Từ điển thuật ngữ Kế toán Kiểm toán English VIetnamese

Từ điển thuật ngữ Kế toán Kiểm toán English VIetnamese giải thích đầy đủ các thuật ngữ chuyên ngành kế toán kiểm toán một cách chính xác, dễ hiểu nhất, mang đến cho bạn một nền tảng lý thuyết cơ bản về ngành kế toán kiểm toán.

S TAY CÔNG TH C, THU T NG TÀI

L i gi i thi u

Các b n sinh viên thân m n,

Trên tay các b n là cu n “S tay công th c, thu t ng tài chính có gi i thích ti ng

Vi t dành cho sinh viên đ i h c chuyên ngành k toán - tài chính” ây là k t qu c a công trình nghiên c u khoa h c sinh viên do hai b n sinh viên ng c Vi t và Ngô Th Thanh Thúy, khóa 6 i h c Help, Malaysia th c hi n Công trình nghiên c u này r t vinh

d đ c là m t ph n đóng góp vào d p k ni m chào m ng 10 n m thành l p Khoa Qu c

t - i h c Qu c gia Hà N i Công trình này đ c th c hi n v i m c đích cung c p m t tài li u tra c u các thu t ng và công th c h tr cho các b n sinh viên trong quá trình h c

N i dung c a cu n s tay bao g m 2 ph n: công th c tài chính b ng ti ng anh đi kèm ví d

và thu t ng tài chính , k toán Anh – Vi t có gi i thích b ng ti ng Vi t Các b n có th tra

c u các công th c và thu t ng ti ng Vi t t ng đ ng c a các thu t ng ho c công th c

ti ng Anh mà các b n g p trong quá trình h c t p, các thu t ng và công th c đ u đ c s p

x p theo th t trong b ng ch cái Do h n ch v th i gian nên cu n s tay này không th tránh kh i nh ng sai sót và h n ch nh t đ nh, chúng tôi r t mong nh n đ c nh ng ý ki n đóng góp c a các b n sinh viên và các th y cô giáo đ cu n s tay này đ c hoàn thi n

h n Chúc các b n luôn đ t k t qu cao và sáng t o trong h c t p

Hà N i, tháng 7 n m 2011

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M i thông tin góp ý xin vui lòng g i: vietdd88@gmail.com

M C L C

A

Annual Percentage Yield

Or,

Example:

An account states that its rate is 6% compounded monthly The rate, or r, would be

.06, and the number of times compounded would be 12 as there are 12 months in a year Putting this into the formula we have

After simplifying, the annual percentage yield is shown as 6.168%

Annuity Payment (PV)

Or,

While,

An annuity is a series of periodic payments that are received at a future date The present value portion of the formula is the initial payout, with an example being the original payout on an amortized loan

Assumptions:

1 the rate does not change,

2 the payments stay the same,

3 the first payment is one period away

The annuity payment formula can be used for amortized loans, income annuities, structured settlements, lottery payouts(see annuity due payment formula if first payment starts immediately), and any other type of constant periodic payments

It is important to remember that the rate per period and the occurrence of periodic payments need to match For example, if the payments are made monthly, then the rate used would be the effective monthly rate

Using the variables from this example, the equation for annuity payments would be

After solving, the amount needed to save per month is $941.77 Real amounts may vary by cents due to rounding

Annuity Payment Factor - PV

Present Value of Annuity

Assumptions

1) The periodic payment does not change

2) The rate does not change

3) The first payment is one period away

Future Value of Annuity Due

Example:

Suppose that an individual would like to calculate their future balance after 5 years with today being the first deposit The amount deposited per year is $1,000 and the account has an effective rate of 3% per year It is important to note that the last cash flow is received one year prior to the end of the 5th year

For this example, we would use the future value of annuity due formula to come to the following equation:

After solving, the balance after 5 years would be $5468.41

Annuity Due Payment - PV

Or,

Example:

An individual who would like to calculate the amount they can withdraw once per year in order to allow their savings to last 5 years Suppose their current balance, which would be the present value, is $5,000 and the effective rate on the savings account is 3%

It is important to remember that the individual's balance on their account will reach

$0 after the 4th year or more specifically, the beginning of the 5th year, however the amount withdrawn will last the entire year composing a total of 5 years

The equation for the annuity due payment formula using present value for this example would be:

After solving, the amount withdrawn once per year starting today would be $1059.97 Actual amounts may vary by a few cents due to rounding

Annuity Due Payment - FV

Example of the Annuity Due Payment Formula Using Future Value

An individual would like to have $5,000 saved within 5 years The individual plans

on making equal deposits per year starting today into an account that has an effective annual rate of 3%

As with any other financial formula, it is important that the rate is expressed per period For example, if the deposits are made monthly, then the monthly rate would be used For this particular example, 3% is the effective annual rate and the deposits are made annually

After putting the variables from this example into the annuity due payment formula using future value, the equation would be

After solving, the amount to be deposited per year, starting today, would be

$914.34 Actual results may vary by a few cents due to rounding

Asset Turnover Ratio

Average Collection Period

Capital Gains Yield

Suppose an account with an original balance of $1000 is earning 12% per year and

is compounded monthly Due to being compounded monthly, the number of periods for one year would be 12 and the rate would be 1% (per month) Putting these variables into the compound interest formula would show

The second portion of the formula would be 1.12683 minus 1 By multiplying the original principal by the second portion of the formula, the interest earned is $126.83

Continuous Compounding

The continuous compounding formula is used to determine the interest earned on

an account that is constantly compounded, essentially leading to an infinite amount of compounding periods

Example:

A simple example of the continuous compounding formula would be an account with an initial balance of $1000 and an annual rate of 10% To calculate the ending balance after 2 years with continuous compounding, the equation would be

This can be shown as $1000 times e (.2) which will return a balance of $1221.40 after the two years For comparison, an account that is compounded monthly will return a balance of $1220.39 after the two years Although the concept of infinite seems that it would return a very large amount, the effect of each compound becomes smaller each time

Current Ratio

The Current Ratio provides a calculable means to determining a company's liquidity in the short term The terms of the equation Current Assets and Current Liabilities references the assets that can be realized or the liabilities that are payable in less than a year

Evaluating the Current Ratio with that of the same company or a comparable company over many years is generally the advised method In addition, it may be beneficial to compare the Current Ratio with other finance ratios including inventory ratios, receivable ratios, and the amount of quick assets, or readily available assets A company that receives payment for the sale of their products more quickly, can remain solvent with a lower Current Ratio compared to a company who receives payments later

D Days in Inventory

Or,

This formula is used to determine how quickly a company is converting their inventory into sales A slower turnaround on sales may be a warning sign that there are problems internally, such as brand image or the product, or externally, such as an industry downturn or the overall economy

Debt Ratio

The debt ratio is a financial leverage ratio used along with other financial leverage ratios to measure a company's ability to handle its obligations If a company is overleveraged, i.e has too much debt, they may find it difficult to maintain their solvency and/or acquire new debt Just as in consumer loans, companies are evaluated when taking

on new obligations to determine their risk of non-repayment Both the total liabilities and total assets can be found on a company's balance sheet

Example:

A company has total assets of $3 million and total liabilities of $2.5 million The total liabilities of $2.5 million would be divided by the total assets of $3 million which gives a debt ratio of 8333

Debt to Equity Ratio (D/E)

The debt to equity ratio is a financial leverage ratio These ratios are used to measure a company's ability to handle its long term and short term obligations Both debt and equity will be found on a company's balance sheet Debt may show as total liabilities and equity may show as total stockholder's equity

Debt to Income Ratio

The debt to income ratio is used in lending to calculate an applicant's ability to meet the payments on the new loan The debt to income ratio may also be referred to as the back end ratio specifically when a new mortgage is requested The term back end ratio, or total debt to income, is used to differentiate the calculation from the housing debt ratio, also called the front end ratio

Dividend Payout Ratio

The dividend payout ratio is the amount of dividends paid to stockholders relative

to the amount of total net income of a company The amount that is not paid out in dividends to stockholders is held by the company for growth The amount that is kept by the company is called retained earnings Net income shown in the formula can be found on the company's income statement

Dividend Yield (Stock)

The formula for the dividend yield is used to calculate the percentage return on a stock based solely on dividends The total return on a stock is the combination of dividends and appreciation of a stock The dividends paid for a company can be found on the statement of retained earnings, which can then be used to calculate dividends per share

Example:

A stock that has paid total annual dividends per share of $1.12, the original stock price for the year was $28 If an individual investor wants to calculate their return on the stock based on dividends earned, he or she would divide $1.12 by $28 Using the formula for this example, the dividend yield would be 4%

Dividends Per Share

Doubling Time

The Doubling Time formula is used in Finance to calculate the length of time required to double an investment or money in an interest bearing account

It is important to note that r in the doubling time formula is the rate per period If

one wishes to calculate the amount of time to double their money in a money market

account that is compounded monthly, then r needs to express the monthly rate and not the

annual rate The monthly rate can be found by dividing the annual rate by 12 With this situation, the doubling time formula will give the number of months that it takes to double money and not years

In addition to expressing r as the monthly rate if the account is compounded monthly, one could also use the effective annual rate, or annual percentage yield, as r in

the doubling time formula

Example:

Jacques would like to determine how long it would take to double the money in his money market account He is earning 6% per year, which is compounded monthly Looking at the doubling time formula, we need to consider that the 6% would need to be divided by 12 in order to come to a monthly rate since the account is compounded

monthly Given this, r in the doubling time formula would be 005 (.06/12) After putting

this into the doubling time formula, we have:

After solving, the doubling time formula shows that Jacques would double his money within 138.98 months, or 11.58 years

As stated earlier, another approach to the doubling time formula that could be used with this example would be to calculate the annual percentage yield, or effective annual

rate, and use it as r The annual percentage yield on 6% compounded monthly would be

6.168% Using 6.168% in the doubling time formula would return the same result of 11.58 years

The formula for doubling time with continuous compounding is used to calculate the length of time it takes doubles one's money in an account or investment that has continuous compounding It is important to note that this formula will return a time to double based on the term of the rate For example, if the monthly rate is used, the answer

to the formula will return the number of months it takes to double If the annual rate is used, the answer will then reflect the number of years to double

Example:

An individual would like to calculate how long it would take to double his investment that earns 6% per year, continuously compounded The individual could either calculate the number of years or calculate the number of months to double his investment

by using the annual rate or the monthly rate Using the doubling time for continuous compounding formula, the time to double at a rate of 6% per year would show

E

Earnings Per Share

The formula for earnings per share, or EPS, is a company's net income expressed

on a per share basis Net income for a particular company can be found on its income statement It is important to note that the earnings per share formula only references common stock and any preferred stock dividends is subtracted from the net income, if applicable

Equity Multiplier

Equivalent Annual Annuity

The equivalent annual annuity formula is used in capital budgeting to show the net present value of an investment as a series of equal cash flows for the length of the investment When comparing two different investments using the net present value

method, the length of the investment (n) is not taken into consideration An investment

with a 15 year term may show a higher NPV than an investment with a 4 year term By showing the NPV as a series of cash flows, the equivalent annual annuity formula provides

a way to factor in the length of an investment

which returns an equivalent annual annuity of $30,192.08

Putting the variables of the 15 year project into the equivalent annual annuity formula shows

which returns an equivalent annual annuity of $17,524.43

Comparing these two projects, the 4 year project will return a higher amount relative to the time of the investment Although the 15 year project has a higher NPV, the 4 year project can be reinvested and have additional earnings for the 11 years that remain on the 15 year project

Estimated Earnings

Or,

The formula above is a simple way of restating how to calculate net income, i.e earnings, based on its estimated components However, the practice of calculating estimated earnings is far more complex

It is important to note that the expenses in the estimated earnings formula should include interest and taxes

F

Future Value

Or,

Future Value (FV) is a formula used in finance to calculate the value of a cash flow

at a later date than originally received This idea that an amount today is worth a different amount than at a future time is based on the time value of money

Example of Future Value Formula

An individual would like to determine their ending balance after one year on an account that earns 5% per month and is compounded monthly The original balance on the account is $1000 For this example, the original balance, which can also be referred to as

initial cash flow or present value, would be $1000, r would be 005(.5%), and n would be

12 (months)

Putting this into the formula, we would have:

After solving, the ending balance after 12 months would be $1061.68

As a side note, notice that 6% of $1000 is $60 The additional $1.68 earned in this example

is due to compounding

Future Value of Annuity

The future value of an annuity formula is used to calculate what the value at a future date would be for a series of periodic payments

Assumption:

1 The rate does not change

2 The first payment is one period away

3 The periodic payment does not change

If the rate or periodic payment does change, then the sum of the future value of each individual cash flow would need to be calculated to determine the future value of the annuity If the first cash flow, or payment, is made immediately, the future value of annuity due formula would be used

Example:

An individual who decides to save by depositing $1000 into an account per year for

5 years, the first deposit would occur at the end of the first year If a deposit was made

immediately, then the future value of annuity due formula would be used The effective annual rate on the account is 2% If she would like to determine the balance after 5 years, she would apply the future value of an annuity formula to get the following equation

The balance after the 5th year would be $5204.04

FV - Continuous Compounding

The future value with continuous compounding formula is used in calculating the later value of a current sum of money Use of the future value with continuous compounding formula requires understanding of 3 general financial concepts, which are time value of money, future value as it applies to the time value of money, and continuous compounding

Example of FV with Continuous Compounding Formula

An example of the future value with continuous compounding formula is an individual would like to calculate the balance of her account after 4 years which earns 4% per year, continuously compounded, if she currently has a balance of $3000

The variables for this example would be 4 for time, t, 04 for the rate, r, and the

present value would be $3000 The equation for this example would be

which return a result of $3520.53

Future Value Factor

The formula for the future value factor is used to calculate the future value of an amount per dollar of its present value The future value factor is generally found on a table which is used to simplify calculations for amounts greater than one dollar (see example below)

G

Geometric Mean Return

The geometric mean return formula is used to calculate the average rate per period

on an investment that is compounded over multiple periods The geometric mean return may also be referred to as the geometric average return

Using the formula for compound interest with different rates, the ending balance after year three can be found by multiplying the balance times 1.20, 1.06, and 1.01 The ending balance after year three would be $1284.72 Notice the differences between the ending balance with incorrectly using the arithmetic mean shown in the prior paragraph and the actual ending balance

The equation for this example using the formula for the geometric mean return would be

which would return 8.71% This answer can be checked by using the compound interest formula which would return $1284.72 as shown in the prior paragraph

Growing Annuity - FV

The formula for the future value of a growing annuity is used to calculate the future amount of a series of cash flows, or payments, that grow at a proportionate rate A growing annuity may sometimes be referred to as an increasing annuity

Example:

An individual who is paid biweekly and decides to save one of her extra paychecks per year One of her net paychecks amounts to $2,000 for the first year and she expects to receive a 5% raise on her net pay every year For this example, we will use 5% on her net pay and not involve taxes and other adjustments in order to hold all other things constant

In an account that has a yield of 3% per year, she would like to calculate her savings balance after 5 years

The growth rate in this example would be the 5% increase per year, the initial cash flow or payment would be $2,000, the number of periods would be 5 years, and rate per period would be 3% Using these variables in the future value of growing annuity formula would show

After solving this equation, the amount after the 5th cash flow would be $11,700.75

Growing Annuity – PV

The present value of a growing annuity formula calculates the present day value of

a series of future periodic payments that grow at a proportionate rate A growing annuity may sometimes be referred to as an increasing annuity A simple example of a growing annuity would be an individual who receives $100 the first year and successive payments increase by 10% per year for a total of three years This would be a receipt of $100, $110, and $121, respectively

Growing Annuity Payment - PV

Growing Annuity Payment - FV

The growing annuity payment formula using future value is used to calculate the first cash flow or payment of a series of cash flows that grow at a proportionate rate A growing annuity may sometimes be referred to as an increasing annuity

be

which would return a present value of $20,000

H Holding Period Return

Example:

An investment in an asset that has an annual appreciation of 10%, 5%, and -2% over three years As stated in the prior section, simply adding the annual appreciation of each year together would be inaccurate as the 5% earned in year two would be on the original value plus the 10% earned in the first year After putting the annual percentages into the holding period return formula, the correct calculation would be:

After solving this equation, the holding period return would be 13.19% for all three years

I

Interest Coverage Ratio

The formula for the interest coverage ratio is used to measure a company's earnings relative to the amount of interest that it pays The interest coverage ratio is considered to be

a financial leverage ratio in that it analyzes one aspect of a company's financial viability regarding its debt

Inventory Turnover Ratio

Or,

The formula for the inventory turnover ratio measures how well a company is turning their inventory into sales The costs associated with retaining excess inventory and not producing sales can be burdensome If the inventory turnover ratio is too low, a company may look at their inventory to appropriate cost cutting

L

Balloon Balance of a Loan

The balloon loan balance formula is used to calculate the amount due at the end of

a balloon loan

A balloon loan, sometimes referred to as a balloon note, is a note that has a term that is shorter than its amortization In other words, the loan payment will be amortized, or calculated, for a certain amount of years but the loan will be paid off before all payments calculated are made, thus leaving a balance due An example would be a note that is calculated for 30 years, but the remaining balance after 10 years must be paid in one full sum This example is commonly referred to as a 10/30 balloon

The loan balloon balance formula can be used for any type of balloon loan and is commonly seen with mortgages and leases

Example:

A $100,000 5/15 balloon mortgage with a 6% annual rate compounded monthly If the loan payment formula is used based on a 15 year amortization, the monthly payment would be $843.86

It is important to remember that private mortgage insurance, property taxes, and homeowner's insurance may be included when an individual makes a payment, but for this example, we are calculating the monthly payment for the loan itself We are also assuming that the first payment is due one month from the start of the loan, or that the interest included in the closing costs was adjusted to accomodate this assumption

For a 5/15 balloon, the loan will be amortized for 15 years, while we are solving for the amount due after the 5th year The variables of the formula would be $100,000 for present value (PV), $843.86 for P (payment), 005 for the rate (the monthly rate for 6% per year), and 60 for the number of periods as there will be 60 months

After putting these variables into the formula, the equation would be

Using this formula, the remaining balance would be $76,008.88

It must be taken into consideration that this remaining amount due would be after the 60th payment is made For an individual that has a loan, they would need to pay the final payment as well as the balloon balance

Loan Payment

Or,

The loan payment formula is used to calculate the payments on a loan The formula used to calculate loan payments is exactly the same as the formula used to calculate payments on an ordinary annuity A loan, by definition, is an annuity, in that it consists of

a series of future periodic payments

Remaining Balance on Loan

Loan to Deposit Ratio

Loan to Value Ratio

The formula for the loan to value ratio is generally used by loan officers and underwriters as part of evaluating an applicant's qualifications Lending institutions have guidelines to determine if a loan applicant qualifies for the loan requested If the loan to value ratio on a particular loan request is outside of the lending institution's guidelines, a higher down payment may be required

The formula for the loan to value ratio is also used specifically in mortgages to determine if private mortgage insurance, or PMI, is required In many cases, PMI is required on a mortgage that has a higher loan to value ratio than 80%, but individual lender programs may vary

which would return $9 per share

Net Present Value

Or,

Example:

Company Shoes For You's who is determining whether they should invest in a new project Shoes for You's will expect to invest $500,000 for the development of their new product The company estimates that the first year cash flow will be $200,000, the second year cash flow will be $300,000, and the third year cash flow to be $200,000 The expected return of 10% is used as the discount rate

The following table provides each year's cash flow and the present value of each cash flow

Year Cash Flow Present Value

0 -$500,000 -$500,000

1 $200,000 $181,818.18

2 $300,000 $247,933.88

3 $200,000 $150,262.96

Net Present Value = $80,015.02

The net present value of this example can be shown in the formula

When solving for the NPV of the formula, this new project would be estimated to be a valuable venture

Net Profit Margin

The net profit margin formula looks at how much of a company's revenues are kept

as net income The net profit margin is generally expressed as a percentage Both net income and revenues can be found on a company's income statement

Example:

A company's income statement shows a net income of $1 million and operating revenues of $25 million By applying the formula, $1 million divided by $25 million would result in a net profit margin of 4% Although the formula is simplistic, applying the concept is important in that 4% of sales will result in after tax profit

Net Working Capital

The formula for net working capital (NWC), sometimes referred to as simply working capital, is used to determine the availability of a company's liquid assets by subtracting its current liabilities

Current Assets are the assets that are available within 12 months Current Liabilities are the liabilities that are due within 12 months

Solve for Number of Periods - PV & FV

While,

The formula for solving for the number of periods is used to calculate the length of

time required for a single cash flow(present value) to reach a certain amount(future value)

based on the time value of money In other words, this formula is used to calculate the

length of time a present value would need to reach the future value, given a certain interest rate

Example:

An individual who would like to determine how long it would take for his $1500 balance in his account to reach $2000 in an account that pays 6% interest, compounded monthly Of course, for this example it is assumed that there will be no deposits nor withdrawals within this timeframe

As previously stated in the prior section, the number of periods and the periodic rate should match one another The 6% annual interest rate is compounded monthly, so

.005(equal to 5%) would be used for r as this is the monthly rate

For this example, the equation to solve for the number of periods would be

Which would result in 57.68 months Of course in real situations the fraction of a month may not be exact due to when the account is credited, there may be charges to the account that must be accounted for, and so on

This can be checked by putting these variables into the present value formula and confirming that in fact there will be a $2000 balance after 57.68 months based on a monthly rate of 5%

P

Payback Period

Example:

An individual is considering investing in straight preferred stock that pays $20 per year in dividends It has been determined that based on risk, the discount rate would be 5% The price the individual would want to pay for this security would be $20 divided by 05(5%) which is calculated to be $400

Example:

An individual wishes to determine how much money she would need to put into her money market account to have $100 one year today if she is earning 5% interest on her account, simple interest

The $100 she would like one year from present day denotes the C 1 portion of the

formula, 5% would be r, and the number of periods would simply be 1

Putting this into the formula, we would have

When we solve for PV, she would need $95.24 today in order to reach $100 one year from now at a rate of 5% simple interest

PV - Continuous Compounding

The present value with continuous compounding formula is used to calculate the current value of a future amount that has earned at a continuously compounded rate There are 3 concepts to consider in the present value with continuous compounding formula: time value of money, present value, and continuous compounding

Time Value of Money, Present Value, and Continuous Compounding

Time Value of Money - The present value with continuous compounding formula

relies on the concept of time value of money Time value of money is the idea that a specific amount today is worth more than the same amount at a future date For example, if one were to be offered $1,000 today or $1,000 in 5 years, the presumption is that today would be preferable

Present Value - The basic premise of present value is the time value of money To

expand upon the prior example, if one were to be offered $1,000 today or $1,250 in 5 years, the answer would not be as obvious as the prior example where both amounts were equal This is where present value comes in The offeree would need a way to determine today's value of the future amount of $1,250 to compare the two options

Continuous Compounding - Continuous Compounding is essentially compounding

that is constant Ordinary compounding will have a compound basis such as monthly, quarterly, semi-annually, and so forth However, continuous compounding is nonstop, effectively having an infinite amount of compounding for a given time

The present value with continuous compounding formula uses the last 2 of these concepts for its actual calculations The cash flow is discounted by the continuously compounded rate factor

Example of the Present Value with Continuous Compounding Formula

An example of the present value with continuous compounding formula would be

an individual who in two years would like to have $1100 in an interest account that is providing an 8% continuously compounded return To solve for the current amount needed

in the account to achieve this balance in two years, the variables are $1,100 is FV, 8% is r, and 2 years is t The equation for this example would be

This would return a result of $937.36

Present Value Factor

The formula for the present value factor is used to calculate the present value per dollar that is received in the future

The present value factor formula is based on the concept of time value of money Time value of

Price to Book Value

The Price to Book Ratio formula, sometimes referred to as the market to book ratio,

is used to compare a company's net assets available to common shareholders relative to the sale price of its stock The formula for price to book value is the stock price per share divided by the book value per share

The stock price per share can be found as the amount listed as such through the secondary stock market

The book value per share is considered to be the total equity for common stockholders which can be found on a company's balance sheet

Price Earnings Ratio

The price to earnings ratio is used as a quick calculation for how a company's stock

is perceived by the market to be worth relative to the company's earnings A higher price to earnings ratio implies that the market values the stock as a better investment than if there was a lower price to earnings ratio, ceteris paribus The increased perceived worth is due to news, speculation, or analysis from investors that the stock has a higher growth potential for the future

Price to Sales Ratio

The formula for price to sales ratio, sometimes referenced as the P/S Ratio, is the perceived value of a stock by the market compared to the revenues of the company

Revenues and sales are synonymous terms and can be found on a company's income statement The price of the stock is the price listed on the stock exchange, or secondary market

R

Rate of Inflation

The rate of inflation formula measures the percentage change in purchasing power

of a particular currency As the cost of prices increase, the purchasing power of the currency decreases

The subscript "x" refers to the initial consumer price index for the period being calculated, or time x And such, subscript "x+1" would be the ending consumer price index for the period calculated, or time x+1

Real Rate of Return

The formula for the real rate of return can be used to determine the effective return

on an investment after adjusting for inflation

The nominal rate is the stated rate or normal return that is not adjusted for inflation

For quick calculation, an individual may choose to approximate the real rate of

return by using the simple formula of nominal rate - inflation rate

For this example of the real rate of return formula, the money market yield is 5%, inflation is 3%, and the starting balance is $1000 Using the real rate of return formula, this example would show

which would return a real rate of 1.942% With a $1000 starting balance, the individual could purchase $1,019.42 of goods based on today's cost This example of the real rate of return formula can be checked by multiplying the $1019.42 by (1.03), the inflation rate plus one, which results in a $1050 balance which would be the normal return on a 5% yield

Receivables Turnover Ratio

The receivables turnover ratio formula, sometimes referred to as accounts receivable turnover, is sales divided by the average of accounts receivables

Sales revenue is the amount a company earns in sales or services from its primary operations Sales revenue can be found on a company's income statement under sales revenue or operating revenue

Average accounts receivable in the denominator of the formula is the average of a company's accounts receivable from its prior period to the current period

Example:

Suppose that the income statement from a company shows operating revenues of $1 million The same company has accounts receivables of $80,000 this period and $90,000 the prior period The average accounts receivables is $85,000 which can be divided into the

$1 million for a ratio of 11.76%

Retention Ratio

Or,

The payout ratio is the amount of dividends the company pays out divided by the net income This formula can be rearranged to show that the retention ratio plus payout ratio equals 1, or essentially 100% That is to say that the amount paid out in dividends plus the amount kept by the company comprises all of net income

The retention ratio, sometimes referred to as the plowback ratio, is the amount of retained earnings relative to earnings Earnings can be referred to as net income and is

found on the income statement Retained earnings is shown in the numerator of the formula as net income minus dividends

Return on Assets

Or,

Net Profit Margin is revenues divided by net income and the asset turnover ratio is net income divided average total assets By multiplying these two together, revenues is cancelled out leaving the formula for return on assets shown on top of the page

The return on assets formula, sometimes abbreviated as ROA, looks at the ability of

a company to utilize its assets to gain a net profit

Return on Equity (ROE)

The formula for return on equity, sometimes abbreviated as ROE, is a company's net income divided by its average stockholder's equity The numerator of the return on equity formula, net income, can be found on a company's income statement

Return on Investment

The formula for return on investment sometimes referred to as ROI or rate of return, measures the percentage return on a particular investment ROI is used to measure profitability for a given amount of time

The return on investment formula is mechanically similar to other rate of change formulas, an example being rate of inflation The base formula for measuring a percentage rate of change is:

For ROI, we are measuring the rate of change of monies due to investing By applying the return on investment formula, we can determine a X% change in monies on

an investment, which is synonymous with a X% return on investment

Risk Premium

The formula for risk premium, sometimes referred to as default risk premium, is the return on an investment minus the return that would be earned on a risk free investment The risk premium is the amount that an investor would like to earn for the risk involved with a particular investment

The US treasury bill (T-bill) is generally used as the risk free rate for calculations

in the US, however in finance theory the risk free rate is any investment that involves no risk

Risk Premium of the Market

The risk premium of the market is the average return on the market minus the risk free rate The term "the market" in respect to stocks can be connoted as an entire index of stocks such as the S&P500 or the Dow The market risk premium can be shown as:

The risk of the market is referred to as systematic risk In contrast, unsystematic risk is the amount of risk associated with one particular investment and is not related to the market As an investor diversifies their investment portfolio, the amount of risk approaches that of the market Systematic and unsystematic risk and their relation to returns is where the many clichés about diversifying your investment portfolio is derived