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Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
1
S TAY CNG THC, THUT NG TI
CHNH C GII THCH TING VIT
DNH CHO SINH VIN I HC CHUYN NGNH
K TON TI CHNH
(dnh cho sinh vin )
Nhm tc gi: ng c Vit
Ng Th Thanh Thy
Hiu nh: PGS.TS. Nguyn Hi Thanh
Th.S.CFA. on Anh Tun
Th.S Chu Vn Hng
H Ni, 2011
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
2
Li gii thiu
Cc bn sinh vin thn mn,
Trn tay cc bn l cun S tay cng thc, thut ng ti chnh c gii thch ting
Vit dnh cho sinh vin i hc chuyn ngnh k ton - ti chnh. y l kt qu ca cng
trnh nghin cu khoa hc sinh vin do hai bn sinh vin ng c Vit v Ng Th
Thanh Thy, kha 6 i hc Help, Malaysia thc hin. Cng trnh nghin cu ny rt vinh
d c l mt phn ng gp vo dp k nim cho mng 10 nm thnh lp Khoa Quc
t - i hc Quc gia H Ni. Cng trnh ny c thc hin vi mc ch cung cp mt
ti liu tra cu cc thut ng v cng thc h tr cho cc bn sinh vin trong qu trnh hc.
Ni dung ca cun s tay bao gm 2 phn: cng thc ti chnh bng ting anh i km v d
v thut ng ti chnh , k ton Anh Vit c gii thch bng ting Vit. Cc bn c th tra
cu cc cng thc v thut ng ting Vit tng ng ca cc thut ng hoc cng thc
ting Anh m cc bn gp trong qu trnh hc tp, cc thut ng v cng thc u c sp
xp theo th t trong bng ch ci. Do hn ch v thi gian nn cun s tay ny khng th
trnh khi nhng sai st v hn ch nht nh, chng ti rt mong nhn c nhng kin
ng gp ca cc bn sinh vin v cc thy c gio cun s tay ny c hon thin
hn. Chc cc bn lun t kt qu cao v sng to trong hc tp.
H Ni, thng 7 nm 2011
Nhm bin son s tay.
Mi thng tin gp xin vui lng gi: [email protected]
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
3
MC LC
1. T in cng thc.....3
2. T in thut ng48
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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,
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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:
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
8
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
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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%.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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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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
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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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.
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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.
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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
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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.
N
Net Asset Value
Example:
A mutual fund with assets of $1 million, liabilities of $100,000, and 100,000
outstanding shares. Putting this information into the variables of the net asset value
formula would show
which would return $9 per share.
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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.
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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
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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
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Perpetuity
Or,
Or,
A perpetuity is a type of annuity that receives an infinite amount of periodic
payments. An annuity is a financial instrument that pays consistent periodic payments. As
with any annuity, the perpetuity value formula sums the present value of future cash flows.
Example:
An individual is offered a bond that pays coupon payments of $10 per year and
continues for an infinite amount of time. Assuming a 5% discount rate, the formula would
be written as
After solving, the amount expected to pay for this perpetuity would be $200.
Preferred Stock
The formula shown is for a simple straight preferred stock that does not have
additional features, such as those found in convertible, retractable, and callable preferred
stocks.
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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.
Present Value
Or,
Present Value (PV) is a formula used in Finance that calculates the present day
value of an amount that is received at a future date. The premise of the equation is that
there is "time value of money".
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 C1 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.
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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
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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.
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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.
Q
Quick Ratio
Or,
The Quick Ratio is used for determining a company's ability to cover its short term
debt with assets that can readily be transferred into cash, or quick assets. The Current
Liabilities portion references liabilities that are payable within one year.
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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.
Example:
An individual who wants to determine how much goods they can buy at the end of
one year after leaving their money in a money market account that earns interest.
For this example of the real rate of return formula, we must assume that the
individual wants to purchase the exact same goods and same proportion of goods that the
consumer price index uses considering that it is used often to measure inflation.
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
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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
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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:
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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 clichs about diversifying your investment portfolio is derived
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Risk Premium on a Stock Using CAPM
The risk premium of a particular investment using the capital asset pricing model is
beta times the difference between the return on the market and the return on a risk free
investment.
As noted earlier, the return on the market minus the return on a risk free investment
is called the market risk premium. From here, the capital asset pricing model can be
rewritten as
Rule of 72
The Rule of 72 is a simple formula used to estimate the length of time required to
double an investment. The rule of 72 is primarily used in off the cuff situations where an
individual needs to make a quick calculation instead of working out the exact time it takes
to double an investment. Also, one is more likely to remember the rule of 72 than the exact
formula for doubling time or may not have access to a calculator that allows logarithms.
Example of Rule of 72
An individual is earning 6% on their money market account would like to estimate
how long it would take to double their current balance. In order for this estimation to be
remotely accurate, we must assume that there will be no withdrawals nor deposits into this
account. We can estimate that it will take approximately 12 years to double the current
balance after dividing 72 by 6.
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S
Simple Interest
The simple interest formula is used to calculate the interest accrued on a loan or
savings account that has simple interest. The simple interest formula is fairly simple to
compute and to remember as principal times rate times time.
Ending Balance with Simple Interest Formula
The ending balance, or future value, of an account with simple interest can be
calculated using the following formula:
Using the prior example of a $1000 account with a 10% rate, after 3 years the
balance would be $1300. This can be determined by multiplying the $1000 original
balance times [1+(10%)(3)], or times 1.30.
Instead of using this alternative formula, the amount earned could be simply added
to the original balance to find the ending balance. Still using the prior example, the
calculation of the formula that is on the top of the page showed $300 of interest. By adding
$300 to the original amount of $1000, the result would be $1300.
Present Value of Stock - Constant Growth
While,
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Required Rate of Return in the Present Value of Stock Formula
The required rate of return variable in the formula for valuing a stock with constant
growth can be determined by a few different methods.
One method for finding the required rate of return is to use the capital asset pricing model.
The capital asset pricing model method looks at the risk of a stock relative to the
risk of the market to determine the required rate of return based on the return on the
market.
Another method that can be used is to determine the required rate of return based
on the present value of dividends. This method also uses the present value of a growing
perpetuity formula and rearranges the formula to calculate the required rate of return. After
rearranging the formula, it is shown as
Which is the dividend yield + growth rate.
The formula for the present value of a stock with constant growth is the estimated
dividends to be paid divided by the difference between the required rate of return and the
growth rate.
The arbitrage pricing theory can also be used which is similar to the capital asset
pricing model but uses various risk factors and the betas for each risk factor to determine
the total risk premium for the stock.
T
Tax Equivalent Yield
The tax equivalent yield formula is used to compare the yield between a tax-free
investment and an investment that is taxed. One of the most common examples of a tax-
free investment is municipal bonds. Municipal bonds are generally issued by local
governments to finance development in its local community.
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Example of Tax Equivalent Yield
An investor who must decide between a bond that pays 6% that is taxed and a bond
that pays 4% but earnings are tax free. His marginal tax rate is 33%. In order to compare
the yield of these two investments, the equation for this example using the tax equivalent
yield formula would be
After solving the formula, the equivalent yield for 4% would be 6.06%. This rate is
higher than the 6% rate from the bond that is taxed and will give a higher after-tax return.
Total Stock Return
Or,
The formula for the total stock return is the appreciation in the price plus any
dividends paid, divided by the original price of the stock. The income sources from a stock
is dividends and its increase in value. The first portion of the numerator of the total stock
return formula looks at how much the value has increased (P1 - P0). The denominator of the
formula to calculate a stock's total return is the original price of the stock which is used due
to being the original amount invested.
Total Stock Return Cash Amount
.
For example, assume that an individual originally paid $1000 for a particular stock
that has paid dividends of $20 and the ending price is $1020. The total return would be $40
which equals $1020 minus $1000, then plus $20.
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Example of the Total Stock Return Formula
Using the prior example, the original price is $1000 and the ending price is $1020.
The appreciation of the stock is then $20. The $20 in price appreciation can then be added
to dividends of $20 which would equal a total return of $40. This can then be divided by
the original price of $1000 which would equal a percentage return of 4%..
W
Weighted Average
The weighted average formula is used to calculate the average value of a particular
set of numbers with different levels of relevance. The relevance of each number is called
its weight. The weights should be represented as a percentage of the total relevancy.
Therefore, all weights should be equal to 100%, or 1.
Example:
An investor who would like to determine his rate of return on three investments.
Assume the investments are proportioned accordingly: 25% in investment A, 25% in
investment B, and 50% in investment C. The rate of return is 5% for investment A, 6% for
investment B, and 2% for investment C. Putting these variables into the formula would be
Which would return a total weighted average of 3.75% on the total amount
invested. If the investor had made the mistake of using the arithmetic mean, the incorrect
return on investment calculated would have been 4.33%. This considerable difference
between the calculations shows how important it is to use the appropriate formula to have
an accurate analysis on how profitable a company is or how well an investment is doing.
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Y
Yield to Maturity
The yield to maturity formula is used to calculate the yield on a bond based on its
current price on the market. The yield to maturity formula looks at the effective yield of a
bond based on compounding as opposed to the simple yield which is found using the
dividend yield formula.
Notice that the formula shown is used to calculate the approximate yield to
maturity. To calculate the actual yield to maturity requires trial and error by putting rates
into the present value of a bond formula until P, or Price, matches the actual price of the
bond. Some financial calculators and computer programs can be used to calculate the yield
to maturity.
Example:
The price of a bond is $920 with a face value of $1000 which is the face value of
many bonds. Assume that the annual coupons are $100, which is a 10% coupon rate, and
that there are 10 years remaining until maturity. This example using the approximate
formula would be
After solving this equation, the estimated yield to maturity is 11.25%.
Yield to Maturity and Present Value of a Bond
The yield to maturity is found in the present value of a bond formula:
For calculating yield to maturity, the price of the bond, or present value of the
bond, is already known. Calculating YTM is working backwards from the present value of
a bond formula and trying to determine what r is.
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Example of YTM with PV of a Bond
Using the prior example, the estimated yield to maturity is 11.25%. However, after
using this rate as r in the present value of a bond formula, the present value would be
$927.15 which is fairly close to the price, or present value, of $920. Other examples may
have a larger difference.
A higher yield to maturity will have a lower present value or purchase price of a
bond. In this example, the estimated yield to maturity shows a present value of $927.15
which is higher than the actual $920 purchase price. Therefore, the yield to maturity will
be a little higher than 11.25%.
Through trial and error, the yield to maturity would be 11.38%, which is found by
adjusting each estimated rate until the present value equals the price of the bond.
Excel is helpful for the trial and error method by setting the spreadsheet so that all
that is required to determine the present value is adjusting a fixed cell that contains the
rate.
Z
Zero Coupon Bond Value
Example:
A 5 year zero coupon bond is issued with a face value of $100 and a rate of 6%.
Looking at the formula, $100 would be F, 6% would be r, and t would be 5 years.
After solving the equation, the original price or value would be $74.73. After 5
years, the bond could then be redeemed for the $100 face value.
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Example of Zero Coupon Bond Formula with Rate Changes
A 6 year bond was originally issued one year ago with a face value of $100 and a
rate of 6%. As the prior example shows, the value at the 6% rate with 5 years remaining
would be $74.73. In this example, we suppose that the interest rates have changed to 5%
since it was originally issued. The formula would be shown as
After solving the equation, the value would be $78.35.
Zero Coupon Bond Effective Yield
.
Zero Coupon Bond Effective Yield Formula vs. BEY Formula
The zero coupon bond effective yield formula shown up top takes into
consideration the effect of compounding. For example, suppose that a discount bond has
five years until maturity. If the number of years is used for n, then the annual yield is
calculated. Considering that multiple years are involved, calculating a rate that takes time
value of money and compounding into consideration is needed. An investment that pays
10% per year is not equivalent to a 10 year discount bond that pays a 100% return after ten
years. The investment that pays 10% can be reinvested and by compounding the returns(or
considering the time value of money), the total return after 10 years would be
Which would equal 259%.
In contrast, the formula for the bond equivalent yield does not take compounding
into consideration. For this reason, the formula for bond equivalent yield is primarily used
to compare discount bonds of short maturity, specifically less than one year.
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A
Abnormal Return: thu nhp bt thng, li nhun siu ngch
L khon li nhun c bit vt qu li nhun bnh qun m ch x nghip thu
c trong mt thi gian nht nh trong qu trnh cnh tranh do s dng nhng thit b, k
thut v cng ngh tin b, u t vo cc ngnh sn xut mi. Khi cc ch x nghip khc
cnh tranh v nm c k thut mi th li nhun c bit trn khng cn na v lc s
hnh thnh t sut li nhun bnh qun.
Trn th trng chng khon, thu nhp bt thng l phn chnh lch gia kt qu
u t ca mt danh mc u t nht nh vi kt qu hot ng ca th trng, thng
c hiu l cc ch s chng khon ni ting nh S&P 500, EURO STOXX 50 hay cc
ch s chng khon quc gia nh Nikkei 225 trong mt khong thi gian nht nh.
Accounting book value: gi tr s sch
L gi tr c rt ra t vic xc nh gi tr cc ti sn. Gi tr s sch ca mt
cng ty l gi tr ca ton b ti sn (tin, nh xng, trang thit b, nguyn vt liu)
c th hin trn s k ton tr i tt c cc khon n v khng bao gm li.
Accounts payable: khon phi tr
L nhng ti khon th hin ngha v phi thanh ton cc khon n ca cng ty i
vi cng ty hoc c nhn khc trn Bng cn i k ton. Thut ng ny thng c s
dng ph bin USA - trong khi thut ng creditors c s dng rng ri ti UK.
Accounts receivable: khon phi thu
L s tin khch hng n doanh nghip do mua chu hng ha hoc dch v.
Accounts receivable turnover ratio: vng quay khon phi thu
Vng quay cc khon phi thu phn nh tc bin i cc khon phi thu thnh
tin mt. H s ny l mt thc o quan trng nh gi hiu qu hot ng ca doanh
nghip, c tnh bng cch ly doanh thu trong k chia cho s d bnh qun cc khon
phi thu trong k.
Vng quay cc khon phi thu hoc k thu tin bnh qun cao hay thp ph thuc
phn nhiu vo chnh sch tn dng nh bn chu, tr chm ca doanh nghip. Nu s vng
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quay khon phi thu thp th hiu qu s dng vn km do vn ca doanh nghip b cc
doanh nghip khc chim dng nhiu. Ngc li, nu s vng quay khon phi thu cao qu
th s gim sc cnh tranh trong hot ng kinh doanh ca doanh nghip, dn ti gim
doanh thu.
Accrued expenses: chi ph tnh dn
L cc chi ph nh tin lng cng nhn v li giy bo n tch t, ngy ny qua
ngy khc, nhng cha ghi s hoc cha thanh ton vo cui k. Cc chi ph ny cn gi l
chi ph cha ghi s.
Acid test (quick) ratio: t s thanh khon nhanh
T s ny cho thy kh nng thanh ton thc s ca doanh nghip. T s thanh
ton nhanh cho bit rng nu hng tn kho ca cng ty b ng, khng ng gi th cng
ty s lm vo kh khn ti chnh gi l khng c kh nng chi tr. iu ny xy ra khi
mt cng ty khng tin tr cc khon n khi chng n hn.
T s thanh khon nhanh c xc nh da vo thng tin t bng cn i ti sn
nhng khng k gi tr hng tn kho vo trong gi tr ti sn lu ng khi tnh ton (nhng
ti sn lu ng c th nhanh chng chuyn i thnh tin), i khi chng c gi l Ti
sn nhanh.
Active account: ti khon hot ng tch cc.
L ti khon c s k thc v s rt tin thng xuyn cp nht trong thi khong
k ton. Ngoi ra, l ti khon th tn dng hay Mc Tn Dng Ngn hng cho bit s
vn v s chi tr tin li o hn trn bo co ti khon khch hng.
Active bond crowd: nhm mua bn tri phiu tch cc.
L nhm d phng, tc l nhm mua bn loi tri phiu t khi c a ra mua
bn. Nh u t mua bn tri phiu trong nhm tch cc s c c hi mua chng khon l
tri phiu vi gi tt hn l trn th trng tr tr v th trng ny chnh lch gia gi
t mua v gi t bn rt xa.
Active box: trong kho tn tr nng ng - tnh nng ng ca chng khon th chp.
Th chp c sn bo m cho s tin vay ca ngi mi gii hay cho v th ti
khon cn bin ca khch hng - ti khon vay tin mua chng khon, mt ni -
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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gi l hp an ton tc l ni chng khon ca khch hng ca ngi mi gii hay ca
chnh ngi mi gii mua bn cho chnh mnh c gi an ton.
Active market: th trng nng ng, th trng mua bn tch cc.
Th trng mua bn mt s lng ln chng khon tri phiu hay hng ha. Chnh
lch gia gi t mua v gi t bn khng cch xa my trong th trng nng ng, t hn
trong mua bn m thm. Ngoi ra, s lng chng khon mua bn trn th trng theo
tng l ln. Cc nh qun l t chc thch loi th trng ny v vic mua bn theo tng l
ln chng khon s t c nh hng lm xo trn bin chuyn gi c khi vic mua bn c
tnh tch cc.
Active trust: u thc ton quyn.
Ti khon y thc trong ngi nhn y quyn c bn phn c bit n nh
thc hin y quyn di chc do mt chc th ra. Ngi nhn y quyn c thm quyn
bn ti sn tr cho ngi ch n v phn phi ti sn cho nhng ngi tha k.
Activity charge: ph hot ng.
L ph tr vo ti khon ngn hng thanh ton gi ph dch v. Vi ph hot ng
s tng vt ln khi s cn i ti khon rt xung thp hn mt mc no , th d nh ph
dch v hng thng trn ti khon chi phiu.Cc ph khc l ph giao dch mua bn da trn
vic s dng ti khon, th d ph tng hng mc trong vic vit chi phiu hay ph dch v
trong vic rt tin bng my t ng.
Adjustable rate preferred stock: c phiu u i li sut iu chnh
Chng khon u i iu chnh chi tr c tc c iu chnh, thng theo tng qu,
da trn s thay i li sut tri phiu chnh ph hay li sut th trng tin t.
Thay i v c tc thng c tnh ton bng mt cng thc xc nh trc. Gn
ging nh cc loi n c li sut th ni, th c phiu u i iu chnh t l c tc thng
c gi n nh v c tc c th c iu chnh b tr cho bin ng gi. Thng thng
vn c mt khong gii hn nht nh c t ra i vi vic iu chnh t l c tc lm
cho loi c phiu ny an ton hn.C phiu u i loi ny hay c pht hnh b sung c
m bo bng th chp hoc bng c phiu bo m khc, tng cng vn cho cc d
n.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
52
After hours deal: giao dch sau gi chnh thc, sau gi ng ca.
L giao dch mua bn trn th trng chng khon kt thc sau khi ng ca
chnh thc mua bn. Thng thng mua bn ny c ghi nhn bo co vo ngy hnh
chnh k tip.
After sight: sau khi thy, sau khi trnh ra.
Thng bo rng hi phiu hay giy bo tr tin s c chi tr sau khi n c
trnh ra nhn chi tr. Ngi bn vn cn quyn s hu s hng ha ang vn chuyn
cho n khi chng t vn chuyn c trnh cho ngn hng chi tr v ngn hng ny chp
nhn.
Aftermarket: th trng sau khi pht hnh.
Mua bn c phn trn th trng chng khon sau khi cng ty pht hnh c phn ra
cng chng. Gi c ca c phn lc ny tng hay gim ty theo cung cu th trng, khng
cn theo gi cn bn nh lc cng ty mi pht hnh c phn.
Aftertax real rate of return: t l li nhun thc sau thu.
T l li nhun thc sau thu l thut ng dng ch s tin m nh u t c
c sau khi iu chnh theo lm pht. S tin ny xut pht t li tc v t bn kim
c trong cc v u t.
Khi xy ra lm pht, gi tr ca ng tin u mt i mt phn, bi vy nh u t
phi theo di t l li nhun thc sau khi ng thu k t khi cam kt v vn. Nh u t
s tm mt t l li nhun tng xng nu khng ni l vt hn t l lm pht.
Agency costs: chi ph y quyn, cc chi ph i l, chi ph i din
L cc chi ph pht sinh t vic thu mt i l thc hin vic ra quyt nh thay
cho bn u thc. Ni cch khc, ngi u quyn, chnh l cc c ng, phi tm cch no
m bo ngi c u quyn (cc nh qun l) hnh ng v quyn li ca ngi
u quyn. Mun t c iu ny cc c ng phi b ra cc "chi ph u quyn" gim
st hot ng ca cc nh qun l v to ra nhng c ch khuyn khch cc nh qun l
theo ui vic ti a ho li ch cho cc c ng ch khng phi ch v li ch c nhn.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Agency problem: vn i din
Vic u quyn gy s tch ri hay s chia ct quyn s hu v quyn qun l mt
doanh nghip. S tch ri gia quyn s hu v quyn qun l doanh nghip lm ny sinh
cc mi lo ngi rng, nhng ngi qun l s theo ui nhng mc tiu rt hp dn i vi
h, song cha chc c li cho cc c ng, cho cng ty.
Allowance: tin chit khu, tin tr cp, tin khu tr.
1. K ton: Ti khon iu chnh tr gi ti sn thng qua ph ca li tc hin
hnh, y l s d tr cho khu hao.
2. Ngn hng: D tr tin vay b mt dng cho s ph s mt theo d kin i vi
n kh i.
3. U thc: Chng thc di chc quyt nh s an ton cho ngi nhn y quyn v
ti sn; th d nh tin tr cp cho ngi ga ba.
4. Mua bn: Khu tr tr gi ho n c ngi bn hng ha chp nhn b
p vo s h hi hay thiu st.
Alpha: h s Alpha.
L mt thc o t sut sinh li da trn ri ro c iu chnh. Alpha ly s
bin ng trong t sut sinh li ca mt qu tng h v so snh t sut sinh li iu
chnh ri ro ca qu vi ch s ca mt danh mc chun. T sut sinh li vt tri ca
qu trong tng quan vi t sut sinh li ca ch s danh mc chun c gi l alpha ca
qu .
Mt alpha dng 1 c ngha l qu c s th hin tt hn ch s danh mc
chun ca n 1%. Tng t nh th, mt alpha m 1 c ngha l qu th hin km
hn ch s danh mc chun ca n 1%
Altered check: chi phiu b sa i.
L chi phiu hay cng c chi tr khc c ngy o hn, s tin hay tn ngi c
tr tin b sa i hay bi xo, hnh ng ny thng nhm mc ch la o. Khi nhn
c chi phiu ny, ngn hng c th t chi chi tr phiu nu nghi ng c s co sa t .
American-style option: hp ng quyn chn theo kiu M
Hp ng quyn chn c thc hin bt c lc no min l trc ngy o hn,
khc vi kiu chu u l phi i n ngy o hn ch khng c thc hin trc.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Amortization schedule: lch trnh tr gp.
Bng thng thng dng trong th chp v tin vay tr gp, cho bit s chi tr o
hn, s tin o hn trong mi k tr gp, gim s cn i vn, s nm cn thanh ton
ht s n.
Amortized loan: n tr gp
L phng thc cho vay m theo cc k tr n gc v li trng nhau, s tin tr
n ca mi k l bng nhau, s li c tnh trn s d n gc v s ngy thc t ca k
hn tr n.
Annual general meeting (AGM): i hi thng nin, i hi ng c ng
L mt cuc hp hng nm ca cc c ng gip cc c ng nm thng tin v hot
ng ca cng ty v cc vn lin quan n cc quyt nh v cng vic ca cng ty.
i hi ng c ng l dp cc c ng cht vn Hi ng qun tr nhng vn
v cng vic kinh doanh ca doanh nghip. Xt v mt quyn lc, i hi ng c ng
v tr cao hn Hi ng qun tr bi v h l ngi b nhim ra cc thnh vin trong Hi
ng qun tr.
Annual percentage rate (APR): t l phn trm theo nm, li sut phn trm bnh qun
nm.
L li sut theo nm ca mt khon vay mn, hoc u t, biu din di dng
mt con s phn trm th hin chi ph theo nm thc s ca qu trong sut thi gian vay.
N bao gm bt k ph hay chi ph ph tri no lin quan n giao dch.
Annual percentage yield (APY): t sut thu nhp nm
L t sut li nhun thc t theo nm, c tnh n tc ng ca li sut kp. Bao gi
APY cng ln hn APR (t sut li nhun nm), v APR ch tnh li sut n. APY cha
tnh n chi ph giao dch khi cho vay, i vay, hay chi ph mi gii chng khon. Cc ngn
hng thng nim yt li sut kp hp dn khch hng n gi tin.
Annuity: dng nin kim
L dng tin bao gm cc khon thu bng nhau xy ra trong cc thi k nh nhau.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Mt sn phm ti chnh ca cc nh ch ti chnh, c th c nhn t mt c
nhn. y l chui cc khon li c gi tr bng nhau tr nh k theo cc giai on bng
nhau. Li tc dng nin kim thng c tr vo cui mi giai on. Nin kim thng
c s dng nh mt cng c m bo lu lng tin mt n nh cho mt c nhn
trong nhng nm ngh hu.
Apportionment: s phn chia.
Phn chia gii tuyn cc quyn, s hu ch hay chi ph gia ngi mua v ngi
bn trong chuyn nhng ti sn. Trong y thc v ti sn, y l s phn chia li tc v
chi ph qun l gia hai hay nhiu ti khon, th d vn v li tc tin li hay phn chia
thu ti sn gia nhng ngi th hng ti sn. Ngc li phn chia l phn b, l li
nhun kim c hay chi ph c a vo mt ti khon c nht nhm kt ton.
Appraisal: nh gi d tnh.
Bng c tnh gi tr th trng ca ti sn do chuyn vin nh gi thit lp da
trn phn tch cc d kin xc thc. Gi tr th trng ca ti sn thng dng lm c s
xc nh gi tr th chp ngn hng cho vay, n c th da trn chi ph thay th, doanh
thu so vi ti sn hay li tc d tnh trong tng lai t s ti sn.
Appraisal costs: nh gi theo chi ph
Phng php ny tnh ton chi ph sn xut v cung ng sn phm hoc dch v v
cng thm phn trm li nhun mong mun. Phng php nh gi ny thch hp hn vi
cc doanh nghip ln hoc nhng doanh nghip hot ng trn mt th trng ch yu
bng gi. Phng php nh gi theo chi ph khng tnh n hnh nh thng hiu v v th
th trng ca doanh nghip. Hn na, khon chi ph ngm c th b qun v th li nhun
thc s thng thp hn mc d ton.
Appraisal value: nh gi theo gi tr
Phng php nh gi ny xc nh gi cho sn phm hoc dch v mc m
khch hng sn sng chi tr, cn c vo nhng li ch h c c t vic tiu dng sn
phm hoc dch v. Nu p dng phng php ny, cn cn nhc nhng li ch c th
mang li cho khch hng v nh gi ca khch hng v nhng li ch ch khng phi
l cc c tnh ca sn phm.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Appreciation: tng gi tr.
1. Tng gi tr ti sn do tng gi tr trn th trng, c nh gi tng, hay tng
li tc kim c khi so vi thi k trc.
2. Tng gi tr mt loi tin t no so vi loi tin t khc m khng c bt c
thay i gi tr chnh thc no c ngha l do nhu cu th trng i hi ch khng phi do
ph gi tin t.
Approved list: bng danh sch c duyt.
1. Ngn hng: tri phiu hay chng khon m ngn hng c th gi li u t,
thng thng cn c trn vic nh gi ca cng ty nh gi tn nhim nh Standard
Poors, Moodys, Fitch v cc cng ty khc. Lut l d tr lin bang gii hn u t ca
ngn hng quc gia trong vic ch c u t vo tri phiu, chng khon c cp u
t c cc cng ty nh gi tn nhim xc nh. Th d, cc tri phiu, chng khon
c Standard Poors nh gi t BBB tr ln. Cc ngn hng cp tiu bang c giy php
kinh doanh cp tiu bang cng chu l thuc quy nh u t nh th, ging ngn hng
quc gia theo o lut d tr lin bang.
2. u t: bng danh sch u t c giao cho ngi nhn y quyn ti sn theo
quy ch tiu bang hay do ban qun tr qu tng h u t thc hin.
Arbitrage: kinh doanh chnh lch gi hoc t gi
Mt phng php mua v bn chng khon ni ring v cc cng c ti chnh ni
chung tranh th mc chnh lch nh v gi. Thut ng kinh doanh chnh lch ri ro
xut hin p dng cho nhng ngi kinh doanh u c mua c phiu ca cc cng ty c
tin n l mc tiu b mua li, vi hy vng kim li khi vic chuyn nhng hon tt.
Arbitrageurs: ngi kinh doanh chnh lch gi
Ngi lm dch v mua v bn cng lc cng mt loi c phn, tin t... nhm vo
s chnh lch gi c gia hai th trng kim li.
Arbitrage Pricing Theory (APT): l thuyt kinh doanh chnh lch gi, l thuyt nh gi
trong iu kin kinh doanh chnh lch gi
L mt m hnh cng c ti chnh v hnh vi u t da trn gi nh rng nu
phn thu hi ca ti sn u t c th c miu t qua cc cu trc cha cc nhn t chnh
hay cc m hnh, phn li nhun d tnh ca mi ti sn trong danh mc u t c th
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
57
c biu din qua s kt hp ca cc hip phng sai ca cc nhn t v cc phn li ca
ti sn. Cc nhn t c th l bt k hoc l cc bin s kinh t v m, nh t sut li nhun,
lm pht, sn xut cng nghip, v.v.. M hnh yu t kt qu c th c s dng to ra
cc danh mc u t theo st ch s th trng, d on v theo di cc ri ro ca mt
chin lc phn b ti sn, hoc d on cc phn ng c th xy ra ca mt danh mc
u t i vi s pht trin kinh t.
Arbitration: trng ti.
Mt hnh thc khc thay cho v kin ti ta n, nhm dn xp tranh chp gia
ngi mi gii v khch hng cng nh gia cc cng ty mi gii chng khon. Theo
thng l cc iu khon phn x trc cc tranh chp c ghi trong tha hip ti khon
vi ngi mi gii, n m bo rng cc tranh chp s c phn x bi bn th ba c tnh
khch quan v khng a ra ta n.
Arms length transaction: giao dch mua bn ngoi
Giao dch mua bn gia nhng ngui cha bit nhau. l trng hp mt ngi
mua sn sng mua v mt ngi bn sn sng bn, mi bn u v li ch ca ring mnh.
Gi c trong giao dch mua bn ny cn c trn tr gi th trng.
ASEAN Free Trade Area (AFTA): khu vc Mu dch T do ASEAN,
L mt tho thun thng mi gia cc nc trong khu vc ng Nam . Quyt
nh thnh lp AFTA c a ra ti Hi ngh Thng nh ASEAN ln th 4, t chc
vo thng 1/1992 ti Singapore. Mc tiu ca AFTA l t do ha thng mi trong cc
nc ASEAN thng qua vic gim n mc ti thiu cc biu thu trong khu vc v xa
b cc hng ro phi thu quan, thu ht u t nc ngoi vo khu vc v khuyn khch cc
ngnh kinh t ASEAN c mt nh hng rng hn v mang tnh th trng khu vc hn
cho cc nn kinh t trong lnh vc sn xut v th trng.
Asked price: gi cho bn
L gi m mt chng khon hay hng ha c cho bn trao i trn th
trng. Ni chung, y l gi thp nht m ngi bn chp nhn bn mt chng khon
ti mt thi im nht nh.
Asset allocation: phn b ti sn
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Phn b danh mc u t hp l vo cc ti sn khc nhau c th gip cn bng
gia ri ro v li nhun. a dng ho danh mc u t s gip t b tn tht do bin ng
bt li ca th trng gy ra hn l ch u t vo mt loi chng khon hay mt loi ti
sn n l. Bn cnh , danh mc u t c a dng ho cng gip t c k hoch
u t lu di
Asset backed securities (ABS): chng khon c m bo bng ti sn
L mt loi chng khon c pht hnh trn c s c s m bo bng mt ti sn
hoc mt dng tin no t mt nhm ti sn gc ca ngi pht hnh. Cu trc ca
chng khon bo m bng ti sn gn nh ging ht chng khon bo m bng th chp.
im khc bit c bn gia hai loi ny l ti sn m bo, vi chng khon
m bo bng th chp l bt ng sn, cn vi chng khon bo m bng ti sn l cc
dng tin hay ni cch khc l cc khon m doanh nghip c quyn hng trong tng lai
nh tin tr gp mua t, mua nh; tin li t ti khon th tn dng...
Asset transformers: chuyn i ti sn
i l trung gian to ra chng khon trung gian huy ng ngun tin tit kim
v kch thch u t. Ngi i vay cui cng pht hnh chng khon s cp ti i l trung
gian, sau i l trung gian bn li chng khon trung gian cho nh u t ban u.
Assumable mortgage: th chp n c sang tay.
Th chp cho ngi vay c quyn k chuyn nhng s n cn thiu trong tng s
n n ngi khc trn c s s tin bn ti sn th chp, m khng b tr tin pht trc.
Ngi mua chp nhn chi tr s tin vay ng thi hn v cc iu khon cho phn cn li
ca th chp v ngi bn vn chu trch nhim th cp i vi s n.
Assumed interest rate: li sut c tha nhn.
T l li tc u t c ty thuc vo cch chn la phng thc bo him nhn
th - duy tr tr tin khng c g thay i khi cht.
Assumption: m nhim, m ng.
Lin i chu trch nhim cc mn n ca ngi khc, thng thng bng tha
hip m nhim trong trng hp m nhim v th chp. Ngi bn chu trch nhim th
cp tr khi ngi cho vay khng bt buc.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
59
At par: theo mnh gi.
Gi bng vi mnh gi hay gi danh ngha ca chng khon.
At limit: theo gi gii hn.
Nh u t ch th cho ngi mi gii mua hay bn chng khon hay hng ha theo
gi n nh. Theo giao dch mua bn vi gi gii hn, nh u t cng cho bit thi hn
ngi mi gii mua bn th d, trong vng 2 ngy.
At risk: ang c ri ro.
Cho thy c nguy c thua l. Nh u t gp vn trch nhim hu hn c th i
quyn c khu tr thu ch khi no h c th chng minh rng h c kh nng nhn bit
nhng ci khng th nhn bit c v li nhun v thua l trong u t. Khng th thc
hin c khu tr nu thnh vin gp vn khng c thng bo y v ri ro kinh t
th d, nu Tng thnh vin bo m s tr li ton b vn cho thnh vin gp vn d cho
vic kinh doanh mo him s thua l.
At the close: vo lc ng ca th trng chng khon.
Lnh mua v bn chng khon trong 30 giy cui ca mt v mua bn ti th
trng chng khon. Ngi mi gii khng bo m cc lnh nh th s c thc hin.
At the market: theo th trng.
Mua bn theo gi th trng khi ang thc hin giao dch mua bn.
At the money: gi tng ng, ho vn.
Theo gi hin hnh, nh trng hp mt hp ng quyn chn c gi thc hin
tng ng hay gn vi gi chng khon hay hp ng giao sau c s.
At the opening: vo lc m ca th trng chng khon.
Lnh ca khch hng a cho ngi mi gii mua hay bn chng khon theo
gi lc th trng m ca. Nu lnh khng c thc hin vo lc ny th s t ng hy
b.
Attachment: tch bin ti sn.
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Lnh trt c quyn thu gi ti sn sau khi ta n quyt nh phn quyt chi tr
cho ch n. Sau khi ta n xt x v quyt nh cng b, ch n phi c giy x l ti sn
c quyn thu gi mt phn lng cng nhn hay giy thu gi ti sn c nhn trong phm
vi quyn hn ni ngi vay c tr thng l th hay phn khu tiu bang. Giy c
quyn gi ti sn th chp, giy ny ni rng s c quyn tch thu ti sn ca ngi vay
thay cho s tin cho vay hay s tin ng trc da trn mc tn dng.
Auction: u gi
L mt qu trnh mua v bn bng cch a ra mn hng cn u gi, ra gi v sau
bn mn hng cho ngi ra gi cao nht. V phng din kinh t, mt cuc u gi l
phng php xc nh gi tr ca mn hng cha bit gi hoc gi tr thng thay i.
Trong mt s trng hp, c th tn ti mt mc gi ti thiu hay cn gi l gi sn; nu
s ra gi khng t n c gi sn, mn hng s khng c bn (nhng ngi a mn
hng ra u gi vn phi tr ph cho ni ngi ph trch vic bn u gi)
Auction method: hnh thc u gi
1. Theo mt hng u gi:
u gi trao i: gm nhng ngi mua rt chuyn nghip, h gim st ln nhau
khng ai c th "la lc" c.
u gi l: dnh cho tc phm ngh thut hay cc mn hng ring r.
u gi s: dnh cho cc b su tp.
2. Theo hnh thc u gi:
English Auction: u gi kiu Anh.
Dutch Auction: u gi kiu H Lan
Sealed first-price Auction (first-price sealed-bid Auction (FPSB)): u gi kn theo
gi th nht
Sealed-bid second-price Auction (Vickrey Auction): u gi kn theo gi th hai
(u gi Vickrey)
Silent Auction: u gi cm
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Bidding fee Auction (penny Auction): u gi kiu thu (u thu)
Buyout Auction: u gi nhng quyn
Reserve auction (reserve price): u gi gi trn
Multi-unit auctions: u gi t hp
Authorized investment: u t c y nhim.
u t do ngi c y quyn thc hin sau khi c ch th vit trong cng c y
thc. i chiu vi u t hp php tun theo lut l ca cc c quan thm quyn v ngn
hng tiu bang hay lut l tiu bang lin quan n cc u t c php thc hin bi cc
ngi c y quyn v ngn hng tit kim h tng u t.
Authorized settlement agent: ngi trung gian c y quyn thanh ton.
Ngn hng c y quyn trnh chi phiu hay chi phiu giao ngay cho ngn
hng d tr lin bang thu nhn. Trong lnh vc th ngn hng, ngn hng c y
quyn thanh ton hi phiu cho vic thanh ton trao i mua bn.
Authorizing resolution: ngh quyt y quyn.
V kin cho php c quan a phng hay chnh quyn a phng pht hnh cng
phiu.
Authorized shares stocks: c phn c thm quyn pht hnh.
S c phn ti a thuc bt c hng loi no trong cng ty c php pht hnh
theo cc iu khon thnh lp cng ty. Thng thng mt cng ty trong tng lai tng
chng khon c thm quyn pht hnh ty theo cc c ng b phiu quyt nh. Cng ty
khng cn phi pht hnh tt c cc c phn c thm quyn pht hnh v c th ngay t lc
u gi li ti thiu s c phn pht hnh h bt thu v chi ph. N cn c gi l
chng khon c thm quyn c pht hnh.
Automated clearing house ACH: thanh ton b tr t ng .
Phng tin thanh ton b tr da trn h thng my tnh i vi trao i bn N
v bn C theo h thng in t gia cc t chc ti chnh. D liu nhp ca ACH c th
c thay th cho chi phiu trong vic chi tr qua li nh th chp, hoc trong ng gp k
thc...
Bn quyn thuc v nhm tc gi, mi sa i b xung vui lng lin h. Xin cm n!
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Automatic stabilizers: cc bin php n nh t ng.
Cc bin php n nh t ng l cc mi quan h lm gim bin ca bin ng
chu k trong mt nn kinh t m khng cn hnh ng trc tip ca chnh ph.
Available credit: tn dng sn c.
Tn dng sn sng c dng mua mi mt ci g, i khi cn c gi l mua
ng. Trong lnh vc th ngn hng, c s khc bit gia s cn i cha tr bnh qun -
cn i hin hnh bnh qun v mc gii hn tn dng c cng nhn trc ca ngi
c th. Ngoi ra, y l phn cha c s dng ca mc tn dng ngn hng.
Available funds: qu sn c.
1. Loi qu ngn hng c th dng p ng yu cu v s trn vay hay c gi
trong danh mc u t, ty thuc vo s cnh tranh th trng, nhu cu tn dng, li sut
th trng v cc yu t khc. Tng s qu tng ng vi s tin mt c trong tay v chi
phiu c cc ngn hng khc chi tr tin mt v tin phi tr t cc ngn hng trn bng
cn i ti khon cng vi tng s tin vay v u t.
2. S cn i c trong ti khon ngi