of Return, Time Value Adjustment, Future Value, Future Value of an Annuity, Sinking Fund, Present Value, Present Value of an Annuity, Capital Recovery and Loan Amortisation, Present Value of Perpetuity, Present Value of Growing Annuities, Value of an Annuity Due, Multi-Period Compounding, Continuous Compounding, Net Present Value, Present Value and Rate of Return , Internal Rate of Return , Internal Rate of Return
Mathcad seven common financial computationsJulio Banks
The most important factor in a marital relationship is the wise management of the family income. I strongly recommend that dating or married couples consider mastering the simple financial calculations in this document. I have transcribed the reference document verbatim to the level allowed by Mathcad. The numerical results exactly match all of the examples provided in the reference article given included at the end of the Mathcad calculations. This last method is useful when borrowing or lending and need to know the interest
rate of return (ROR) being paid or collected, respectively. Henceforth, let us refer to i simply, as ROR.
Comparison of Simple and Compound Interest.pptssuser96ac0b
Simple and Compound interest as applicable in finance, taking loans mortgage etc and the overall effect on total payout, a comparison to help make better choices in long term incuding total payout and monthly burden
Quiz #2This Quiz counts for 15 of the course grade. Make s.docxcatheryncouper
Quiz #2
This Quiz counts for 15% of the course grade. Make sure you SHOW ALL WORK and LABEL IT CLEARLY. You MUST provide financial calculator inputs AND the answer. Answer-Only responses, even if correct, WILL NOT receive full credit.
Part 1 (12 points) __________
1. If we know the amount for which a coin was purchased thirty (30) years ago, and the annual rate at which its value has grown, finding the VALUE TODAY is a:
a. Future Value (FV) calculation
b. Present Value (PV) calculation
c. Annuity Calculation (because the growth rate remains constant for each of the fifty years)
d. A Perpetuity (because the present value of any sum fifty years out has VERY LITTLE PV)
2. Monthly principal and interest payments under a loan contract with a fixed interest rate and under which the loan will be paid down to $0 after the last payment; with payments beginning ONE MONTH AFTER the borrower gets the Loan Proceeds are in the form of:
a. A Perpetuity
b. A Consol
c. An Annuity DUE
d. An ORDINARY Annuity
3. The button on the TVM row on a financial calculator which is NOT USED in a simple lump sum FUTURE VALUE problem is:
a. the Present Value (PV) key
b. the Future Value (FV) key
c. the Interest Rate (I/Y) key
d. the Payment (PMT) key
e. the Number of Periods (N) key
4. Which one of the following will increase the PRESENT VALUE of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.
a. increase in the time period
b. increase in the rate of return
c. decrease in the future value
d. decrease in the rate of return
5. Which of the following statements is TRUE?
a. In an annuity due there is one less “interest” period than in an ordinary annuity
b. For the same stream of Cash Flows (CFs), the future value of an annuity due is GREATER THAN the future value of an ordinary annuity.
c. The “default assumption” with annuity CFs is that they take the form of an annuity due.
6. Which one of the following statements is correct?
a. The present value of an annuity increases when the interest rate increases.
b. The present value of an annuity is unaffected by the number of the annuity payments.
c. The future value of an annuity is unaffected by the amount of each annuity payment.
d.The present value of an annuity increases when the interest rate decreases.
7. The future value of a series of Cash Flows over time can be computed by:
a. computing the future value of the average cash flow and multiplying that amount by the number of cash flows.
b. summing the amount of each of the individual cash flows and multiplying the summation by (1 + r)t, where t equals the total number of cash flows.
c.summing the future values of each of the individual cash flows.
d. discounting each of the individual cash flows and summing the results.
8. ( TRUE or FALSE ) In a “pure discount” Loan, the borrower receives the full amount of the Loan Note at ori ...
Define conflict and conflict behavior in organizations
Distinguish between functional and dysfunctional conflict
Understand different levels and types of conflict in organizations
Analyze conflict episodes and the linkages among them
Explain why conflict arises, and identify the types and sources of conflict in organizations.
Describe conflict management strategies that managers can use to resolve conflict effectively.
Understand the nature of negotiation and why integrative bargaining is more effective than distributive negotiation.
,managing conflict ,politics ,and negotiation
,
capital budgeting
,
concept of capital budgeting
,
the capital budgeting process
,
significance of capital budgeting
,
classification of investment project proposals
,
techniques of capital budgeting
,
types of project
basic organization of computer
,
input unit
,
output unit
,
storage unit
,
arithmetic logic unit (alu)
,
computer codes
,
computer for organization
,
business communication
,
payroll system
,
management information system
operating system
,
os
,
what is an os?
,
types of os
,
logical architecture of a computer system
,
basic task perform by os
,
task switching
,
utility software
,
main functions of an os
,
ddata communications and computer networks
,
basic elements of a communication system
,
coaxial cable
,
star network
,
data transmission media
,
ring network
,
hybrid network
,
completely connected network
,
multi-access bus network
,
network linking devices
,
network interface card (nic)
International Business basic concept of international business
,
approaches to international business/ modes of ent
,
barriers to international business
,
absolute advantage and comparative advantage
Latino Buying Power - May 2024 Presentation for Latino CaucusDanay Escanaverino
Unlock the potential of Latino Buying Power with this in-depth SlideShare presentation. Explore how the Latino consumer market is transforming the American economy, driven by their significant buying power, entrepreneurial contributions, and growing influence across various sectors.
**Key Sections Covered:**
1. **Economic Impact:** Understand the profound economic impact of Latino consumers on the U.S. economy. Discover how their increasing purchasing power is fueling growth in key industries and contributing to national economic prosperity.
2. **Buying Power:** Dive into detailed analyses of Latino buying power, including its growth trends, key drivers, and projections for the future. Learn how this influential group’s spending habits are shaping market dynamics and creating opportunities for businesses.
3. **Entrepreneurial Contributions:** Explore the entrepreneurial spirit within the Latino community. Examine how Latino-owned businesses are thriving and contributing to job creation, innovation, and economic diversification.
4. **Workforce Statistics:** Gain insights into the role of Latino workers in the American labor market. Review statistics on employment rates, occupational distribution, and the economic contributions of Latino professionals across various industries.
5. **Media Consumption:** Understand the media consumption habits of Latino audiences. Discover their preferences for digital platforms, television, radio, and social media. Learn how these consumption patterns are influencing advertising strategies and media content.
6. **Education:** Examine the educational achievements and challenges within the Latino community. Review statistics on enrollment, graduation rates, and fields of study. Understand the implications of education on economic mobility and workforce readiness.
7. **Home Ownership:** Explore trends in Latino home ownership. Understand the factors driving home buying decisions, the challenges faced by Latino homeowners, and the impact of home ownership on community stability and economic growth.
This SlideShare provides valuable insights for marketers, business owners, policymakers, and anyone interested in the economic influence of the Latino community. By understanding the various facets of Latino buying power, you can effectively engage with this dynamic and growing market segment.
Equip yourself with the knowledge to leverage Latino buying power, tap into their entrepreneurial spirit, and connect with their unique cultural and consumer preferences. Drive your business success by embracing the economic potential of Latino consumers.
**Keywords:** Latino buying power, economic impact, entrepreneurial contributions, workforce statistics, media consumption, education, home ownership, Latino market, Hispanic buying power, Latino purchasing power.
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
NO1 Uk Black Magic Specialist Expert In Sahiwal, Okara, Hafizabad, Mandi Bah...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
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Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
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#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Introduction to Indian Financial System ()Avanish Goel
The financial system of a country is an important tool for economic development of the country, as it helps in creation of wealth by linking savings with investments.
It facilitates the flow of funds form the households (savers) to business firms (investors) to aid in wealth creation and development of both the parties
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
US Economic Outlook - Being Decided - M Capital Group August 2021.pdfpchutichetpong
The U.S. economy is continuing its impressive recovery from the COVID-19 pandemic and not slowing down despite re-occurring bumps. The U.S. savings rate reached its highest ever recorded level at 34% in April 2020 and Americans seem ready to spend. The sectors that had been hurt the most by the pandemic specifically reduced consumer spending, like retail, leisure, hospitality, and travel, are now experiencing massive growth in revenue and job openings.
Could this growth lead to a “Roaring Twenties”? As quickly as the U.S. economy contracted, experiencing a 9.1% drop in economic output relative to the business cycle in Q2 2020, the largest in recorded history, it has rebounded beyond expectations. This surprising growth seems to be fueled by the U.S. government’s aggressive fiscal and monetary policies, and an increase in consumer spending as mobility restrictions are lifted. Unemployment rates between June 2020 and June 2021 decreased by 5.2%, while the demand for labor is increasing, coupled with increasing wages to incentivize Americans to rejoin the labor force. Schools and businesses are expected to fully reopen soon. In parallel, vaccination rates across the country and the world continue to rise, with full vaccination rates of 50% and 14.8% respectively.
However, it is not completely smooth sailing from here. According to M Capital Group, the main risks that threaten the continued growth of the U.S. economy are inflation, unsettled trade relations, and another wave of Covid-19 mutations that could shut down the world again. Have we learned from the past year of COVID-19 and adapted our economy accordingly?
“In order for the U.S. economy to continue growing, whether there is another wave or not, the U.S. needs to focus on diversifying supply chains, supporting business investment, and maintaining consumer spending,” says Grace Feeley, a research analyst at M Capital Group.
While the economic indicators are positive, the risks are coming closer to manifesting and threatening such growth. The new variants spreading throughout the world, Delta, Lambda, and Gamma, are vaccine-resistant and muddy the predictions made about the economy and health of the country. These variants bring back the feeling of uncertainty that has wreaked havoc not only on the stock market but the mindset of people around the world. MCG provides unique insight on how to mitigate these risks to possibly ensure a bright economic future.
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
1. Time Value of Money
“The value of money varies in terms of
time.”
-Prof. Dr. Md. Jahirul Hoque
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. 9/29/20194
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. 9/29/20196
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. 9/29/20197
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. 9/29/20198
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:
FVn = PV x (1+i)n
Computing the future value in the
example:
FV2 = $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 $30,000
in 18 years if the interest rate is 8%? This is
an example of the present value of a lump
sum.
Again we can solve it using a programmed
calculator, solving the math
Md. Azizur Rahman
12. The general equation for present value is:
Computing the present value in the example:
Solve for the Present Value
n
n
i1
FV
PV
47.507,7$
8%1
$30,000
PV 18
13.
14. Annuities
• Two or more periodic payments
• All payments are equal in size.
• Periods between each payment are
equal in length.
Md. Azizur Rahman
15. 9/29/201915
Types of Annuity
i. Ordinary Annuity: Payments or receipts occur at the
end of each period.
ii. Annuity 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 $1,000
annually into an account at the end of each
of the next 5 years. If the account pays
12% annually, what is the value of the
account at the end of 5 years? This is a
future value of an annuity example.
We can solve this problem using a
programmed calculator, solving the math,
or using Table 5.3.
17. Solve for the Future Value of an Annuity
The general equation for a FV of an annuity is:
The FV of the annuity in the example is:
i
1i1
xPMTFVA
n
n
85.352,6$
12%
112%1
x000,1$FVA
5
5
18. Present Value of an Annuity
You plan to withdraw $1,000 annually from
an account at the end of each of the next 5
years. If the account pays 12% annually,
what must you deposit in the account today?
This is an example of a present value of an
annuity.
We can solve this problem using a
programmed calculator, solving the math, or
using Table 5.4.
19. Solve for the Present Value of an Annuity
The general equation for PV of an annuity is:
The PV of the annuity in the example is:
i
i1
1
-1
xPMTPVA
n
n
78.604,3$
12%
12%1
1
-1
x000,1$PVA
5
5
20.
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.
– inom = nominal annual interest rate
– m = number of compounding periods per year
– n = number of years
nxm
nom
n
m
i
1xPVFV
24. Compounding Periods Other Than Annual
A $1,000 investment earns 6% annually
compounded monthly for 2 years.
2x12
2
12
6%
1x000,1$FV
16.127,1$0.5%1x000,1$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.
– inom = nominal annual interest rate
– m = number of compounding periods per year
– n = number of years
nxm
nom
n
m
i
1
FV
PV
26. 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:
– inom = nominal annual rate
– m = number of compounding periods in 1 year
1
m
i
1RateAnnualEffective
m
nom
27. 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
28. SINKING FUND
Vs
AMORTIZATION
SINKING FUND: With the sinking fund we begin with a fund of
zero taka 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(
xSR n
i
i
29. 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 xR
i
30. 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 in Period t.
(Payment - Interest from Step 2)
4. Determine ending balance in Period t.
(Balance - principal payment from Step 3)
5. Start again at Step 2 and repeat.
Steps to Amortizing a Loan
31. Julie Miller is borrowing $10,000 at a compound
annual interest rate of 12%. Amortize the loan
if annual payments are made for 5 years.
Step 1: Payment
PV0 = R (PVIFA i%,n)
$10,000 = R (PVIFA 12%,5)
$10,000 = R (3.605)
R = $10,000 / 3.605 = $2,774
Amortizing a Loan Example
32. Amortizing a Loan Example
End of
Year
Payment Interest Principal Ending
Balance
0 --- --- --- $10,000
1 $2,774 $1,200 $1,574 8,426
2 2,774 1,011 1,763 6,663
3 2,774 800 1,974 4,689
4 2,774 563 2,211 2,478
5 2,775 297 2,478 0
$13,871 $3,871 $10,000
[Last Payment Slightly Higher Due to Rounding]
33. Using the Amortization
Functions of the Calculator
Press:
2nd Amort
2 ENTER
2 ENTER
Results:
BAL = 6,662.91* ↓
PRN = -1,763.99* ↓
INT = -1,011.11* ↓
Year 2 information only
*Note: Compare to 3-82
34. Using the Amortization
Functions of the Calculator
Press:
2nd Amort
1 ENTER
5 ENTER
Results:
BAL = 0.00 ↓
PRN =-10,000.00 ↓
INT = -3,870.49 ↓
Entire 5 Years of loan information
(see the total line of 3-82)
35. Usefulness of Amortization
2. Calculate Debt Outstanding -- The
quantity of outstanding debt may be used
in financing the day-to-day activities of the
firm.
1. Determine Interest Expense -- Interest
expenses may reduce taxable income of
the firm.
36. 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.