• Discounted Cash Flow
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Mergers and acquisitions - Business valuation
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discounted cash flow (DCF)
valuation
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Business value - Philosophy
While it would be very desirable to
translate all forms of business value to a
single economic measure (e.g.,
discounted cash flow), many practitioners
and theorists believe this is either not
feasible or theoretically impossible.
Therefore, advocates of business value
believe that the best approach is to
measure and manage multiple forms of
value as they apply to each stakeholder
group.
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Business value - Shareholder Value
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For a privately held company, the
value of the firm after debt must be
estimated using one of several
valuation methods, s.a. discounted
cash flow or others.
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Ant colony optimization - Others
*Discounted cash flows in project
schedulingW. N. Chen, J. ZHANG and H.
Chung, Optimizing Discounted Cash
Flows in Project Scheduling--An Ant
Colony Optimization Approach, IEEE
Transactions on Systems, Man, and
Cybernetics--Part C: Applications and
Reviews Vol.40 No.5 pp.64-77, Jan. 2010.
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Valuation (finance) - Valuation overview
1
#Absolute value models that determine the
present value of an asset's expected
future cash flows. These kinds of models
take two general forms: multi-period
models such as discounted cash flow
models or single-period models such as
the Gordon model. These models rely on
mathematics rather than price observation.
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Valuation (finance) - Business valuation
For a Valuation using discounted cash
flows|valuation using the discounted cash
flow method, one first estimates the future
cash flows from the investment and then
estimates a reasonable discount rate after
considering the riskiness of those cash
flows and interest rates in the capital
markets. Next, one makes a calculation to
compute the present value of the future
cash flows.
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Valuation (finance) - Net asset value method
This method can also be used to value
heterogeneous portfolios of investments,
as well as nonprofits, for which discounted
cash flow analysis is not relevant
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Levelised energy cost - Cost factors
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To evaluate the total cost of production of
electricity, the streams of costs are
converted to a net present value using the
time value of money. These costs are all
brought together using discounted cash
flow.
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Fossil-fuel power station - Relative cost by generation source
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These costs occur over the 30–50 year life
of the fossil fuel power plants, using
discounted cash flows. In general large
fossil plants are attractive due to their low
initial capital costs—typically around
£750–£1000 per kilowatt electrical
compared to perhaps £1500 per kilowatt
for onshore wind.
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Economics of new nuclear power plants - Capital costs
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The discounted cash flow|discount rate
chosen to cost a nuclear power plant's
capital over its lifetime is arguably the
most sensitive parameter to overall costs.
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Patent valuation - Income-based method
1
# Discounted cash flow method: This
method aims to estimate future cash
flows, which are projected and after
discounted by applying an appropriate
discount factor. The main source of
information to estimate the cash flows
is generally the business plan of the
company that exploits or intends to
exploit the asset.
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ILUC - EPA Renewable Fuel Standard
1
EPA's draft analysis stated that ILUC can
produce significant near-term GHG
emissions due to land conversion, but
that biofuels can pay these back over
subsequent years. EPA highlighted two
scenarios, varying the time horizon and
the discounted cash flow|discount rate
for valuing emissions. The first assumed
a 30 year time period uses a 0 percent
discount rate (valuing emissions equally
regardless of timing). The second
scenario used a 100 year time period and
a 2% discount rate.
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Internal rate of return
1
It is also called the discounted cash flow
rate of return (DCFROR).Project
Economics and Decision Analysis, Volume
I: Deterministic Models, M.A.Main, Page
269 In the context of savings and loans
the IRR is also called the effective interest
rate
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Internal rate of return - Problems with using internal rate of return
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Since IRR does not consider cost of
capital, it should not be used to
compare projects of different
duration. Modified Internal Rate of
Return (MIRR) does consider cost of
capital and provides a better
indication of a project's efficiency in
contributing to the firm's discounted
cash flow.
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Outline of finance - Fundamental financial concepts
1
** Discounted cash
flow
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Net present value
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NPV is a central tool in discounted cash
flow (DCF) analysis and is a standard
method for using the time value of money
to appraise long-term projects
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Stock valuation - Fundamental criteria (fair value)
The most theoretically sound 'stock
valuation method', called income
valuation or the discounted cash flow
('DCF') method, involves 'discounting of
the profits' (dividends, earnings, or cash
flows) the stock will bring to the
stockholder in the foreseeable future, and
a final value on disposal.William F.
Sharpe, Investments, Prentice-Hall, 1978,
pp. 300 et.seq. The discounted rate
normally includes a risk premium which is
commonly based on the capital asset
pricing model.
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Stock valuation - Fundamental criteria (fair value)
Contested inputs included the
terminal growth rate, the equity
premium puzzle|equity risk
premium, and
beta.[http://blogs.law.harvard.edu/co
rpgov/2010/07/16/delaware-providesguidance-regarding-discounted-cashflow-analysis/ Delaware Provides
Guidance Regarding Discounted Cash
Flow Analysis]
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Stock valuation - Limited high-growth period approximation
When a stock has a significantly higher
growth rate than its peers, it is sometimes
assumed that the earnings growth rate will be
sustained for a short time (say, 5 years), and
then the growth rate will Regression toward
the mean|revert to the mean. This is probably
the most rigorous approximation that is
practical.[http://www.moneychimp.com/article
s/valuation/dcf.htm Discounted Cash Flow
Calculator for Stock Valuation]
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Microeconomics - Opportunity cost
This kind of reasoning is a very
important part of the calculation of
discount rates in discounted cash flow
investment valuation methodologies
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Corporate finance - Investment and project valuation
Harvey each project's value will be
estimated using a discounted cash flow
(DCF) valuation, and the opportunity
with the highest value, as measured by
the resultant net present value (NPV)
will be selected (applied to Corporate
Finance by Joel Dean (economist)|Joel
Dean in 1951)
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Corporate finance - Investment and project valuation
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The NPV is greatly affected by the
discounted cash flow|discount rate
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Grid parity - Pricing solar
If one makes the not-unrealistic
assumption that the discounted cash
flow|discount rate will be similar to the
inflation rate of grid power, then one
can calculate the levelized cost simply
by dividing the original capital cost by
the total amount of electricity produced
over the system's lifetime.
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Discounting - Other discounts
For 'discounts' in marketing, see
discounts and allowances, sales
promotion, and pricing. The article on
Discounted Cash Flow provides a nice
example about discounting and risks
in real estate investments.
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Financial model - Accounting
*Business valuation, especially
discounted cash flow, but including
other Valuation (finance)|valuation
problems
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The Theory of Investment Value
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thesis, which was amongst the first to
articulate the theory of Discounted
Cash Flow (DCF) based valuation, and
in particular, dividend based
valuation.
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The Theory of Investment Value - Theory
While Williams did not originate the idea of present
value,http://www.in-themoney.com/artandpap/I%20Present%20Value.doc he
substantiated the concept of Valuation using discounted cash
flows|discounted cash flow valuation and is generally
regarded as having developed the basis for the dividend
discount model
(DDM).http://www.cfainstitute.org/cfaprog/university/pdf/Equity
Promo.pdf, http://www.finance-andphysics.org/Library/Articles3/scienceandfinance/science.htm
Through his approach to modelling and forecasting cash
flows—which he called “algebraic budgeting”—Williams was
also a pioneer of the Pro forma#Business|pro forma modeling
of financial statements.[http://roundtable.informs.org/publicaccess/min061a.htm] Here, Williams (Theory, ch
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The Theory of Investment Value - Theory
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Today, “evaluation by the rule of present worth”,
applied in conjunction with an Capital asset pricing
model#Asset-specific required return|asset
appropriate discount rate mdash; usually derived
using the capital asset pricing model of modern
portfolio theory (Harry Markowitz and William
Forsyth Sharpe|William Sharpe), or the arbitrage
pricing theory (Stephen Ross (economist)|Stephen
Ross) mdash; is probably the most widely used
stock valuation method amongst institutional
investors;http://www.investopedia.com/articles/03/
011403.asp see List of finance topics#Discounted
cash flow valuation|List of valuation topics
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Working capital
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Net working capital (NWC) is calculated as
current assets minus current
liabilities.[http://www.differencebetween.co
m/difference-between-gross-workingcapital-and-vs-net-working-capital/ Gross
Working Capital vs Net working Capital] It
is a derivation of working capital, that is
commonly used in valuation techniques
such as DCFs (Discounted cash flows)
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Business valuation - Income, asset and market approaches
Generally, the income approaches
determine value by calculating the
net present value of the benefit stream
generated by the business (discounted
cash flow); the asset-based
approaches determine value by
adding the sum of the parts of the
business (net asset value); and the
market approaches determine value
by comparing the subject company to
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Business valuation - Income approaches
There are several different income
approaches, including capitalization of
earnings or cash flows, discounted future
cash flows (discounted cash flow|DCF),
and the excess earnings method (which is
a hybrid of asset and income apprope of
benefit stream to which it is applied)
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Business valuation - Discount or capitalization rates
* In discounted cash flow|DCF
valuations, the discount rate, often an
estimate of the cost of capital for the
business is used to calculate the net
present value of a series of projected
cash flows.
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Business valuation - Option pricing approaches
1
Thus, for companies facing uncertainty of this
type, the stock price may (should) be seen as
the sum of the value of existing businesses
(i.e., the discounted cash flow|discounted
cash flow value) plus any real option
value.Alfred Rappaport and Michael
Mauboussin (Columbia Business School):
[http://www.expectationsinvesting.com/tutorial
11.shtml How Do You Assess The Value of A
Company's Real Options?] Equity valuations
here, may (should) thus proceed likewise
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Working capital management - Investment and project valuation
Harvey each project's value will be
estimated using a discounted cash
flow (DCF) valuation, and the
opportunity with the highest value, as
measured by the resultant net present
value (NPV) will be selected (applied
to Corporate Finance by Joel Dean
(economist)|Joel Dean in 1951)
1
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Working capital management - Investment and project valuation
1
The NPV is greatly affected
by the discounted cash
flow|discount rate
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Capital budgeting - Capital Budgeting Definition
1
Each potential project's value should be
estimated using a discounted cash flow
(DCF) valuation, to find its net present
value (NPV)
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Capital budgeting - Capital Budgeting Definition
1
Popular methods of capital budgeting
include net present value (NPV),
internal rate of return (IRR),
discounted cash flow (DCF) and
payback period.
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Capital budgeting - Real options
1
The discounted cash flow methods
essentially value projects as if they
were risky bonds, with the promised
cash flows known
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Mixed-use development - Criticism
Another issue is that short-term
discounted cash flow has become the
standard way to measure the success
of income-generating development,
resulting in disposable suburban
designs that make money in the short
run but are not as successful in the
medium to long term as walkable,
mixed-use environments.
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Real options valuation - Applicability of standard techniques
ROV is often contrasted with more
standard techniques of capital budgeting,
such as discounted cash flow (DCF)
analysis / net present value (NPV)
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Real estate appraisal - The income capitalization approach
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Alternatively, multiple years of net
operating income can be valued by a
discounted cash flow analysis (DCF)
model
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Yield (finance) - Real Estate Property
Equivalent Yield lies somewhere in
between the initial yield and
reversionary yield, it encapsulates the
Discounted cash flow|DCF of the
property with rents rising (or falling)
from the current annualised rent to the
underlying estimated rental value (ERV)
less costs that are incurred along the
way. The discount rate used to
calculate the net present value (NPV) of
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Yield (finance) - Real Estate Property
The calculation not only takes into
account all costs, but other
assumptions including rent reviews
and void periods. A trial and error
method can be used to identify the
equivalent yield of a Discounted cash
flow|DCF, or if using Excel, the goal
seek function can be used.
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Investment analysis - Business valuation
There are commonly three pillars to
valuing business entities: comparable
company analyses, discounted cash flow
analysis, and precedent transaction
analysis
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Fundamental analysis - Procedures
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The determined growth rates (of income
and cash) and risk levels (to determine the
discounted cash flow|discount rate) are
used in various valuation models. The
foremost is the discounted cash flow
model, which calculates the present value
of the future
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Discounted cash flow
1
In finance, 'discounted cash flow' ('DCF')
analysis is a method of valuing a project,
company, or financial asset|asset using
the concepts of the time value of money
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Discounted cash flow
1
Discounted cash flow analysis is widely
used in investment finance, real estate
developer|real estate development,
corporate financial management and
patent valuation.
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Discounted cash flow - History
1
Following the stock market crash of
1929, discounted cash flow analysis
gained popularity as a valuation
method for stocks
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Valuation using multiples - Disadvantages
* Dependence on correctly valued
peers: The use of multiples only
reveals patterns in relative values, not
absolute values such as those
obtained from valuation using
discounted cash flows|discounted
cash flow valuations. If the peer group
as a whole is incorrectly valued (such
as may happen during a stock market
bubble) then the resulting multiples
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Valuation using multiples - Advantages
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* Simplicity: Their very simplicity and
ease of calculation makes multiples
an appealing and user-friendly
method of assessing value. Multiples
can help the user avoid the potentially
misleading precision of other, more
‘precise’ approaches such as
discounted cash flow valuation or
EVA, which can create a false sense of
comfort.
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Terminal value (finance)
1
It is most often used in multi-stage
discounted cash flow analysis, and
allows for the limitation of cash flow
projections to a several-year period
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Terminal value (finance)
Thus, the terminal value allows for the
inclusion of the value of future cash flows
occurring beyond a several-year projection
period while satisfactorily mitigating many of
the problems of valuing such cash flows. The
terminal value is calculated in accordance
with a stream of projected future free cash
flows in discounted cash flow analysis. For
whole-company Valuation (finance)|valuation
purposes, there are two methodologies used
to calculate the Terminal Value.
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Free cash flow - Uses of the metric
1
According to the discounted cash flow
valuation model, the Intrinsic value
(finance)|intrinsic value of a company
is the present value of all future free
cash flows, plus the cash proceeds
from its eventual sale. The
presumption is that the cash flows are
used to pay dividends to the
shareholders. Bear in mind the
lumpiness discussed below.
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Residual income valuation - Concept
1
It is thus possible that a value deemed
positive using a traditional discounted
cash flow (DCF) approach may be
negative here
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Residual income valuation - Comparison with other valuation methods
1
As can be seen, the residual income
valuation formula is similar to the
dividend discount model (DDM) (and
to other discounted cash flow (DCF)
valuation models), substituting future
residual earnings for dividend (or free
cash) payments (and the cost of equity
for the weighted average cost of
capital).
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Adjusted present value
1
Technically, an APV valuation model
looks similar to a standard Discounted
cash flow|DCF model. However,
instead of weighted average cost of
capital|WACC, cash flows would be
discounted at the unlevered cost of
equity, and tax shields at either the
cost of debt (Myers) or following later
academics also with the unlevered
cost of
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Intrinsic value (finance) - Options
:IV_ \mathrm out-of-the-moneySee
also|Valuation using discounted cash
flows|John Burr Williams#Theory
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Intrinsic value (finance) - Options
In valuing Stock|equity, securities
analysts may use fundamental
analysis—as opposed to technical
analysis—to estimate the intrinsic
value of a company. Here the intrinsic
characteristic considered is the
expected cash flow production of the
company in question. Intrinsic value
is therefore defined to be the present
value of all expected future net cash
flows to the company; it is calculated
via discounted cash flow valuation.
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Pensions crisis - U.S. State-level issues
*, the state pension shortfall ranges
between $700 billion and $3 trillion,
depending on the discounted cash
flow|discount rate used to value the future
obligations. The $700 billion figure is
based on using a discount rate in the 8%
range representative of historical pension
fund investment returns, while the $3
trillion represents a discount rate in the 5%
range representative of historical Treasury
bond (risk-free) yields.
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Actuarial - History
For example, one traditional actuarial
method suggests that changing the asset
allocation mix of investments can change
the value of liabilities and assets (by
changing the discounted cash
flow|discount rate assumption)
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Income approach
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While there are quite a few acceptable
methods under the rubric of the income
approach, most of these methods fall into
three categories: direct capitalization,
discounted cash flow, and gross income
multiplier.
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Income approach - Direct Capitalization
If either cash flows or risk levels are
expected to change, then direct
capitalization fails and a discounted cash
flow method must be used.
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Income approach - Discounted Cash Flow
1
The Discounted cash flow model is analogous to net
present value estimation in finance
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P/E ratio - Interpretation
1
Using discounted cash flow analysis,
the impact of earnings growth and
inflation can be evaluated. Using
constant historical earnings growth
rate of 3.8 and post-war SP 500 returns
of 11% (including 4% inflation) as the
discount rate, the fair P/E is obtained
as 14.42. A stock growing at 10% for
next five years would have a fair P/E
of 18.65.
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Value investing - Further evolution
1
One modern model of calculating value
is the discounted cash flow model
(DCF), where the value of an asset is
the sum of its future cash flows,
discounted back to the present.
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Copenhagen Consensus - Results
1
Kåre Fog further pointed out that the future
benefits of emissions reduction were
Discounted Cash Flow|discounted at a
higher rate than for any of the other 27
proposals,http://www.lomborgerrors.dk/CopCons2008.htm stating so
there is an obvious reason why the climate
issue always is ranked last in Lomborg's
environmental studies.
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Debt cash flow
'Debt Cash Flow' is a finance term
describing a firm's non-Equity cash
flows. Theoretically, adding the
discounted Debt Cash Flow to the
discounted Flows to equity (also known
as Equity Cash Flows) will give the
firm's enterprise value. The Enterprise
value is the valuation obtained by
calculating the Discounted Cash Flow
(also DCF).
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Debt cash flow
The term Debt Cash Flow is not in
common usage; hence it is likely that
when the acronym DCF is used the
meaning is Discounted cash flow.
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Stochastic modeling - Means
1
For example, in application, applying
the best estimate (defined as the
mean) of investment returns to
discount a set of cash flows will not
necessarily give the same result as
assessing the best estimate to the
discounted cash flows.
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Bond valuation
1
Hence, the value of a bond is obtained
by discounting the bond's expected
cash flows to the present using an
appropriate discounted cash
flow|discount rate
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Economics of climate change mitigation - Discount rates
1
Discounting can either be prescriptive or
descriptive. The descriptive approach is
based on what discount rates are
observed in the behaviour of people
making every day decisions (the private
discounted cash flow|discount rate) (IPCC,
2007c:813). In the prescriptive approach,
a discount rate is chosen based on what is
thought to be in the best interests of future
generations (the social discount rate).
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Earnings growth - Overview
1
Earnings growth rate is a key value that is
needed when the Discounted cash
flow|DCF model, or the Gordon's model is
used for stock valuation.
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Earnings growth - On-line valuation calculators
1
*[http://www.moneychimp.com/articles/
valuation/dcf.htm
http://www.moneychimp.com/articles/v
aluation/dcf.htm]: Discounted Cash
Flows Calculator that assumes that a
higher growth can be sustained for a
limited number of years.
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International Valuation Standards Committee - Technical Information Papers (TIPs)
1
There are currently three finalized TIPs on
Discounted Cash Flows, The Cost
Approach for Tangible Assets and The
Valuation of Intangible Assets. The
Standards Board are currently working on
additional papers[http://ivsc.org/library List
of Drafts].
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RNPV
In finance, 'rNPV' (risk-adjusted net
present value) or 'eNPV' (expected NPV)
is a method to value risky future cash
flows. rNPV modifies the standard NPV
calculation of discounted cash flow (DCF)
analysis by adjusting (multiplying) each
cash flow by the estimated probability that
it occurs (the estimated success rate). In
the language of probability theory, the
rNPV is the expected value.
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Minimum acceptable rate of return
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A common method for evaluating a hurdle
rate is to apply the discounted cash flow
method to the project, which is used in net
present value models
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Share price - History
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Following this, the next stage was the
use of discounted cash flows, based on
the time value of money, to estimate the
intrinsic value of stock.
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Mortgage yield
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In finance, 'mortgage yield' is a measure of
yield (finance)|yield of Mortgage-backed
security|mortgage-backed bonds. It is also
known as cash flow yield. The mortgage
yield, or cash flow yield, of a mortgagebacked bond is the monthly compounded
discounted cash flow|discount rate at which
net present value of all future cash flows from
the bond will be equal to the present price of
the bond.Choudhry, Moorad. Capital Market
Instruments: Analysis and Valuation, (FT
Press, 2002), p. 208.
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Discount rate
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* in investment financing,
discounted cash flow
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Discount rate
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** in environmental economics, and more
generally in assessing the general welfare
impacts of government policies, social
discount rate (the basic mathematics is the
same as discounted cash flow, but the
cash value of human lives etc. can only be
crudely estimated)
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Sustainable growth rate - Sustainable growth rates (SGR) from a financial perspective
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The sustainable growth rate model has
implications for valuation models, as
for instance the Gordon model and
other discounted cash flow models
require a growth estimate that can be
sustained for many years. The
sustainable growth rate can be a check
if business plans are reasonable.
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NOPLAT
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'Net operating profit less adjusted taxes'
('NOPLAT') refers to total operating profits
for a firm with adjustments made for taxes.
It represents the profits generated from a
company's core operations after
subtracting the income taxes related to the
core operations. NOPLAT is often used as
an input in creating valuation using
discounted cash flows|discounted cash
flow valuation models.
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