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mathematical programming

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Definition of mathematical programming

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mathematical programming

a variety of techniques used
to allocate limited resources among activities to achieve a
specific objective

Mathematical programming

An operations research technique that solves problems in which an optimal
value is sought subject to specified constraints. mathematical programming models include linear
programming, quadratic programming, and dynamic programming.

Related Terms:

integer programming

a mathematical programming technique in which all solutions for variables must be restricted to whole numbers

linear programming

a method of mathematical programming used to solve a problem that involves an objective function and multiple limiting factors or constraints long-term variable cost a cost that was traditionally viewed as a fixed cost

Integer programming

Variant of linear programming whereby the solution values must be integers.

Linear programming

Technique for finding the maximum value of some equation subject to stated linear constraints.

Planning, programming and budgeting system (PPBS)

A method of budgeting in which budgets are allocated to projects or programmes rather than to responsibility centres.

Zero-one integer programming

An analytical method that can be used to determine the solution to a capital
rationing problem.

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objective function

the linear mathematical equation that
states the purpose of a linear programming problem

Zero-one integer programming

An analytical method that can be used to determine the solution to a capital
rationing problem.

Discrete random variable

A random variable that can take only a certain specified set of discrete possible
values - for example, the positive integers 1, 2, 3, . . .

Point and figure chart

A price-only chart that takes into account only whole integer changes in price, i.e., a
2-point change. Point and figure charting disregards the element of time and is solely used to record changes
in price.

Account Value

The sum of all the interest options in your policy, including interest.

Accumulated Value

An amount of money invested plus the interest earned on that money.

acid test ratio (also called the quick ratio)

The sum of cash, accounts receivable, and short-term marketable
investments (if any) is divided by
total current liabilities to compute this ratio. Suppose that the short-term
creditors were to pounce on a business and not agree to roll over the
debts owed to them by the business. In this rather extreme scenario, the
acid test ratio reveals whether its cash and near-cash assets are enough
to pay its short-term current liabilities. This ratio is an extreme test that
is not likely to be imposed on a business unless it is in financial straits.
This ratio is quite relevant when a business is in a liquidation situation
or bankruptcy proceedings.

Adjusted Cash Flow Provided by Continuing Operations

Cash flow provided by operating
activities adjusted to provide a more recurring, sustainable measure. Adjustments to reported cash
provided by operating activities are made to remove such nonrecurring cash items as: the operating
component of discontinued operations, income taxes on items classified as investing or financing activities, income tax benefits from nonqualified employee stock options, the cash effects of purchases and sales of trading securities for nonfinancial firms, capitalized expenditures, and other nonrecurring cash inflows and outflows.

Adjusted present value (APV)

The net present value analysis of an asset if financed solely by equity
(present value of un-levered cash flows), plus the present value of any financing decisions (levered cash
flows). In other words, the various tax shields provided by the deductibility of interest and the benefits of
other investment tax credits are calculated separately. This analysis is often used for highly leveraged
transactions such as a leverage buy-out.

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agency problems

Conflicts of interest between the firm’s owners and managers.

All equity rate

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

All-in cost

Total costs, explicit and implicit.

All or none

Requirement that none of an order be executed unless all of it can be executed at the specified price.

All-or-none underwriting

An arrangement whereby a security issue is canceled if the underwriter is unable
to re-sell the entire issue.


assign based on the use of a cost driver, a cost predictor,
or an arbitrary method


the systematic assignment of an amount to a recipient
set of categories annuity a series of equal cash flows (either positive or negative) per period


The process of storing costs in one account and shifting them to other
accounts, based on some relevant measure of activity.

Allocation base A measure of activity or volume such as labour

hours, machine hours or volume of production
used to apportion overheads to products and

Allowance for bad debts

An offset to the accounts receivable balance, against which
bad debts are charged. The presence of this allowance allows one to avoid severe
changes in the period-to-period bad debt expense by expensing a steady amount to
the allowance account in every period, rather than writing off large bad debts to
expense on an infrequent basis.

Allowance for doubtful accounts

A contra account related to accounts receivable that represents the amounts that the company expects will not be collected.

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Allowance for Doubtful Accounts

An estimate of the uncollectible portion of accounts receivable
that is subtracted from the gross amount of accounts receivable to arrive at the estimated collectible

Allowance method

A method of adjusting accounts receivable to the amount that is expected to be collected based on company experience.

approximated net realizable value at split-off allocation

a method of allocating joint cost to joint products using a
simulated net realizable value at the split-off point; approximated
value is computed as final sales price minus
incremental separate costs

Arbitrage-free option-pricing models

Yield curve option-pricing models.

Asset allocation decision

The decision regarding how an institution's funds should be distributed among the
major classes of assets in which it may invest.

Asset-specific Risk

The amount of total risk that can be eliminated by diversification by
creating a portfolio. Also known as company-specific risk or
unsystematic risk.

Balloon maturity

Any large principal payment due at maturity for a bond or loan with or without a a sinking
fund requirement.

Benefit Value

The amount of cash payable on a benefit.

Bond value

With respect to convertible bonds, the value the security would have if it were not convertible
apart from the conversion option.

Book value

A company's book value is its total assets minus intangible assets and liabilities, such as debt. A
company's book value might be more or less than its market value.


An asset’s cost basis minus accumulated depreciation.

Book Value

The value of an asset as carried on the balance sheet of a
company. In reference to the value of a company, it is the net worth
(equity) of the company.

Book value

An asset’s original cost, less any depreciation that has been subsequently incurred.

book value

Net worth of the firm’s assets or liabilities according
to the balance sheet.

book value and book value per share

Generally speaking, these terms
refer to the balance sheet value of an asset (or less often of a liability) or
the balance sheet value of owners’ equity per share. Either term emphasizes
that the amount recorded in the accounts or on the books of a business
is the value being used. The total of the amounts reported for
owners’ equity in its balance sheet is divided by the number of stock
shares of a corporation to determine the book value per share of its capital


The theoretical amount per share that each stockholder would receive if a company’s assets were sold on the balance sheet’s date. Book value equals:
(Stockholders’ equity) / (Common stock shares outstanding)

Book value per share

The ratio of stockholder equity to the average number of common shares. Book value
per share should not be thought of as an indicator of economic worth, since it reflects accounting valuation
(and not necessarily market valuation).

Book Value per Share

The book value of a company divided by the number of shares

Borrower fallout

In the mortgage pipeline, the risk that prospective borrowers of loans committed to be
closed will elect to withdraw from the contract.

business-value-added activity

an activity that is necessary for the operation of the business but for which a customer would not want to pay

cafeteria plan a “menu” of fringe benefit options that include

cash or nontaxable benefits


An option that gives the right to buy the underlying futures contract.


a. An option to buy a certain quantity of a stock or commodity for a
specified price within a specified time. See Put.
b. A demand to submit bonds to the issuer for redemption before the maturity date.
c. A demand for payment of a debt.
d. A demand for payment due on stock bought on margin.

Call an option

To exercise a call option.

Call date

A date before maturity, specified at issuance, when the issuer of a bond may retire part of the bond
for a specified call price.

Call money rate

Also called the broker loan rate , the interest rate that banks charge brokers to finance
margin loans to investors. The broker charges the investor the call money rate plus a service charge.

Call option

An option contract that gives its holder the right (but not the obligation) to purchase a specified
number of shares of the underlying stock at the given strike price, on or before the expiration date of the
Call premium
Premium in price above the par value of a bond or share of preferred stock that must be paid to
holders to redeem the bond or share of preferred stock before its scheduled maturity date.

Call Option

A contract that gives the holder the right to buy an asset for a
specified price on or before a given expiration (maturity) date

call option

Right to buy an asset at a specified exercise price on or before the exercise date.

Call price

The price, specified at issuance, at which the issuer of a bond may retire part of the bond at a
specified call date.

Call price

The price for which a bond can be repaid before maturity under a call provision.

Call protection

A feature of some callable bonds that establishes an initial period when the bonds may not be

Call provision

An embedded option granting a bond issuer the right to buy back all or part of the issue prior
to maturity.

Call risk

The combination of cash flow uncertainty and reinvestment risk introduced by a call provision.

Call swaption

A swaption in which the buyer has the right to enter into a swap as a fixed-rate payer. The
writer therefore becomes the fixed-rate receiver/floating rate payer.


A financial security such as a bond with a call option attached to it, i.e., the issuer has the right to
call the security.

Callable bond

A bond that allows the issuer to buy back the bond at a
predetermined price at specified future dates. The bond contains an embedded
call option; i.e., the holder has sold a call option to the issuer. See Puttable

callable bond

Bond that may be repurchased by the issuer before maturity at specified call price.

Capital allocation

decision allocation of invested funds between risk-free assets versus the risky portfolio.

Capital Consumption Allowance

See depreciation.

Capital Cost Allowance (CCA)

The annual depreciation expense allowed by the Canadian Income Tax Act.


What a company collected when it sold stock for more than the par value per share.

Carrying value

Book value.

cash flow from operating activities, or cash flow from profit

This equals the cash inflow from sales during the period minus the cash
outflow for expenses during the period. Keep in mind that to measure
net income, generally accepted accounting principles require the use of
accrual-basis accounting. Starting with the amount of accrual-basis net
income, adjustments are made for changes in accounts receivable,
inventories, prepaid expenses, and operating liabilities—and depreciation
expense is added back (as well as any other noncash outlay
expense)—to arrive at cash flow from profit, which is formally labeled
cash flow from operating activities in the externally reported statement
of cash flows.

Cash flow from operations

A firm's net cash inflow resulting directly from its regular operations
(disregarding extraordinary items such as the sale of fixed assets or transaction costs associated with issuing
securities), calculated as the sum of net income plus non-cash expenses that were deducted in calculating net

Cash Flow Provided by Operating Activities

With some exceptions, the cash effects of transactions
that enter into the determination of net income, such as cash receipts from sales of goods
and services and cash payments to suppliers and employees for acquisitions of inventory and

Cash Flow Provided or Used from Financing Activities

Cash receipts and payments involving
liability and stockholders' equity items, including obtaining cash from creditors and repaying
the amounts borrowed and obtaining capital from owners and providing them with a return on,
and a return of, their investments.

Cash Flow Provided or Used from Investing Activities

Cash receipts and payments involving
long-term assets, including making and collecting loans and acquiring and disposing of
investments and productive long-lived assets.


A section on the cash-flow statement that shows how much cash a company raised by selling stocks or bonds this year and how much was paid out for cash dividends and other finance-related obligations.


A section on the cashflow statement that shows how much cash came in and went out because of various investing activities like purchasing machinery.


A section on the cash-flow Stockholders’ equity statement that shows how much cash came into a company and how much went out during the normal course of business.

Cash-surrender value

An amount the insurance company will pay if the policyholder ends a whole life
insurance policy.

Cash Surrender Value

This is the amount available to the owner of a life insurance policy upon voluntary termination of the policy before it becomes payable by the death of the life insured. This does not apply to term insurance but only to those policies which have reduced paid up values and cash surrender values. A cash surrender in lieu of death benefit usually has tax implications.

Cash Surrender Value

Benefit that entitles a policy owner to an amount of money upon cancellation of a policy.

Cash value added (CVA)

A method of investment appraisal that calculates the ratio of the net present value of an
investment to the initial capital investment.

Chinese wall

Communication barrier between financiers (investment bankers) and traders. This barrier is
erected to prevent the sharing of inside information that bankers are likely to have.

Company-specific risk

Related: Unsystematic risk

Companyspecific Risk

See asset-specific risk

Conversion value

Also called parity value, the value of a convertible security if it is converted immediately.

cost allocation

the assignment, using some reasonable basis,
of any indirect cost to one or more cost objects

Cost of limited partner capital

The discount rate that equates the after-tax inflows with outflows for capital
raised from limited partners.

Covered call

A short call option position in which the writer owns the number of shares of the underlying
stock represented by the option contracts. Covered calls generally limit the risk the writer takes because the
stock does not have to be bought at the market price, if the holder of that option decides to exercise it.

Covered call writing strategy

A strategy that involves writing a call option on securities that the investor
owns in his or her portfolio. See covered or hedge option strategies.

Deferred call

A provision that prohibits the company from calling the bond before a certain date. During this
period the bond is said to be call protected.

Depreciation Allowances

Tax deductions that businesses can claim when they spend money on investment goods.

Deterministic models

Liability-matching models that assume that the liability payments and the asset cash
flows are known with certainty. Related: Compare stochastic models

Discontinued Operations

Net income and the gain or loss on disposal of a business segment whose assets and operations are clearly distinguishable from the other assets and operations of an entity.

Dynamic asset allocation

An asset allocation strategy in which the asset mix is mechanistically shifted in
response to -changing market conditions, as in a portfolio insurance strategy, for example.

Dynamic hedging

A strategy that involves rebalancing hedge positions as market conditions change; a
strategy that seeks to insure the value of a portfolio using a synthetic put option.

Economic Value Added (EVA)

Operating profit, adjusted to remove distortions caused by certain accounting rules, less a charge
to cover the cost of capital invested in the business.

economic value added (EVA)

a measure of the extent to which income exceeds the dollar cost of capital; calculated
as income minus (invested capital times the cost of capital percentage)

economic value added (EVA)

Term used by the consulting firm Stern Stewart for profit remaining after deduction of the cost
of the capital employed.

economically reworked

when the incremental revenue from the sale of reworked defective units is greater than
the incremental cost of the rework

Effective call price

The strike price in an optional redemption provision plus the accrued interest to the
redemption date.

Exercise value

The amount of advantage over a current market transaction provided by an in-the-money

Exit value

The value that an asset is expected to have at the time it is sold at a predetermined
point in the future.

Expected value

The weighted average of a probability distribution.

Expected Value

The value of the possible outcomes of a variable weighted by the
probabilities of each outcome

Expected value of perfect information

The expected value if the future uncertain outcomes could be known
minus the expected value with no additional information.

Extraordinary positive value

A positive net present value.

Extrapolative statistical models

models that apply a formula to historical data and project results for a
future period. Such models include the simple linear trend model, the simple exponential model, and the
simple autoregressive model.

Face value

See: Par value.

Face Value

The nominal value of a security. Also called the par value.

Face value

The maturity value of a security. Also known as par value,
principal value, or redemption value.







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