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1






S TAY CÔNG THC, THUT NG TÀI
CHÍNH CÓ GII THÍCH TING VIT
DÀNH CHO SINH VIÊN I HC CHUYÊN NGÀNH
K TOÁN ậ TÀI CHÍNH
(dành cho sinh viên )

Nhóm tác gi: ng c Vit
Ngô Th Thanh Thúy
Hiu đính: PGS.TS. Nguyn Hi Thanh
Th.S.CFA. oàn Anh Tun
Th.S Chu Vn Hùng





Hà Ni, 2011
Bn quyn thuc v nhóm tác gi, mi sa đi b xung vui lòng liên h. Xin cm n


2

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
Nhóm biên son s tay.
Mi thông tin góp ý xin vui lòng gi:
















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MC LC

1. T đin công thc………………………………………… 3
2. T đin thut ng……………………………………………48


























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4

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,

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5
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.

Annuity Payment - FV


.
Or,


Example:
An individual who would like to calculate the amount they would need to save per
year to have a balance of $5,000 after 5 years. For this example, it is assumed that the
effective rate per year would be 3%.
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

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6
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

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7
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:

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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




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9
Average Collection Period


Or,


B
Bond Equivalent Yield



C

Capital Asset Pricing Model (CAPM)

Or,


When regression analysis is applied to the capital asset pricing model based on
prior returns, the formula will be shown as above. Alpha is considered to be the risk free
rate and epsilon is considered to be the error in the regression.

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10
Capital Gains Yield



Or,

Or,

Which is another way of stating a change in (Delta) price divided by the original
stock price.
Compound Interest



Example:
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.

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11
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.


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12
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.
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13

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%.

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14


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.
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15
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.
.
Doubling Time – Continuous Compounding


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.
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16

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.
Example:
Using the prior example of comparing one project with a 4 year term and another
project with a 15 year term, the NPV of the 4 year project is $100,000 and the NPV of the
15 year project is $150,000. The rate used for both is 8%. Putting the variables of the 4
year project in the equivalent annual annuity formula shows

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.
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17
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.
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18
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
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19
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


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20
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).
Example:
Using the prior example of 12% compounded monthly, the future value factor
formula for one year would show

Where 1%, or .01, is the rate per period and 12 is the number of periods. By solving this
equation, the future value factor for 12 periods at 1% per period would be 1.1268.
As previously stated, the future value factor is generally found on a table that is
used for quick calculations for amounts greater than one dollar. With this example, assume
that an individual is attempting to calculate the value after one year for the amount of $500
today based on a 12% nominal annual rate compounded monthly. By looking at the future
value factor table, the individual would find 1.1268. Since this factor is based on $1, the
factor can then be multiplied by the $500 to find a future value of $563.40.

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.
Example:

$1000 in a money market account that earns 20% in year one, 6% in year two, and
1% in year three.
It would be incorrect to use the arithmetic mean of adding the rates together and
dividing them by three. With this example, the arithmetic mean would be 9%, as shown by
summing the rates and dividing by three. By incorrectly using this method, the ending
balance of 9% per year would return a balance of $1295.03.
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21
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
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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

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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.

Growing Perpetuity- PV

.
A growing perpetuity is a series of periodic payments that grow at a proportionate
rate and are received for an infinite amount of time. An example of when the present value
of a growing perpetuity formula may be used is commercial real estate. The rental cash
flows could be considered indefinite and will grow over time.
Example:
An annual cash flow of $1000 that will continue indefinitely. This cash flow is
expected to grow at 5% per year and the required return used for the discount rate is 10%.
The equation for this example of the present value of a growing perpetuity formula would
be

which would return a present value of $20,000.

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H
Holding Period Return


Or,

The formula for the holding period return is used for calculating the return on an
investment over multiple periods.
If the periodic rates are unknown, the holding period return could be calculated
with the following formula

Earnings include dividends. The appreciation of an asset, also referred to as capital
gains, would be the increase in value of the asset which would be calculated by subtracting
the initial value of the investment from the ending value.
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.




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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.