This document discusses stated and effective annual interest rates. It begins by explaining how corporate finance textbooks typically cover the calculation of stated and effective annual interest rates. However, it notes that textbooks often fail to provide additional important context. Specifically, textbooks do not clarify that interest is usually paid at the end of a period, not the beginning, and do not address whether rates with different compounding methods are truly equivalent. The document then provides an expanded explanation of these issues and cautions readers to think critically about interest rate conversions.
Using Excel for TVM calculations REV2There are 4 methods to d.docxdickonsondorris
Using Excel for TVM calculations REV2:
There are 4 methods to do TVM calculations:
1. the longhand method of multiplying exponential formulas
2. using any of the 4 TVM tables
3. using excel
4. using a financial calculator
In my opinion method 1 is too difficult. #2 takes too long; #3 I cannot help anyone with as every different calculator has its own 100 page instruction book
The easiest way is learning to use excel.
A. To use excel, hit the “Fx” toolbar, and choose “financial” functions from the pulldown menu
To do any kind of present value problem, go to the PV function
To do any kind of FV problem, go to the FV function
Whichever function you choose will open a window into which you will type in data
Guidelines to follow:
B. The “rate” means the decimal format of the discount or interest rate PER PERIOD to use; if its 5%, type in .05….if its 12% type in .12.
If instead of annual compounding, for example if problem dealt with semiannual compounding, and annual rate was 10%, you would type in .05.
C. “Periods” means the number of compounding periods. If problem is 10 years, compounded annually, type in 10; if its 10 years compounded semi-annually, type in 20
D. means what the future sum would be.
E. “Payment” field would only be filled in if its an annuity [a stream of equal periodic payments like a car loan or mortgage], in which case you would type in the size of the periodic payment. Otherwise, leave it blank.
F. Generally money paid in [like to a bank], should have a negative sign, and your answer will come out positive then
Specific examples:
1. For determining the PV of some future some, use the PV function, type in your discount rate as a decimal, type in the number of periods, and type in the future value. If its an annuity, type in the $ amount of the periodic payment in the “payment” field.
2. For determining the Future value of some present sum, use the FV function and enter info as above whether its one present sum, or its an annuity stream
3. If instead of a simple end of period annuity problem, its an “annuity due” problem [payment on the first day of the period vs., the last day, like an ordinary annuity], type “1” into the “type” field
4. Determining the effective annual rate: EAR
Go to financial section of Fx toolbar, using pull down window to get “effective”. Type in the nominal or stated ANNUAL percentage rate[APR], as a decimal[12% would be .12] and type in the number of compounding periods per year[if monthly compounding type in 12; if weekly compounding type in 52]. The answer should ALWAYS be >ANNUAL rate you typed in, unless its annual compounding in which case APR=EAR
5. Loan payment: to determine the size of the equal periodic loan payment, use the “payment” function, PMT. Type in the loan interest rate per period, as a decimal; if its an annual 12%, then its 1% per month, for example. Type the value of the money to be borrowed, in PV; type in the number of loan periodic payments. If you want the mo ...
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
Cfa level 1 quantitative analysis e book part 1parmanandiskool
The given e-book discusses Quantitative Analysis module for CFA L-1 .It is part-1 of the series and for other parts visit our site https://www.educorporatebridge.com/freebies3.php
Lecture 12816 and 20216 for chapters 3+43 Evaluation m.docxsmile790243
Lecture 1/28/16 and 2/02/16 for chapters 3+4
3 Evaluation methods for working with financial statements.
The first is RATIO ANALYSIS.
This helps you evaluate the financial performance of a company.
Chapter 3+4 are combined. You try to answer one main question: How ratio
analysis is used to evaluate the financial performance of a company.
In order to do ratio analysis you need data, and the data comes from financial
statements. The two main statements that we used to calculate the ratio: balance
sheet and income statement. 3 & 4 chapters are accounting review. He imported info
that reminds us of those two statements. All we need to study is this power point.
Review of balance sheet:
How finance people read balance sheet is a bit different because it fits our needs.
Balance sheet is two sides. One side is called assets and other side is called liabilities
and equity.
The assets side is everything the company owns.
The liability side is everything the company owes others.
Other definition could be, the assets could be considered the companies investment.
If asset is the companies the investments then liabilities is where we get the money
from to fund the investments.
Capital budgeting team from finance determines if they can afford the projects and
liabilities they can afford before accounting department gets its it.
Assets should always equal the liabilities.
Bonds are long term debt. Total debt equals depts. Plus equity. Short‐term debt is
current liabilities and long term debt is bonds. Short term is like A.P., s‐t notes
payable, current liabilities.
Total assets tell you the value of the company.
The value=D + E.
Income statements = revenues‐expenses=net income or net loss.
They show whether the company makes profit or losses, revenues and expenses.
The very important number is net income. Whether it is positive or negative.
If it positive then perfect, everyone is happy…to a certain extent.
As soon as you have profit, you have to deduct taxes (corporate taxes)
The rest is divided between dividends and retained earnings, depends how much is
distributed where. Depends on many factors. They usually start by putting a lot in
retained earning and use it as an internal source of finance, the management will do
anything they can do in order to maximize RE.
The ratio we use to calculate the RE from Net Income is called the
RETENTION RATIO= THE RATIO THAT WE USE TO CALCULATE RETAINED
EARNING FROM NET INCOME.
The name of the ratio that goes to dividends from net income is called dividend
payout ratio.
Revenues maybe up to 90% of them comes from SALES. The other 10% come from
like investments from shares you receive dividends, you receive INTERESTS from
BONDS.
Expenses, since most of the money comes from sales then the most of the expenses
come from COGS. The rest is salaries, maintenance etc.
Sales‐COGS=Gross profit‐rest=net incomes‐taxes=real net income that goes two
ways.
Earning per share=EPS =Total ne ...
3 Evaluation methods for working with financial statements.The f.docxtamicawaysmith
3 Evaluation methods for working with financial statements.
The first is RATIO ANALYSIS.
This helps you evaluate the financial performance of a company.
Chapter 3+4 are combined. You try to answer one main question: How ratio analysis is used to evaluate the financial performance of a company.
In order to do ratio analysis you need data, and the data comes from financial statements. The two main statements that we used to calculate the ratio: balance sheet and income statement. 3 & 4 chapters are accounting review. He imported info that reminds us of those two statements. All we need to study is this power point.
Review of balance sheet:
How finance people read balance sheet is a bit different because it fits our needs.
Balance sheet is two sides. One side is called assets and other side is called liabilities and equity.
The assets side is everything the company owns.
The liability side is everything the company owes others.
Other definition could be, the assets could be considered the companies investment.
If asset is the companies the investments then liabilities is where we get the money from to fund the investments.
Capital budgeting team from finance determines if they can afford the projects and liabilities they can afford before accounting department gets its it.
Assets should always equal the liabilities.
Bonds are long term debt. Total debt equals depts. Plus equity. Short-term debt is current liabilities and long term debt is bonds. Short term is like A.P., s-t notes payable, current liabilities.
Total assets tell you the value of the company.
The value=D + E.
Income statements = revenues-expenses=net income or net loss.
They show whether the company makes profit or losses, revenues and expenses.
The very important number is net income. Whether it is positive or negative.
If it positive then perfect, everyone is happy…to a certain extent.
As soon as you have profit, you have to deduct taxes (corporate taxes)
The rest is divided between dividends and retained earnings, depends how much is distributed where. Depends on many factors. They usually start by putting a lot in retained earning and use it as an internal source of finance, the management will do anything they can do in order to maximize RE.
The ratio we use to calculate the RE from Net Income is called the
RETENTION RATIO= THE RATIO THAT WE USE TO CALCULATE RETAINED EARNING FROM NET INCOME.
The name of the ratio that goes to dividends from net income is called dividend payout ratio.
Revenues maybe up to 90% of them comes from SALES. The other 10% come from like investments from shares you receive dividends, you receive INTERESTS from BONDS.
Expenses, since most of the money comes from sales then the most of the expenses come from COGS. The rest is salaries, maintenance etc.
Sales-COGS=Gross profit-rest=net incomes-taxes=real net income that goes two ways.
Earning per share=EPS =Total net incomes/shares outstanding. Means like $162/100= $1.62 means eve ...
Usse average internal rate of return (airr), don't use internal rate of retur...Futurum2
This is to document the email correspondences with Prof. Peter M. DeMarzo (Stanford University) and Prof. Carlo Alberto Magni with regards to Average Internal Rate of Return in Dec 2015.
Using Excel for TVM calculations REV2There are 4 methods to d.docxdickonsondorris
Using Excel for TVM calculations REV2:
There are 4 methods to do TVM calculations:
1. the longhand method of multiplying exponential formulas
2. using any of the 4 TVM tables
3. using excel
4. using a financial calculator
In my opinion method 1 is too difficult. #2 takes too long; #3 I cannot help anyone with as every different calculator has its own 100 page instruction book
The easiest way is learning to use excel.
A. To use excel, hit the “Fx” toolbar, and choose “financial” functions from the pulldown menu
To do any kind of present value problem, go to the PV function
To do any kind of FV problem, go to the FV function
Whichever function you choose will open a window into which you will type in data
Guidelines to follow:
B. The “rate” means the decimal format of the discount or interest rate PER PERIOD to use; if its 5%, type in .05….if its 12% type in .12.
If instead of annual compounding, for example if problem dealt with semiannual compounding, and annual rate was 10%, you would type in .05.
C. “Periods” means the number of compounding periods. If problem is 10 years, compounded annually, type in 10; if its 10 years compounded semi-annually, type in 20
D. means what the future sum would be.
E. “Payment” field would only be filled in if its an annuity [a stream of equal periodic payments like a car loan or mortgage], in which case you would type in the size of the periodic payment. Otherwise, leave it blank.
F. Generally money paid in [like to a bank], should have a negative sign, and your answer will come out positive then
Specific examples:
1. For determining the PV of some future some, use the PV function, type in your discount rate as a decimal, type in the number of periods, and type in the future value. If its an annuity, type in the $ amount of the periodic payment in the “payment” field.
2. For determining the Future value of some present sum, use the FV function and enter info as above whether its one present sum, or its an annuity stream
3. If instead of a simple end of period annuity problem, its an “annuity due” problem [payment on the first day of the period vs., the last day, like an ordinary annuity], type “1” into the “type” field
4. Determining the effective annual rate: EAR
Go to financial section of Fx toolbar, using pull down window to get “effective”. Type in the nominal or stated ANNUAL percentage rate[APR], as a decimal[12% would be .12] and type in the number of compounding periods per year[if monthly compounding type in 12; if weekly compounding type in 52]. The answer should ALWAYS be >ANNUAL rate you typed in, unless its annual compounding in which case APR=EAR
5. Loan payment: to determine the size of the equal periodic loan payment, use the “payment” function, PMT. Type in the loan interest rate per period, as a decimal; if its an annual 12%, then its 1% per month, for example. Type the value of the money to be borrowed, in PV; type in the number of loan periodic payments. If you want the mo ...
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
Cfa level 1 quantitative analysis e book part 1parmanandiskool
The given e-book discusses Quantitative Analysis module for CFA L-1 .It is part-1 of the series and for other parts visit our site https://www.educorporatebridge.com/freebies3.php
Lecture 12816 and 20216 for chapters 3+43 Evaluation m.docxsmile790243
Lecture 1/28/16 and 2/02/16 for chapters 3+4
3 Evaluation methods for working with financial statements.
The first is RATIO ANALYSIS.
This helps you evaluate the financial performance of a company.
Chapter 3+4 are combined. You try to answer one main question: How ratio
analysis is used to evaluate the financial performance of a company.
In order to do ratio analysis you need data, and the data comes from financial
statements. The two main statements that we used to calculate the ratio: balance
sheet and income statement. 3 & 4 chapters are accounting review. He imported info
that reminds us of those two statements. All we need to study is this power point.
Review of balance sheet:
How finance people read balance sheet is a bit different because it fits our needs.
Balance sheet is two sides. One side is called assets and other side is called liabilities
and equity.
The assets side is everything the company owns.
The liability side is everything the company owes others.
Other definition could be, the assets could be considered the companies investment.
If asset is the companies the investments then liabilities is where we get the money
from to fund the investments.
Capital budgeting team from finance determines if they can afford the projects and
liabilities they can afford before accounting department gets its it.
Assets should always equal the liabilities.
Bonds are long term debt. Total debt equals depts. Plus equity. Short‐term debt is
current liabilities and long term debt is bonds. Short term is like A.P., s‐t notes
payable, current liabilities.
Total assets tell you the value of the company.
The value=D + E.
Income statements = revenues‐expenses=net income or net loss.
They show whether the company makes profit or losses, revenues and expenses.
The very important number is net income. Whether it is positive or negative.
If it positive then perfect, everyone is happy…to a certain extent.
As soon as you have profit, you have to deduct taxes (corporate taxes)
The rest is divided between dividends and retained earnings, depends how much is
distributed where. Depends on many factors. They usually start by putting a lot in
retained earning and use it as an internal source of finance, the management will do
anything they can do in order to maximize RE.
The ratio we use to calculate the RE from Net Income is called the
RETENTION RATIO= THE RATIO THAT WE USE TO CALCULATE RETAINED
EARNING FROM NET INCOME.
The name of the ratio that goes to dividends from net income is called dividend
payout ratio.
Revenues maybe up to 90% of them comes from SALES. The other 10% come from
like investments from shares you receive dividends, you receive INTERESTS from
BONDS.
Expenses, since most of the money comes from sales then the most of the expenses
come from COGS. The rest is salaries, maintenance etc.
Sales‐COGS=Gross profit‐rest=net incomes‐taxes=real net income that goes two
ways.
Earning per share=EPS =Total ne ...
3 Evaluation methods for working with financial statements.The f.docxtamicawaysmith
3 Evaluation methods for working with financial statements.
The first is RATIO ANALYSIS.
This helps you evaluate the financial performance of a company.
Chapter 3+4 are combined. You try to answer one main question: How ratio analysis is used to evaluate the financial performance of a company.
In order to do ratio analysis you need data, and the data comes from financial statements. The two main statements that we used to calculate the ratio: balance sheet and income statement. 3 & 4 chapters are accounting review. He imported info that reminds us of those two statements. All we need to study is this power point.
Review of balance sheet:
How finance people read balance sheet is a bit different because it fits our needs.
Balance sheet is two sides. One side is called assets and other side is called liabilities and equity.
The assets side is everything the company owns.
The liability side is everything the company owes others.
Other definition could be, the assets could be considered the companies investment.
If asset is the companies the investments then liabilities is where we get the money from to fund the investments.
Capital budgeting team from finance determines if they can afford the projects and liabilities they can afford before accounting department gets its it.
Assets should always equal the liabilities.
Bonds are long term debt. Total debt equals depts. Plus equity. Short-term debt is current liabilities and long term debt is bonds. Short term is like A.P., s-t notes payable, current liabilities.
Total assets tell you the value of the company.
The value=D + E.
Income statements = revenues-expenses=net income or net loss.
They show whether the company makes profit or losses, revenues and expenses.
The very important number is net income. Whether it is positive or negative.
If it positive then perfect, everyone is happy…to a certain extent.
As soon as you have profit, you have to deduct taxes (corporate taxes)
The rest is divided between dividends and retained earnings, depends how much is distributed where. Depends on many factors. They usually start by putting a lot in retained earning and use it as an internal source of finance, the management will do anything they can do in order to maximize RE.
The ratio we use to calculate the RE from Net Income is called the
RETENTION RATIO= THE RATIO THAT WE USE TO CALCULATE RETAINED EARNING FROM NET INCOME.
The name of the ratio that goes to dividends from net income is called dividend payout ratio.
Revenues maybe up to 90% of them comes from SALES. The other 10% come from like investments from shares you receive dividends, you receive INTERESTS from BONDS.
Expenses, since most of the money comes from sales then the most of the expenses come from COGS. The rest is salaries, maintenance etc.
Sales-COGS=Gross profit-rest=net incomes-taxes=real net income that goes two ways.
Earning per share=EPS =Total net incomes/shares outstanding. Means like $162/100= $1.62 means eve ...
Similar to Stated and effective interest rate (20)
Usse average internal rate of return (airr), don't use internal rate of retur...Futurum2
This is to document the email correspondences with Prof. Peter M. DeMarzo (Stanford University) and Prof. Carlo Alberto Magni with regards to Average Internal Rate of Return in Dec 2015.
Use average internal rate of return (airr), don't use internal rate of return...Futurum2
This is to document email correspondence with Prof. Carlo Alberto Magni with regards to the use of Average Internal Rate of Return (AIRR) instead of Internal Rate of Return (IRR)
A quick comment on pablo fernandez' article capm an absurd model draftFuturum2
This is to document email correspondence with Prof. Peter M. DeMarzo (Stanford University, USA) and Ignacio Velez-Pareja (Columbia) with regards to the article by Pablo Fernandez posted at SSRN.com under the title "CAPM: An Absurd Model"
Summing up about growing and non growing perpetuities wacc levered and tax sa...Futurum2
In this note we reconsider in detail the proper discount rate for cash flows in perpetuity, the present value of tax savings and the calculation of terminal value. The note clarifies the use of real discount rates and concludes with a formulation that is inflation-neutral for a given assumption on the discount rate for the tax savings. We find that the only discount rate for tax savings that makes the value of the perpetuity inflation-neutral is Kd, the cost of debt. We also reconsider the intuitive approach to calculate the cost of capital for perpetuities from the nominal rates that compose that cost of capital, and then
converting it into real cost of capital using Fisher relationship.
BYD SWOT Analysis and In-Depth Insights 2024.pptxmikemetalprod
Indepth analysis of the BYD 2024
BYD (Build Your Dreams) is a Chinese automaker and battery manufacturer that has snowballed over the past two decades to become a significant player in electric vehicles and global clean energy technology.
This SWOT analysis examines BYD's strengths, weaknesses, opportunities, and threats as it competes in the fast-changing automotive and energy storage industries.
Founded in 1995 and headquartered in Shenzhen, BYD started as a battery company before expanding into automobiles in the early 2000s.
Initially manufacturing gasoline-powered vehicles, BYD focused on plug-in hybrid and fully electric vehicles, leveraging its expertise in battery technology.
Today, BYD is the world’s largest electric vehicle manufacturer, delivering over 1.2 million electric cars globally. The company also produces electric buses, trucks, forklifts, and rail transit.
On the energy side, BYD is a major supplier of rechargeable batteries for cell phones, laptops, electric vehicles, and energy storage systems.
where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
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 get verified on Coinbase Account?_.docxBuy bitget
t's important to note that buying verified Coinbase accounts is not recommended and may violate Coinbase's terms of service. Instead of searching to "buy verified Coinbase accounts," follow the proper steps to verify your own account to ensure compliance and security.
what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
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
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @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
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
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 price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
1. www.futurumcorfinan.com
Page 1
What Corporate Finance Textbooks Don’t Tell
You about Stated/Nominal vs Effective Annual
Interest Rates
Time is money (Benjamin Franklin)
“If time is money, shouldn’t we count those benjamins?”
Note:
IVP = Ignacio Velez-Pareja (Associate Professor of Finance at Universidad Tecnológica de
Bolívar in Cartagena, Colombia)
Karnen : Sukarnen (a student in corporate finance)
Introduction
We could find the explanations about the calculation of Stated and Effective Annual Interest
Rates (SAIR vs EAIR) in most of standard corporate finance textbooks, mainly put under the
Sukarnen
DILARANG MENG-COPY, MENYALIN,
ATAU MENDISTRIBUSIKAN
SEBAGIAN ATAU SELURUH TULISAN
INI TANPA PERSETUJUAN TERTULIS
DARI PENULIS
Untuk pertanyaan atau komentar bisa
diposting melalui website
www.futurumcorfinan.com
2. www.futurumcorfinan.com
Page 2
chapter “The Time Value of Money”. The basic idea behind SAIR and EAIR is that, it is not
always be possible to assume that compounding or discounting is an annual process, that is,
cash flows (inflows or outflows) arise either at the start or the end of the year. We could see this
in real practice, where:
the contractual payment for interest charge on loan is incurred on a semi-annual basis
or a quarterly basis;
interest charge on credit cards is applied on a monthly basis;
a fixed deposit scheme may offer daily compounding;
a car dealer may quote an interest rate on a monthly basis.
How should we compare interest rates that are quoted for different periods?
Thus, to have the “apples with apples” comparison, it is necessary to determine the effective
annual percentage rate, or effective annual interest rate.
The classic example of the section in the standard corporate finance textbooks regarding the
conversion of stated into the effective annual interest rate is as follows1
:
3-5b Stated Versus Effective Annual Interest Rates
Both consumers and businesses need to make objective comparisons of loan costs or
investment returns over different compounding periods. To put interest rates on a common
basis for comparison, we must distinguish between stated and effective annual interest rates.
The stated annual rate is the contractual annual rate charged by a lender or promised by a
borrower. The effective annual rate (EAR), also known as the true annual return, is the annual
rate of interest actually paid or earned. The effective annual rate reflects the effect of
compounding frequency, whereas the stated annual rate does not. We can best illustrate the
differences between stated and effective rates with numerical examples.
Using the notation introduced earlier, we can calculate the effective annual rate by substituting
values for the stated annual rate (r) and the compounding frequency (m) into Equation 3.14:
1
Megginson, William L., and Scott B. Smart. Introduction to Corporate Finance. Mason (USA): South-Western, a
part of Cengage Learning. 2009. Chapter 3 : The Time Value of Money. Page 109-110.
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We can apply this equation using data from preceding examples.
Not surprisingly, the maximum effective annual rate for a given stated annual rate occurs when
interest compounds continuously. The effective annual rate for this extreme case can be found
by using the following equation:
For the 8 percent stated annual rate (r = 0.08), substitution into Equation 3.14a results in an
effective annual rate of 8.33 percent, as follows:
At the consumer level in the United States, “truth-in-lending laws” require disclosure on credit
cards and loans of the annual percentage rate (APR).The APR is the stated annual rate found
by multiplying the periodic rate by the number of periods in one year. For example, a bank credit
card that charges 1.5 per-cent per month has an APR of 18 percent (1.5% per month x 12
months per year). However, the actual cost of this credit card account is determined by
calculating the annual percentage yield (APY ), which is the same as the effective annual rate.
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For the credit card example, 1.5 percent per month interest has an effective annual rate of
[(1.015)^12 – 1] = 0.1956, or 19.56 percent. If the stated rate is 1.75 percent per month, as is
the case with many U.S. credit card accounts, the APY is a whopping 23.14 percent. In other
words, if you are carrying a positive credit card balance with an interest rate like this, pay it off
as soon as possible!
Discussions
Unfortunately, most of these corporate finance textbooks just stop there without exploring
further and don’t even give words of caution to all those undergraduate students, which might
be the first time being exposed to the calculation of SAIR and EAIR.
There are two things I would like to “add” to the explanation of SAIR and EAIR.
First, the book doesn’t tell you that the “interest” is paid at the end of the period (known
as “in arrears”), and not at the beginning of the period (known as “in advance”).
In certain situation, the “interest” is collected in advance.
If this is the case, then how to calculate this periodic rate?
For instance,
Debt interest rate = 8% per annum
Quarters in one year = 4
Debt periodic interest rate?
Per textbook, it should be = (1+8%)^(1/4) -1 = 1.94%, since if we (1+1.94%)^4 - 1 = 8%.
To give you a bit expanded idea about this periodical interest rate, we have:
a) 8% per annum (this is effective rate compounded 1x)...and the question is how much
the effective rate for one year if it is compounded 4 times...then effective one year =
(1+8%/4)^4 - 1...Then we have 8.24% effective per year, or 2% per quarter.
b) 8% per annum is the effective rate for 4 times compounded, then per quarter,
(1+8%)^(1/4) -1 = 1.94% per quarter.
But, all above calculation as per textbook is standing on the assumption that the interest is
collected or paid at the end of the period/quarter, and not in advance or at the beginning of
the quarter.
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Periodical interest rate in advance (= iPad) is determined as follows:
iPad = i/(1+i) and
i= iPad/(1-i_ad)
t=0 t=1
P P(1+i) at the end.
P(1-i_ad) P in advance
First case i = P(1+i)/P -1 = i (paid at the end of period).
Second case
i = P/P(1-i_ad) -1 = (P - P(1-i_ad))/[P(1-i_ad)] - 1 = i = iPad/(1-i_ad).
Or,
iPad = i/(1+i), then
i = iPad (1+i), then
i = iPad + iPad * i, then
i – (iPad * i) = iPad, then
i * (1 – iPad) = iPad, then
i = iPad/(1-i_ad)
The other way around,
iPad = i/(1+i)
So, if we put into the above example, the periodical/quarterly interest rate paid/collected in
advance is:
1 - (1/(1+8%)^(1/4)) = 1.91%, which if we compounded it four times (1+1.91%)^4- 1, we won't
get 8% per annum, as this interest is paid/collected in advance instead of in arrears.
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As a recap, where:
i is periodical interest at the end of period, and
iPad is in advance.
If iPad=1.91% then i=1.947%
(1+i)^(1/4) is (1+i_periodical).
Second, by doing the conversion between compounding methods as explained in the
corporate finance textbooks, are they really “equivalent”?
I give one extreme example.
Suppose:
r1 is the annual rate with continuous compounding.
r2is the equivalent compounded m times per annum times per annum.
Then we have:
= (1 + r2/m)^m = e^r1
= r1 = m * ln (1 + r2/m), then
= r2 = m (e^(r1/m) – 1)
If we carefully look at the cash flows for this interest, then r1 and r2 above are based on
different cash flows, and in what financial sense, we could say that they are equivalent?
Think about it next time before just jumping to use all formulas given in the standard corporate
finance textbooks.
Ignacio Velez-Pareja (IVP) comments:
When you contract a loan, usually they specify the non-compounded rate (in Spanish, we say
nominal rate). However, if you have contracted the loan on a monthly or quarterly basis, then
you find the periodic rate (8%/12, 8%/4, etc.) It is this way of paying the interest that makes the
artificial compounded (we call it in Spanish, effective rate).
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Hence, you have on a quarterly basis, 8% as non-compounded rate, 2% as a periodic
(quarterly) rate and the compounded rate. There is a very simple relationship between non-
compounded and periodical rates, as follows
1.Compounded: periodical rate times number of periods
2.Periodical; compounded rate /number of periods.
I don't give a penny for the compounded rate. That is a mathematical fiction. The most
relevant rate is the periodical rate (many people think it is the compounded rate and you could
tell me how many firms you know that pay interest on the basis of a compounded rate?) The
rate that should be used in WACC (for instance) should be the periodical. That one is the most
important rate, because that rate is the one you need to calculate the actual interest payment
and the sum of all those interest payments are what you deduct from the Income tax report.
Follow?
Hence,
If you have 8% per annum, compounded quarterly, you already know that the periodical is 2%.
That rate is the one the bank uses to calculate the interest you have to pay. The compounded is
(1+8%/4)^4-1= 8.2432%
BUT that 8.2432% has no real meaning. In fact, do you know that the assumption behind that
calculation is that you can save (or invest) exactly at the same rate you borrow money? It is as if
the bank has one window where it gives you the loan at, say 2% per quarter, and another one
where they pay you 2% per quarter. HOWEVER, that is true for the bank, because in
equilibrium, the money it receives from you is invested (most times) at the same rate you pay.
This is the considerations I give to my students:
Assume you have several people with different ways to "keep" the money and you will tell me
which is their opportunity cost.
They have two options: a) To pay a loan of 1,000 at the end of year with interest of 8% (you will
pay 1000+80 interest). b) to pay 20 per quarter and 1000 at the end of year. (20, 20, 20, 1020).
For instance:
1.Keeps the money in a safe box. Opportunity cost = 0%
2.Keeps the money in a savings account Opportunity cost 0.5% per month
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3.Keeps the money in a CD Opportunity cost 1.2% per month
4.Keeps the money in a savings account Opportunity cost 2% per quarter
5.Keeps the money in a CD maturity 1 year Opportunity cost 8% per annum
6.Keeps the money in a savings account Opportunity cost 2.5% per quarter
If each of them contracts a loan to be paid quarterly at (% per annum with quarterly payments of
2% interest).
What each individual will prefer, a) or b)?. The capitalized cost is as said, 8.2432% per annum.
Will that loan cost the same to all of them? Figure out the case of the person with his money in
the safe box: will it cost more if she pays the loan in a lump sum at the end of the year (1,080)
or if she pays 20, 20, 20, 1020?.
The assumption in the compounded rate is that it is the same for ALL of them: 8.2432% per
annum. Is that true? Will it cost more or less for case 6? For case 1? For case 5?
Would you say that the extra cost of paying a) or b) is the same for all of them? I think it
is not the same and yet, the compounded rate is the same for all!!!
Karnen:
Ignacio, interesting, as you showed above that they have two options:
a) To pay a loan of 1,000 at the end of year with interest of 8% (you will pay 1000+80 interest).
b) To pay 20 per quarter and 1000 at the end of year. (20, 20, 20, 1020).
I don't think that two options could have the same interest rate, the risk of cash flows could be
different as far as I could see, with option b) looks safer, yet the compounded rate as the
textbooks taught us, that the rates for both options are the same.
IVP:
Dear Karnen
I see you are picking the most fictional case! Perpetuities!
However, that continuous interest applies to formulas such as the Black-Scholes model for
financial options.
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This is a cash flow that you receive instantaneously, every Nano second. Can you even imagine
that?
Yet, I have seen, occasionally, a bank offering that interest rate. The difference with a practical
daily rate is nil.
It is a mathematical conception that exists only in the imagination. It says the effective rate of a
non-compounded rate of, say, 12% per annum, compounded instantaneously. It is as if money
were a liquid that flows through a Cane into your bank account. Just science fiction.
Note: The first perpetuities were issued in the 12th century in Italy, France and Spain. They
were initially and intentionally to circumvent the usury laws of the Catholic Church. that is
because no loan principal repayment, they were not considered as loans.
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