Definition of rate of return

rate of return

Total income per period per dollar invested.

Rate of Return

return on invested capital (calculated as a percentage). Often an investor has, as one of their investment criteria, a minimum acceptable rate of return on an acquisition.

After-tax real rate of return

Money after-tax rate of return minus the inflation rate.

Arithmetic average (mean) rate of return

Arithmetic mean return.

Average rate of return (ARR)

The ratio of the average cash inflow to the amount invested.

Dollar-weighted rate of return

Also called the internal rate of return, the interest rate that will make the
present value of the cash flows from all the subperiods in the evaluation period plus the terminal market value
of the portfolio equal to the initial market value of the portfolio.

Incremental internal rate of return

IRR on the incremental investment from choosing a large project
instead of a smaller project.

Internal rate of return

Dollar-weighted rate of return. Discount rate at which net present value (NPV)
investment is zero. The rate at which a bond's future cash flows, discounted back to today, equals its price.

Money rate of return

Annual money return as a percentage of asset value.

Portfolio internal rate of return

The rate of return computed by first determining the cash flows for all the
bonds in the portfolio and then finding the interest rate that will make the present value of the cash flows
equal to the market value of the portfolio.

Rate of return ratios

Ratios that are designed to measure the profitability of the firm in relation to various
measures of the funds invested in the firm.

Riskless rate of return

The rate earned on a riskless asset.

Time-weighted rate of return

Related: Geometric mean return.

RATE OF RETURN ON STOCKHOLDERS’ EQUITY

The percentage return or profit that management made on each dollar stockholders invested in a company. Here’s how you figure it:
(Net income) / (Stockholders’ equity)

RATE OF RETURN ON TOTAL ASSETS

The percentage return or profit that management made on each dollar of assets. The formula is:
(Net income) / (Total assets)

Accounting rate of return (ARR)

A method of investment appraisal that measures
the profit generated as a percentage of the
investment – see return on investment.

Internal rate of return (IRR)

A discounted cash flow technique used for investment appraisal that calculates the effective cost of capital that produces a net present value of zero from a series of future cash flows and an
initial capital investment.

Target rate of return pricing

A method of pricing that estimates the desired return on investment to be achieved from the
fixed and working capital investment and includes that return in the price of a product/service.

internal rate of return (IRR)

The precise discount rate that makes the
present value (PV) of the future cash returns from a capital investment
exactly equal to the initial amount of capital invested. If IRR is higher
than the company’s cost-of-capital rate, the investment is an attractive
opportunity; if less, the investment is substandard from the cost-ofcapital
point of view.

Internal Rate of Return (IRR)

The discount rate that equates the present value of the net cash
inflows with the present value of the net cash outflows
(investments). The IRR measures the profitability (rate of return) of
an investment in a project or security.

accounting rate of return (ARR)

the rate of earnings obtained on the average capital investment over the life of a capital project; computed as average annual profits divided by average investment; not based on cash flow

internal rate of return (IRR)

the expected or actual rate of
return from a project based on, respectively, the assumed
or actual cash flows; the discount rate at which the net
present value of the cash flows equals zero

Internal rate of return

a. The average annual yield earned by an investment during the period held.
b. The effective rate of interest on a loan.
c. The discount rate in discounted cash flow analysis.
d. The rate that adjusts the value of future cash receipts earned by an investment so that interest earned equals the original cost.
See Yield to maturity.

Internal rate of return

The rate of return at which the present value of a series of future
cash flows equals the present value of all associated costs. This measure is most
commonly used in capital budgeting.

book rate of return

Accounting income divided by book value.
Also called accounting rate of return.

internal rate of return (IRR)

Discount rate at which project NPV = 0.

Multiple rates of return

More than one rate of return from the same project that make the net present value
of the project equal to zero. This situation arises when the IRR method is used for a project in which negative
cash flows follow positive cash flows. For each sign change in the cash flows, there is a rate of return.

discount rate

the rate of return on investment that would be required by a prudent investor to invest in an asset with a specific level risk. Also, a rate of return used to convert a monetary sum, payable or receivable in the future, into present value.

Alpha equation

The alpha of a fund is determined as follows:
[ (sum of y) -((b)(sum of x)) ] / n
where:
n =number of observations (36 months)
b = beta of the fund
x = rate of return for the S&P 500
y = rate of return for the fund

Annual percentage yield (APY)

The effective, or true, annual rate of return. The APY is the rate actually
earned or paid in one year, taking into account the affect of compounding. The APY is calculated by taking
one plus the periodic rate and raising it to the number of periods in a year. For example, a 1% per month rate
has an APY of 12.68% (1.01^12).

Annualized holding period return

The annual rate of return that when compounded t times, would have
given the same t-period holding return as actually occurred from period 1 to period t.

Asset pricing model

A model for determining the required rate of return on an asset.

Asset pricing model

A model, such as the Capital Asset Pricing Model (CAPM), that determines the required
rate of return on a particular asset.

Basis price

Price expressed in terms of yield to maturity or annual rate of return.

Beta equation (Mutual Funds)

The beta of a fund is determined as follows:
[(n) (sum of (xy)) ]-[ (sum of x) (sum of y)]
[(n) (sum of (xx)) ]-[ (sum of x) (sum of x)]
where: n = # of observations (36 months)
x = rate of return for the S&P 500 Index
y = rate of return for the fund

Beta equation (Stocks)

The beta of a stock is determined as follows:
[(n) (sum of (xy)) ]-[(sum of x) (sum of y)]
[(n) (sum of (xx)) ]-[(sum of x) (sum of x)]
where: n = # of observations (24-60 months)
x = rate of return for the S&P 500 Index
y = rate of return for the stock

Bull CD, Bear CD

A bull CD pays its holder a specified percentage of the increase in return on a specified
market index while guaranteeing a minimum rate of return. A bear CD pays the holder a fraction of any fall in
a given market index.

Corporate taxable equivalent

rate of return required on a par bond to produce the same after-tax yield to
maturity that the premium or discount bond quoted would.

Cost of lease financing

A lease's internal rate of return.

Country beta

Covariance of a national economy's rate of return and the rate of return the world economy
divided by the variance of the world economy.

Efficient Market Hypothesis

In general the hypothesis states that all relevant information is fully and
immediately reflected in a security's market price thereby assuming that an investor will obtain an equilibrium
rate of return. In other words, an investor should not expect to earn an abnormal return (above the market
return) through either technical analysis or fundamental analysis. Three forms of efficient market hypothesis
exist: weak form (stock prices reflect all information of past prices), semi-strong form (stock prices reflect all
publicly available information) and strong form (stock prices reflect all relevant information including insider
information).

Factor model

A way of decomposing the factors that influence a security's rate of return into common and
firm-specific influences.

Fisher effect

A theory that nominal interest rates in two or more countries should be equal to the required real
rate of return to investors plus compensation for the expected amount of inflation in each country.

Geometric mean return

Also called the time weighted rate of return, a measure of the compounded rate of
growth of the initial portfolio market value during the evaluation period, assuming that all cash distributions
are reinvested in the portfolio. It is computed by taking the geometric average of the portfolio subperiod
returns.

Holding period return

The rate of return over a given period.

Implied volatility

The expected volatility in a stock's return derived from its option price, maturity date,
exercise price, and riskless rate of return, using an option-pricing model such as Black/Scholes.

Intrinsic value of a firm

The present value of a firm's expected future net cash flows discounted by the
required rate of return.

Profitability ratios

Ratios that focus on the profitability of the firm. Profit margins measure performance
with relation to sales. rate of return ratios measure performance relative to some measure of size of the
investment.

Total return

In performance measurement, the actual rate of return realized over some evaluation period. In
fixed income analysis, the potential return that considers all three sources of return (coupon interest, interest
on interest, and any capital gain/loss) over some i nvestment horizon.

Treynor Index

A measure of the excess return per unit of risk, where excess return is defined as the
difference between the portfolio's return and the risk-free rate of return over the same evaluation period and
where the unit of risk is the portfolio's beta.

Yield

The percentage rate of return paid on a stock in the form of dividends, or the effective rate of interest
paid on a bond or note.

Yield to maturity

The percentage rate of return paid on a bond, note or other fixed income security if you
buy and hold it to its maturity date. The calculation for YTM is based on the coupon rate, length of time to
maturity and market price. It assumes that coupon interest paid over the life of the bond will be reinvested at
the same rate.

RETURN ON INVESTMENT (ROI)

In its most basic form, the rate of return equals net income divided by the amount of money invested. It can be applied to a particular product or piece of equipment, or to a business as a whole.

capital budgeting

Refers generally to analysis procedures for ranking
investments, given a limited amount of total capital that has to be allocated
among the various capital investment opportunities of a business.
The term sometimes is used interchangeably with the analysis techniques
themselves, such as calculating present value, net present value,
and the internal rate of return of investments.

capital investment analysis

Refers to various techniques and procedures
used to determine or to analyze future returns from an investment
of capital in order to evaluate the capital recovery pattern and the
periodic earnings from the investment. The two basic tools for capital
investment analysis are (1) spreadsheet models (which I strongly prefer)
and (2) mathematical equations for calculating the present value or
internal rate of return of an investment. Mathematical methods suffer
from a lack of information that the decision maker ought to consider. A
spreadsheet model supplies all the needed information and has other
advantages as well.

financial leverage

The equity (ownership) capital of a business can serve
as the basis for securing debt capital (borrowing money). In this way, a
business increases the total capital available to invest in its assets and
can make more sales and more profit. The strategy is to earn operating
profit, or earnings before interest and income tax (EBIT), on the capital
supplied from debt that is more than the interest paid on the debt capital.
A financial leverage gain equals the EBIT earned on debt capital
minus the interest on the debt. A financial leverage gain augments earnings
on equity capital. A business must earn a rate of return on its assets
(ROA) that is greater than the interest rate on its debt to make a financial
leverage gain. If the spread between its ROA and interest rate is unfavorable,
a business suffers a financial leverage loss.

Cost of Capital

The minimum rate of return a company must earn in order to meet
the rate of return required by the investors (providers of capital) of
the company

Cost of Common Stock

The rate of return required by the investors in the common stock of
the company. A component of the cost of capital.

Cost of Equity

Same as the cost of common stock. Sometimes viewed as the
rate of return stockholders require to maintain the market value of
the company's common stock.

Cost of Preferred Stock

The rate of return required by the investors in the preferred stock of
a company. A component of the cost of capital.

Effective Annual Yield

Annualized rate of return on a security computed using compound
interest techniques

Risk Premium

The additional rate of return required on a risky project
(investment) when compared to a risk-free project (investment)

Risk-free Rate

The rate of return on an investment with known future benefits; a
riskless rate of return, often estimated using the return earned on
short-term U.S. Treasury securities

Security Market Line

A graph illustrating the equilibrium relationship between the
expected rate of return on securities and their risk as measured by
the beta coefficient

Yield to Maturity

The measure of the average rate of return that will be earned on a
debt security held until it matures

discount rate

the rate of return used to discount future cash
flows to their present value amounts; it should equal or
exceed an organization’s weighted average cost of capital

dividend growth method

a method of computing the cost
of common stock equity that indicates the rate of return
that common shareholders expect to earn in the form of
dividends on a company’s common stock

Fisher rate

the rate of return that equates the present values
of the cash flows of all projects being considered; it is the
rate of indifference

hurdle rate

a preestablished rate of return against which
other rates of return are measured; it is usually the cost of
capital rate when used in evaluating capital projects

judgmental method (of risk adjustment)

an informal method of adjusting for risk that allows the decision maker
to use logic and reason to decide whether a project provides
an acceptable rate of return

net present value method

a process that uses the discounted
cash flows of a project to determine whether the
rate of return on that project is equal to, higher than, or
lower than the desired rate of return

opportunity cost of capital

the highest rate of return that
could be earned by using capital for the most attractive alternative
project(s) available

return on capital

income; it is equal to the rate of return multiplied by the amount of the investment

weighted average cost of capital

a composite of the cost of the various sources of funds that comprise a firm’s capital structure; the minimum rate of return that must be earned on new investments so as not to dilute shareholder value

Volatility

a. Another general term for sensitivity. b. The standard deviation
of the annualized continuously compounded rate of return of an asset. c. A
measure of uncertainty or risk.

Yield to maturity

A measure of the average rate of return that will be earned
on a bond if held to maturity.

Hurdle rate

The minimum rate of return that a capital purchase proposal must pass
before it can be authorized for acquisition. The hurdle rate should be no lower than
a company’s incremental cost of capital.

company cost of capital

Expected rate of return demanded by investors in a company, determined by the average risk of the company’s assets and operations.

IRR

See internal rate of return.

MM's proposition II

The required rate of return on equity increases as the firm’s debt-equity ratio increases.

opportunity cost of capital

Expected rate of return given up by investing in a project.

project cost of capital

Minimum acceptable expected rate of return on a project given its risk.

weighted-average cost of capital (WACC)

Expected rate of return on a portfolio of all the firm’s securities, adjusted for tax savings due to interest payments.

Rule of 72

This is a very important rule to know. The rule is that the number 72 divided by the rate of return of your investment equals the number of years it takes for your investment to double.
For example
* At 1% your money will double in 72 years.
* At 2% your money will double in 36 years.
* At 3% your money will double in 24 years.
* At 4% your money will double in 18 years.
* At 5% your money will double in 14.4 years.
* At 6% your money will double in 12 years.
* At 7% your money will double in 10.3 years.
* At 8% your money will double in 9 years.
* At 9% your money will double in 8 years.
* At 10% your money will double in 7.2 years.

Discount Rate

A rate of return used to convert a monetary sum, payable or receivable in the future, into present value.

Discounted Cash Flow

Techniques for establishing the relative worth of a future investment by discounting (at a required rate of return) the expected net cash flows from the project.

Hurdle Rate

A pre-determined benchmark rate of return. If the rate of return expected from the project or investment falls below the benchmark, the projected investment will no longer be accepted.

Risk-Free Rate

The rate of return obtainable on government of Canada treasury bills.

Risk Premium

The difference between the required rate of return on a riskless asset with the same expected life.

guaranteed investment certificate (GIC)

A GIC is an investment that gives you a guaranteed rate of return over a fixed period of time, usually between 30 days and 5 years. GICs are available from banks, trust companies, and other financial institutions.

risk

Risk measures the possibility that your investment may lose or gain value as compared to the expected rate of return. Risk is different from uncertainty, which is not measurable.

CARs (cumulative abnormal returns)

a measure used in academic finance articles to measure the excess returns an investor would have received over a particular time period if he or she were invested in a particular stock.
This is typically used in control and takeover studies, where stockholders are paid a premium for being taken over. Starting some time period before the takeover (often five days before the first announced bid, but sometimes a longer period), the researchers calculate the actual daily stock returns for the target firm and subtract out the expected market returns (usually calculated using the firm’s beta and applying it to overall market movements during the time period under observation).
The excess actual return over the capital asset pricing model-determined expected return market is called an ‘‘abnormal return.’’ The cumulation of the daily abnormal returns over the time period under observation is the CAR. The term CAR(-5, 0) means the CAR calculated from five days before the
announcement to the day of announcement. The CAR(-1, 0) is a control premium, although Mergerstat generally uses the stock price five days before announcement rather than one day before announcement as the denominator in its control premium calculation. However, the CAR for any period other than (-1, 0) is not mathematically equivalent to a control premium.

Abnormal returns

Part of the return that is not due to systematic influences (market wide influences). In
other words, abnormal returns are above those predicted by the market movement alone. Related: excess
returns.

Accelerated cost recovery system (ACRS)

Schedule of depreciation rates allowed for tax purposes.

Accelerated depreciation

Any depreciation method that produces larger deductions for depreciation in the
early years of a project's life. Accelerated cost recovery system (ACRS), which is a depreciation schedule
allowed for tax purposes, is one such example.

Active portfolio strategy

A strategy that uses available information and forecasting techniques to seek a
better performance than a portfolio that is simply diversified broadly. Related: passive portfolio strategy

Adjustable rate preferred stock (ARPS)

Publicly traded issues that may be collateralized by mortgages and MBSs.

All equity rate

The discount rate that reflects only the business risks of a project and abstracts from the
effects of financing.

Amortizing interest rate swap

Swap in which the principal or national amount rises (falls) as interest rates
rise (decline).

Annual percentage rate (APR)

The periodic rate times the number of periods in a year. For example, a 5%
quarterly return has an APR of 20%.

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