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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]

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    3

    MC LC

    1. T in cng thc.....3

    2. T in thut ng48

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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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

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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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    25

    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 -

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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.

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    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.

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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.

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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.

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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.

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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

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    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

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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.

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    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.

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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

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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...

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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