Definition of Present value

Present value

The amount of cash today that is equivalent in value to a payment, or to a stream of payments,
to be received in the future.

Present value

Today’s value of an investment that yields some future value
when invested to earn compounded interest at a known interest rate.; i.e., the
future value at a known period in time discounted by the interest rate over that
time period.

Present Value

The amount due on an obligation less any interest on that obligation that would
be expected to accrue under market interest-rate conditions over the period prior to settlement. On
an interest-bearing liability, the amount owed on the liability, the principal, is its present value.
Interest is paid in addition to that present value amount. On a noninterest-bearing liability, the
amount owed is considered to include interest. To calculate present value, the liability must be discounted to remove that interest. The liability amount, excluding interest, would be the noninterest-
bearing liability's present value.

NPV (net present value of cash flows)

Same as PV, but usually includes a subtraction for an initial cash outlay.

PV (present value of cash flows)

the value in today’s dollars of cash flows that occur in different time periods.
present value factor equal to the formula 1/(1 - r)n, where n is the number of years from the valuation date to the cash flow and r is the discount rate.
For business valuation, n should usually be midyear, i.e., n = 0.5, 1.5, . . .

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.

Net adjusted present value

The adjusted present value minus the initial cost of an investment.

Net present value (NPV)

The present value of the expected future cash flows minus the cost.

Net present value of growth opportunities

A model valuing a firm in which net present value of new
investment opportunities is explicitly examined.

Net present value of future investments

The present value of the total sum of NPVs expected to result from
all of the firm's future investments.

Net present value rule

An investment is worth making if it has a positive NPV. Projects with negative NPVs
should be rejected.

Present value factor

Factor used to calculate an estimate of the present value of an amount to be received in
a future period.

Present value of growth opportunities (NPV)

Net present value of investments the firm is expected to make
in the future.

Net present value (NPV)

A discounted cash flow technique used for investment appraisal that calculates the present value of future cash flows and deducts the initial capital investment.

net present value (NPV)

Equals the present value (PV) of a capital investment
minus the initial amount of capital that is invested, or the entry cost
of the investment. A positive NPV signals an attractive capital investment
opportunity; a negative NPV means that the investment is substandard.

present value (PV)

This amount is calculated by discounting the future
cash returns from a capital investment. The discount rate usually is the
cost-of-capital rate for the business. If PV is more than the initial amount
of capital that has to be invested, the investment is attractive. If less,
then better investment alternatives should be found.

Net Present Value (NPV)

The present value of all future cash inflows minus the present value
of all cash outflows

Present Value (PV)

The dollar value at the present time (year zero) of a single cash
flow or a stream of future cash flows. The present value is
calculated by discounting the future cash flows.

net present value (NPV)

the difference between the present values of all cash inflows and outflows for an investment project

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

present value (PV)

the amount that one or more future cash
flows is worth currently, given a specified rate of interest

present value index

see profitability index

Net present value

A discounted cash flow methodology that uses a required rate of
return (usually a firm’s cost of capital) to determine the present value of a stream of
future cash flows, resulting in a net positive or negative value.

net present value (NPV)

present value of cash flows minus initial investment.

present value (PV)

value today of a future cash flow.

present value of growth opportunities (PVGO)

Net present value of a firm’s future investments.

Present Value (PV)

The value now of a future receipt or stream of receipts, calculated using a specified interest rate.

Net Present Value (NPV) Method

A method of ranking investment proposals. NPV is equal to the present value of the future returns, discounted at the marginal cost of capital, minus the present value of the cost of the investment.

Present Value (PV)

Are equity instruments that take no security against assets, have flexible terms of repayment and pay fixed or floating dividends.

ADF (annuity discount factor)

the present value of a finite stream of cash flows for every beginning $1 of cash flow.

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.

fractional interest discount

the combined discounts for lack of control and marketability. g the constant growth rate in cash flows or net income used in the ADF, Gordon model, or present value factor.

Gordon model

present value of a perpetuity with growth.
The end-ofyear Gordon model formula is: 1/(r - g)
and the midyear formula is: SQRT(1 + r)/(r - g).

PPF (periodic perpetuity factor)

a generalization formula invented by Abrams that is the present value of regular but noncontiguous cash flows that have constant growth to perpetuity.

Annuity factor

present value of $1 paid for each of t periods.

Cost-benefit ratio

The net present value of an investment divided by the investment's initial cost. Also called
the profitability index.

Crossover rate

The return at which two alternative projects have the same net present value.

Discount factor

present value of $1 received at a stated future date.

Discounted cash flow (DCF)

Future cash flows multiplied by discount factors to obtain present values.

Discounted dividend model (DDM)

A formula to estimate the intrinsic value of a firm by figuring the
present value of all expected future dividends.

Discounting

Calculating the present value of a future amount. The process is opposite to compounding.

Dividend discount model (DDM)

A model for valuing the common stock of a company, based on the
present value of the expected cash flows.

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.

Economic income

Cash flow plus change in present value.

Equivalent annual benefit

The equivalent annual annuity for the net present value of an investment project.

Equivalent annual cash flow

Annuity with the same net present value as the company's proposed investment.

Exchange risk

The variability of a firm's value that results from unexpected exchange rate changes or the
extent to which the present value of a firm is expected to change as a result of a given currency's appreciation
or depreciation.

Extraordinary positive value

A positive net present value.

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.

Intrinsic value of a firm

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

Macaulay duration

The weighted-average term to maturity of the cash flows from the bond, where the
weights are the present value of the cash flow divided by the price.

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.

Net advantage of refunding

The net present value of the savings from a refunding.

Net advantage to leasing

The net present value of entering into a lease financing arrangement rather than
borrowing the necessary funds and buying the asset.

NPV

See: Net present 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.

Profitability index

The present value of the future cash flows divided by the initial investment. Also called
the benefit-cost ratio.

Put-call parity relationship

The relationship between the price of a put and the price of a call on the same
underlying security with the same expiration date, which prevents arbitrage opportunities. Holding the stock
and buying a put will deliver the exact payoff as buying one call and investing the present value (PV) of the
exercise price. The call value equals C=S+P-PV(k).

Value additivity principal

Prevails when the value of a whole group of assets exactly equals the sum of the
values of the individual assets that make up the group of assets. Stated differently, the principle that the net
present value of a set of independent projects is just the sum of the net present values of the individual projects.

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.

Discounted cash flow (DCF)

A method of investment appraisal that discounts future cash flows to present value using a discount rate, which is the risk-adjusted cost of capital.

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.

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.

discounted cash flow (DCF)

Refers to a capital investment analysis technique
that discounts, or scales down, the future cash returns from an
investment based on the cost-of-capital rate for the business. In essence,
each future return is downsized to take into account the cost of capital
from the start of the investment until the future point in time when the
return is received. present value (PV) is the amount resulting from discounting
the future returns. present value is subtracted from the entry
cost of the investment to determine net present value (NPV). The net
present value is positive if the present value is more than the entry cost,
which signals that the investment would earn more than the cost-ofcapital
rate. If the entry cost is more than the present value, the net
present value is negative, which means that the investment would earn
less than the business’s cost-of-capital rate.

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.

weighted-average cost of capital

Weighted means that the proportions of
debt capital and equity capital of a business are used to calculate its
average cost of capital. This key benchmark rate depends on the interest
rate(s) on its debt and the ROE goal established by a business. This is a
return-on-capital rate and can be applied either on a before-tax basis or
an after-tax basis. A business should earn at least its weighted-average
rate on the capital invested in its assets. The weighted-average cost-ofcapital
rate is used as the discount rate to calculate the present value
(PV) of specific investments.

Continuous Discounting

The process of calculating the present value of a stream of future
cash flows by discounting over a continuous period of time

Discount Rate

The rate of interest used to calculate the present value of a stream
of future cash flows

Discounting

The process of calculating the present value of a stream of future
cash flows

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.

Profitability Index

A method for determining the profitability of an investment. It is
calculated by dividing the present value of the future net cash flows
by the initial cash investment.

discounting

the process of reducing future cash flows to present value amounts

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

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

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

profitability index (Pl)

a ratio that compares the present value of net cash flows to the present value of the net investment

Future value

The value that a sum of money (the present value) earning
compound interest will have in the future.

Macaulay duration

A widely used measure of price sensitivity to yield
changes developed by Frederick Macaulay in 1938. It is measured in years and
is a weighted average-time-to-maturity of an instrument. The Macaulay
duration of an income stream, such as a coupon bond, measures how long, on
average, the owner waits before receiving a payment. It is the weighted
average of the times payments are made, with the weights at time T equal to
the present value of the money received at time T.

Discounted cash flow

A technique that determines the present value of future cash
flows by applying a rate to each periodic cash flow that is derived from the cost of
capital. Multiplying this discount by each future cash flow results in an amount that
is the present value of all the future cash flows.

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.

annuity factor

present value of an annuity of $1 per period.

discount factor

present value of a $1 future payment.

discount rate

Interest rate used to compute present values of future cash flows.

dividend discount model

Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

equivalent annual cost

The cost per period with the same present value as the cost of buying and operating a machine.

NPV

See net present value.

profitability index

Ratio of net present value to initial investment.

PV

See present value.

yield to maturity

Interest rate for which the present value of the bond’s payments equals the price.

Discounting

Calculating the present value of a future payment.

Yield

The interest rate that makes the present value of a stream of future payments associated with an asset equal to the current price of that asset. Also called yield to maturity. See also current yield.

Gain-on-Sale Accounting

Up-front gain recognized from the securitization and sale of a pool
of loans. Profit is recorded for the excess of the sales price and the present value of the estimated
interest income that is expected to be received on the loans above the amounts funded on the loans
and the present value of the interest agreed to be paid to the buyers of the loan-backed securities.

Sales-type Lease

Lease accounting used by a manufacturer who is also a lessor. Up-front gross
profit is recorded for the excess of the present value of the lease payments to be received across
a lease term over the cost to manufacture the leased equipment. Interest income also is recognized
on the lease receivable as it is earned over the lease term.

Capitalization Rate

A discount rate used to find the present value of a series of future cash receipts. Sometimes called discount rate.

Capitalize

In Finance: to find the present value of a stream of cash flows.
In Accounting: to reflect costs of the balance sheet rather than charge them off through the income statement, as to capitalize major repairs to a fixed asset.

Discount Rate

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

Discounting

The process of finding the present value of a series of future cash flows. Discounting is the reverse of compounding.

Residual Value

Typically estimated based on the present value of the after-tax cash flows expected to be earned after the forecast period.

Bond value

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

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