Summary Corporate Finance
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Summary Corporate Finance Made by Lennard Schoemaker Based on The fundamentals of financial managment 13th edition
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Summary-Corporate-finance_
Transcript of Summary Corporate Finance
Summary
Corporate
Finance
Made by Lennard Schoemaker
Based on The fundamentals of financial managment 13th edition
Contents General information per .......................................................................................................................... 4
Chapter 1 ............................................................................................................................................. 4
Definitions Ch1 ................................................................................................................................ 4
Chapter 6 ............................................................................................................................................. 5
Definitions Chapter 6 ....................................................................................................................... 5
Chapter 3 ............................................................................................................................................. 6
Definitions Chapter 3 ....................................................................................................................... 6
Chapter 4 ............................................................................................................................................. 7
Definitions Chapter 4 ....................................................................................................................... 7
Chapter 5 ............................................................................................................................................. 8
Definitions Chapter 5 ....................................................................................................................... 8
Chapter 7 ........................................................................................................................................... 10
Definitions Chapter 7 ..................................................................................................................... 10
Chapter 8 ........................................................................................................................................... 10
Defections Chapter 8 ..................................................................................................................... 10
Chapter 12 ......................................................................................................................................... 11
Definitions Chapter 12 ................................................................................................................... 11
Chapter 13 ......................................................................................................................................... 11
Definitions Chapter 13 ................................................................................................................... 11
Chapter 15 -> Important.................................................................................................................... 12
Definitions Chapter 15 ................................................................................................................... 12
Chapter 16 ......................................................................................................................................... 13
Definitions Chapter 16 ................................................................................................................... 13
Chapter 17 ......................................................................................................................................... 14
Definitions Chapter 17 ................................................................................................................... 14
Formulas ................................................................................................................................................ 16
Definition of 'Weighted Average Cost Of Capital - WACC' ................................................................ 16
Definition of 'Cash Conversion Cycle - CCC' ...................................................................................... 16
Definition of 'Days Sales Of Inventory - DSI'/ DIO ............................................................................. 17
Definition of 'Days Sales Outstanding - DSO' .................................................................................... 17
Definition of 'Days Payable Outstanding - DPO' ................................................................................ 18
Definition of 'Net Present Value - NPV' ............................................................................................. 18
Definition of 'Present Value - PV' ...................................................................................................... 19
Definition of 'Internal Rate Of Return - IRR' ...................................................................................... 19
Definition of 'Required Rate Of Return - RRR' ................................................................................... 19
Investopedia explains 'Required Rate Of Return - RRR' ................................................................ 20
Definition of 'Economic Value Added - EVA' ..................................................................................... 20
Definition of 'Profitability Index' ....................................................................................................... 20
Definition of 'Return On Investment - ROI' ....................................................................................... 21
Definition of 'Payback Period' ........................................................................................................... 21
Definition of 'Earnings Before Interest & Tax - EBIT' ......................................................................... 21
Definition of 'Cost Of Goods Sold - COGS' ......................................................................................... 22
Definition of 'Capital Asset Pricing Model - CAPM' ........................................................................... 22
Definition of ‘Depreciation Tax Shield’ – DTS .................................................................................... 22
Formulas Financial Accounting .............................................................................................................. 23
Basic Information Corporate Finance .................................................................................................... 26
Cash Flow And Relationships Between Financial Statement - Free Cash Flow ............................. 28
Definition of 'Cost Of Equity' ......................................................................................................... 28
Definition of 'Cost Of Debt' ........................................................................................................... 29
Future Value .................................................................................................................................. 29
Present Value ................................................................................................................................ 30
Discounted Cash Flow Valuation - Perpetuities ............................................................................ 33
Net Present Value And Internal Rate Of Return - Introduction To Net Present Value And Internal
Rate Of Return ............................................................................................................................... 33
Net Present Value And Internal Rate Of Return - Profitability Index ............................................ 34
Calculating the Cost of Equity........................................................................................................ 35
Cost Of Capital - Cost Of Debt And Preferred Stock .............................................................. 37
Financial Leverage And Capital Structure Policy ........................................................................... 38
Financial Leverage And Capital Structure Policy - Financial Leverage .......................................... 39
General information per The summary is made in the order that was used in the lectures. For an overview of the order please
check the syllabus that was provided at the beginning of the course.
In order to maintain clarity about the definitons the following marks have been made.
Green = Definition related to a formula
Yellow = Important information which has been frequently been used in cases/Questions
Gray = Alternative way of defining the term
Besides the summary of the definitions there is also an overview of the Financial Accounting
formulas and an overview of all important subjects + formulas of CF.
Chapter 1
Definitions Ch1
Financial Management
o Financial management is concerned with the acquisition, financing, and management
of assets with some overall goal in mind.
o Financial management can be broken down into three major areas: The investment,
financing, and asset management decisions.
Dividend payout ratio
o Annual cash dividend divided by annual earning
o Dividends per share divided by earning per share
o The ration indicates the percentage of a company’s earnings that is paid out to
shareholder in cash
Profit maximization
o Maximizing a firms earnings after taxes (EAT)
o Profit maximization is one of the most common and proper objectives of a firm that
operates on a profit basis
Earnings per share (EPS)
o Earnings after taxes (EAT) divided by the number of common share outstanding
Agent(s)
o Individual authorized by another person, called the principal, to act on the latter’s
behalf
Agency (theory)
o A branch of economics relating to the behavior of principals (such as their owners)
and their agents (such as managers)
Corporate social responsibility (CSR)
o A business outlook that acknowledges a firm’s responsibilities to its stakeholders and
the natural environments.
Stakeholders
o All constituencies with a stake in the fortunes of the company. They include
shareholder, creditors, customers, employees, suppliers, and local and international
communities in which the firm operates.
Sustainability
o Meeting the needs of the present without compromising the ability of future
generations to meet their own needs.
Chapter 6
Definitions Chapter 6
Financial (statement) analysis
o The art of transforming data form financial statements into information that is useful
for informed decision making.
Balance Sheet (overview of all costs -> page 130)
o A summary of a firm’s financial position on a given data that shows total assets= total
liabilities + owners’ equity
o On a balance sheet each site of the sheet should be the same number
o Cash are always considered a asset
Income statement
o A summary of a firm’s revenue and expenses over a specific period ending with net
income or loss for the period
o An income statement shows which changes in the balances have occurred.
o Thus an income statement does not state any balances!
Liquid
Cash Equivalents
o Highly liquid, short term marketable securities that are readily convertible to known
amounts of cash and generally have remaining maturities of three months or less at
the time of acquisition.
Shareholder Equity
o Total assets minus total liabilities. Alternatively, the book value of a company’s
common stock (at par) plus additional paid-in capital and retained earnings.
Cost of Goods Sold (COGS)
o Products (inventor able costs) that become period expenses only when the products
are sold; equals beginning inventory plus costs of goods purchase or manufactures
minus ending inventory
Statement of retained earnings
o A financial statement summarizing the changes in retained earnings for a stated
period – resulting from earnings (or losses) and dividends paid. This statement is
often combined with the income statement.
Financial Ratio (page 157 book)
o An index that relates to accounting numbers and is obtained by dividing one number
by the other
o Ratios are used because they allow a better tool to compare different figures
because they look at the ratio and not the amount.
Liquidity Ratios (page 157 book)
o Ratios that measure a firm’s ability to meet short term obligations
Current Ratio (page 157 book)
o Current assets divided by current liabilities.
o It shows a firm’s ability to cover its current liabilities with its current assets.
Liquidity
o The ability of an asset to be converted into cash without significant price concession
Acid-Test (quick) ratio (page 157 book)
o Current assets less inventories divided by current liabilities.
o It shows a firm’s ability to meet current liabilities with it’s most liquid (quick) assets.
Debt ratios (page 157 book)
o Ratios that show the extent to which the firm is financed by debt.
Coverage ratios (page 140 book)
o Ratios that relate the financial charges of a firm to its ability to service, or cover,
them.
Interest Coverage ratio (page 157 book)
o Earnings before interest and taxes divided by interest charges.
o It indicates a firm’s ability to cover interest changes.
o It is also called times interest earned
Activity Ratio (page 157 book)
o Ratios that measure how effectively the firm is using its assets
Aging Accounts receivables (page 157 book)
o The process of classifying accounts receivable by their age outstanding as of a given
date
Stockout
o Not having enough items in inventory to fill an order
Operating Cycle
o The length of time from the commitment of cash for purchases until the collection of
receivables resulting the sale of goods or services.
Cash Cycle
o The length of time from the outlay of cash for the purchases until the collection of
receivables resulting from the sale of goods or services.
o Also called cash conversion cycle
Profitability ratios (page 157 book)
o Ratios that relate profits to sales and investments.
Common size analysis
o An analysis of percentage financial statements where all balance sheet items are
divided by total assets and all income statements items are divided by net sales or
revenues.
Index analysis
o An analysis of percentage financial statements where all balance sheet or income
statement figures for a base year equal 100.0 (percent) and subsequent financial
statements items are expressed as percentages of their values in the base year.
Chapter 3
Definitions Chapter 3
Interest
o Money paid (earned) for the use of money
Simple interest
o Interest paid (earned) on only the original amount, or principal borrowed (lent)
Future value
o The value at some future time of a present amount of money, or a series of
payments, evaluated at a given interest rate.
o Also known as the terminal value
Present value
o The current value of a future amount of money, or a series of payments, evaluated at
a given interest rate
Compound interest
o Interest paid (earned) on any previous interest earned, as wel as on the principal
borrowed (lent)
Discount rate
o Interest rate used to convert future values to present values
Annuity
o A series of equal payments or receipts occurring over a specified number of periods.
o In an ordinary annuity, payments or receipts occur at the end of each period; in an
annuity due, payments or receipts occur at the beginning of each period.
Perpetuity
o An ordinary annuity whose payments or receipts continue forever
Nominal (stated) interest rate
o A rate of interest quoted for a year that has not been adjusted for frequency of
compounding. If interest is compounded more than once a year, the effective
interest rate will be higher than the nominal rate.
Effective annual interest rate
o The actual rate of interest (paid) after adjusting the nominal rate for factor such as
the number of compounding periods per year.
Amortization Schedule
o A table showing the repayments schedule
Chapter 4
Definitions Chapter 4
Liquidation Values
o The amount of money that could be realized if an asset or a group of assets (e.g. a
firm) is sold separately from its operating organization
Going Concern value
o The amount a firm could be sold for as a continuing operating business
Book value
o (1)an asset: the accounting value of an asset – the asset’s cost minus its accumulated
depreciation;
o (2) a firm: total assets minus liabilities and preferred stock as listed on the balance
sheet
Market value
o The market price at which an asset trades
Intrinsic Value
o The price a security ”ought to have” based on all factors bearing on valuation
Bond
o A long term debt instrument issued by a corporation or government
Face Value
o The stated value of an asset. In the case of a bond the face value is usually $1000
Coupon rate
o The started rate of interest on a bond;
o the annual interest payment divided by the bond’s face value
Consol
o A bond that never matures
o A perpetuity in the form of a bond
Zero Coupon-bond
o A bond that pays no interest but sells at a deep discount form its face value
o It provides compensation in the form of price appreciation
Preferred Stock
o A type of stock that promises a (usually) fixed dividend, but at the discretion of the
board of directors. It has preference over common stock in the payments of
dividends and claims on assets.
Common Stock
o Securities that represent the ultimate ownership (and risk) position in the
corporation.
Yield to Maturity (YTM)
o The expected rate of return on a bond if bought at its current market price and held
to maturity
Interpolate
o Estimate an unknown number that lies somewhere between two known numbers
Bond Discount
o The amount by which the face value of a bond exceeds its current price
Bond Premium
o The amount by which the current price of a bond exceeds its face value
Interest Rate risk
o Also known as Yield
o The variation in the market price of a security cause by changes in interest rates
Chapter 5
Definitions Chapter 5
Return
o Income received on an investment plus any change in market price, usually
expressed as a percentage of the beginning market price of the investment.
Risk
o The variability of returns from those that are expected
Probability distribution
o A set of possible values that a random variable can assume and their associated
probabilities of occurrence.
Expected return
o The weighted average of possible returns with the weights b3eing the probabilities
of occurrence.
Standard deviation
o A statistical measure of the variability of a distribution around its mean. It is the
square root of the variance.
Coefficient of variation (CV)
o The ratio of the standard deviant of a distribution to the mean of that distribution. It
is a measure of relative risk.
Certainty Equivalent (CE)
o The amount of cash someone would require with certainty at a point in time to make
the individual indifferent between that certain amount and an amount expected to
be received with risk at the same point in time.
Risk Averse
o Term applied to an investor who demands a higher expected return, the higher the
risk.
o High risk - > high return.
Portfolio
o A combination of two or more securities or assets
Covariance
o A statistical measure of the degree to which two variables (e.g. securities’ returns)
move together. A positive value means that , on average, they move in the same
direction.
Systematic Risk
o The variability of return on stocks or portfolios associated with changes in return on
the market as a whole.
Unsystematic Risk
o The variability of return of stocks or portfolios not explained by general market
movements. It is avoidable through diversification.
Capital Asset Pricing model (CAPM)
o A model that describes the relationship between risk and expected (required) return
o In this model, a security’s expected (required) return is the risk-free rate plus a
premium based on the systematic risk of the security
Standard & Poor’s 500 stock index
o A market-value-weighted-index of 500 large capitalization common stocks selected
form a board cross-section of industry groups. It is used as a measure of overall
market performance.
Characteristic Line(p107)
o A line that describes the relationship between an individual security’s return and
returns on the market portfolio.
o The slope of this line is the beta
Beta
o An index of systematic risk.
o It measures the sensitivity of a stock’s returns to changes in returns on the market
portfolio.
o The beta of portfolio is simply a weighted average of the individual stock betas in the
portfolio
Security market Line (SML)
o A line that describes the linear relationship between expected rates of return of
returns individual securities (ad portfolio) and systematic risk, as measure by beta.
Adjusted Beta
o An estimate of security’s future beta that involves modifying the security’s historical
(measured) beta owing to the assumption that the security beta has a tendency to
move over time toward the average beta for the market or the company’s industry.
Efficient financial market
o A financial market in which current prices fully reflect all available relevant
information.
Chapter 7
Definitions Chapter 7
Flow of funds statement
o A summary of a firm’s changes in financial position form one period to another;
o It is also called a sources and uses of funds statement or a statement of changes in
financial position.
Statement of cash flows
o A summary of a firm’s cash receipts and cash payments during a period of time.
Cash budget ( Begroting)
o A firm’s forecast of future cash flows arising from collections and disbursements,
usually on a monthly basis.
Forecast financial statements
o Expected future financial statements based on conditions that management expects
to exist and actions it expects to take.
Chapter 8
Defections Chapter 8
Net working capital
o Current assets minus current liabilties
Gross working capital
o The firm’s investment in current assets (like cash and marketable securities,
receivables, and inventory)
Working capital management
o The administration of the firm’s current assets and the financing needed to support
current assets.
Permanent working capital
o The amount of current assets required to meet a firm’s long-term minimum needs
Temporary working capital
o The amount of current assets that varies with the seasonal requirements
Hedging
o A method of financing where each asset would be offset with a financing instrument
of the same approximate.
Spontaneous financing
o Trade credit, and other payables and accruals, that arise spontaneously in the firm’s
day-today operations.
Chapter 12
Definitions Chapter 12
Capital budgeting
o The process of identifying, analyzing, and selecting investments projects whose
returns (cash flows) are expected to extend beyond one year.
Sunk Costs
o Unrecoverable pas outlays that, as they cannot be recovered, should not affect
present actions or future decision.
Opportunity costs
o What is lost by not taking the next best-best investment alternative
Depreciable basis
o In tax accounting the fully installed cost of an asset. This is the amount that, by law,
may be written off over time for tax purposes.
Capitalized expenditures
o Expenditures that may provide benefits into the future and therefore are treated as
capital outlays an not as expenses of the period in which they were incurred.
Chapter 13
Definitions Chapter 13
Discounted cash flow (DCF)
o Any method of investment project evaluation and selection that adjusts cash flows
over time for the time value of money.
Payback Period (PBP) -> NOT DISCOUNTED
o The period of time required for the cumulative expected cash flows form an
investment project to equal the initial cash outflow.
Internal rate of return (IRR)
o The discount rate that equates the present value of the future net cash flows form an
investments project with the project’s initial cash outflows.
Interpolate
o Estimate an unknown number that lies somewhere between two know numbers.
Hurdle rate
o The minimum required rate of return on an investment in a discounted cash flow
analysis;
o The rate at which a project is acceptable.
Net present value (NPV)
o The present value of an investment project’s net cash flows minus the project’s initial
cash outflow
NPV profile
o A graph showing the relationship between an project’s net present value and the
discount rate employed.
Profitability index (PI)
o The ratio of the present value of a project’s future net cash flows to the project’s
initial cash outflow.
Independent project
o A project whose acceptance (or rejection) does not prevent the acceptance for other
project under consideration
Depended project
o A project whose acceptance depends on acceptance of one or more other projects.
Mutually Exclusive project
o A project whose acceptance precludes the acceptance of one or more alternative
projects.
Capital Rationing
o A situation where a constraint (or budget ceiling) is placed on the total size of capital
expenditures during a particular period.
Sensitivity Analysis
o Type of ”what if” uncertainty analysis in which variables are changed from a base
case in order to determine their impact on a project’s measured results, such as net
present value or internal rate of return
Chapter 15 -> Important
Definitions Chapter 15
Cost of capital
o The required rate of return on the various types of financing. The overall cost of
capital is a weighted average of the individual required rates of return (costs)
Cost of equity capital
o The required rate of return on a investment of the common shareholders of the
company.
Cost of debt (capital)
o The required rate of return on investment of the lenders of a company.
Cost of preferred stock (capital)
o The required rate of return on investment of the preferred shareholder o the
company.
Flotation Costs
o The costs associated with the issueing securities, such as underwriting, legal, listing,
and printing fees.
Net operating profit after tax (NOPAT)
o A company’s potential after tax net profit if it was all-equity-financed or “unlevered”
Economic value added (EVA)
o A measure of business performance. It is a type of economic in profit, which is equal
to a company’s after tax net operating profit minus a dollar costs pf capital charge(
and possibility including some adjustments.)
Subsidiary
o A company which has more tha half of its vorint share owned by another company
Risk adjusted discount rate (RADR)
o A required rate of return (discount rate) that is increased relative to the firm’s overall
costs of capital for projects or groups showing greater than ”average” risk and
decreased for projects or groups showing less than “average” risk.
Indifference curve
o The line representing all combination of expected return and risk that provide an
investor with an equal amount of satisfaction.
Chapter 16
Definitions Chapter 16
Leverage
o The use of fixed costs in an attempt to increase (or lever up) profitability
Operating Leverage
o The use of fixed operating costs by the firm
Financial Leverage
o The use of fixed costs by the firm the British expression is gearing.
Break even analysis
o (see book)
Break even point
o (see book)
Unit Contribution margin
o (See book)
Degree of operating leverage (DOL)
o The percentage change in a firm’s operating profit (EBIT) resulting form a 1 percent
change in output(sales)
Business Risk
o The inherent uncertainty in the physical operations of the firm. Its impact is shown in
the variability of the firm’s operating income. (EBIT)
Indifference Point
o EBIT – EPS indifference point) the level of EBIT that produces the same level of EPS
for two (or more alternative capital structures.
EBIT-EPS break even analysis
o Analysis of the effect of financing alternative on earning per share. The break-even
point is the EBIT level where EPS is het same for two (or more) alternative.
Degree of Financial leverage (DFL)
o The percentage of change in a firm’s earning per share (EPS) resulting form a 1
percent change in the operating profit (EBIT)
Cash Insolvency
o Inability to pay obligations as the fall due
Financial Risk
o The added variability in earnings per share (EPS) – plus the risk of possible insolvency
– that is induced by the use of financial leverage.
Total firm risk
o The variability in earnings per share (EPS). It is the sum of business plus financial risk.
Total or combined leverage
o The us of both fixed operating and financing costs by the firm
Degree of total leverage (DTL)
o The percentage change in a firm’s earning per share (EPS )( resulting form a 1
percent change in output (sales). This is also equal to a firm’s degree of operating
leverage (DOL) times its degree of financial leverage (FDL) at a particular level of
output (sales)
Deb capacity
o The maximum amount of debt (and other fixed charge financing) that a firm can
adequately service.
Coverage Ratios
o Ratios that relate the financial charges of a firm to its ability to service, or cover,
them.
Interest coverage ratios
o Earnings before interest and taxes divided by interest charges. It indicates a firm’s
ability to cover interest charges.
o It is also called times interest earned.
Chapter 17
Definitions Chapter 17
Capital structure
o The mix (or portion ) of a firm’s permanent long-term financing represented by debt,
preferred stock, and common stock equity
Capitalization rate
o The discount rate used to determine the present value of a stream of expected
future cash flows
Net operating income ( NOI) approach (to capital structure)
o A theory of capital structure in which the weighted average cost of capital (WACC)
and the total value of the firm remain constant as financial leverage is changed.
Recapitalization
o An alteration of a firm’s capital structure. For example , a firm may sell bonds to
acquire the cash necessary to repurchase some of its outstanding common stock.
Traditional approach (to capital structure)
o A theory of capital structure in which there exists and optimal capital structure and
where management can increase the total value of the firm through the judicious
use of financial leverage.
Optimal capital structure
o The capital structure that minimizes the firm’s costs of capital and thereby maximizes
the value of the firm.
Arbitrage
o Finding two assets that are essentially the same, buying the cheaper, and selling the
more expensive.
Agency costs
o See book
Tax shield
o A tax deductible expense.
o The expense protects (shields) and equivalent dollar amount of revenue being taxed
by reducing taxable income.
Formulas
Definition of 'Weighted Average Cost Of Capital - WACC'
A calculation of a firm's cost of capital in which each category of capital is
proportionately weighted. All capital sources - common stock, preferred
stock, bonds and any other long-term debt - are included in a WACC
calculation. All else equal, the WACC of a firm increases as the beta and rate
of return on equity increases, as an increase in WACC notes a decrease in
valuation and a higher risk.
The WACC equation is the cost of each capital component multiplied by its
proportional weight and then summing:
Where:
Re = cost of equity
Rd = cost of debt
E = market value of the firm's equity
D = market value of the firm's debt
V = E + D
E/V = percentage of financing that is equity
D/V = percentage of financing that is debt
Tc = corporate tax rate
Businesses often discount cash flows at WACC to determine the Net Present
Value (NPV) of a project, using the formula:
NPV = Present Value (PV) of the Cash Flows discounted at WACC.
Definition of 'Cash Conversion Cycle - CCC'
A metric that expresses the length of time, in days, that it takes for a
company to convert resource inputs into cash flows. The cash conversion
cycle attempts to measure the amount of time each net input dollar is tied up
in the production and sales process before it is converted into cash through
sales to customers. This metric looks at the amount of time needed to sell
inventory, the amount of time needed to collect receivables and the length of
time the company is afforded to pay its bills without incurring penalties.
Also known as "cash cycle."
Calculated as:
Where:
DIO represents days inventory outstanding
DSO represents days sales outstanding
DPO represents days payable outstanding
Definition of 'Days Sales Of Inventory - DSI'/ DIO
A financial measure of a company's performance that gives investors an idea
of how long it takes a company to turn its inventory (including goods that are
work in progress, if applicable) into sales. Generally, the lower (shorter) the
DSI the better, but it is important to note that the average DSI varies from
one industry to another.
Here is how the DSI is calculated:
Also known as days inventory outstanding (DIO).
Definition of 'Days Sales Outstanding - DSO'
A measure of the average number of days that a company takes to collect
revenue after a sale has been made. A low DSO number means that it takes
a company fewer days to collect its accounts receivable. A high DSO number
shows that a company is selling its product to customers on credit and taking
longer to collect money.
Days sales outstanding is calculated as:
Definition of 'Days Payable Outstanding - DPO'
A company's average payable period. Days payable outstanding tells how
long it takes a company to pay its invoices from trade creditors, such as
suppliers. DPO is typically looked at either quarterly or yearly.
The formula to calculate DPO is written as: ending accounts payable / (cost of
sales/number of days). These numbers are found on the balance sheet and
the income statement.
Definition of 'Net Present Value - NPV'
The difference between the present value of cash inflows and the present
value of cash outflows. NPV is used in capital budgeting to analyze the
profitability of an investment or project.
The following is the formula for calculating NPV:
where:
Ct = net cash inflow during the period
Co= initial investment
r = discount rate, and
t = number of time periods
In addition to the formula, net present value can often be calculated using
tables, as well as spreadsheets such as Microsoft Excel.
Definition of 'Present Value - PV'
The current worth of a future sum of money or stream of cash flows given a
specified rate of return. Future cash flows are discounted at the discount rate,
and the higher the discount rate, the lower the present value of the future
cash flows. Determining the appropriate discount rate is the key to properly
valuing future cash flows, whether they be earnings or obligations.
Also referred to as "discounted value".
Definition of 'Internal Rate Of Return - IRR'
The discount rate often used in capital budgeting that makes the net present
value of all cash flows from a particular project equal to zero. Generally
speaking, the higher a project's internal rate of return, the more desirable it
is to undertake the project. As such, IRR can be used to rank several
prospective projects a firm is considering. Assuming all other factors are
equal among the various projects, the project with the highest IRR would
probably be considered the best and undertaken first.
IRR is sometimes referred to as "economic rate of return (ERR)."
Definition of 'Required Rate Of Return - RRR'
The minimum annual percentage earned by an investment that will induce
individuals or companies to put money into a particular security or project.
The required rate of return (RRR) is used in both equity valuation and in
corporate finance.
Investors use the RRR to decide where to put their money. They compare the
return of an investment to all other available options, taking the risk-free rate
of return, inflation and liquidity into consideration in their calculation. For
investors using the dividend discount model to pick stocks, the RRR affects
the maximum price they are willing to pay for a stock. The RRR is also used
in calculations of net present value in discounted cash flow analysis.
Corporations use the RRR to decide if they should pursue a new project or
business expansion; in corporate finance, the RRR is equal to the weighted
average cost of capital (WACC).
Investopedia explains 'Required Rate Of Return - RRR'
You might require a return of 9% per year to consider a stock investment
worthwhile, assuming that you can easily sell the stock and inflation is 3%
per year. Your reasoning is that if you don't receive a 9% return, which is
really a 6% return after inflation, then you'd be better off putting your money
in a CD that earns a risk-free 3% per year (really 0% after inflation). You
aren't willing to take on the additional risk of investing in stocks, which can
be volatile and whose returns are not guaranteed, unless you can earn a 6%
premium over the risk-free CD. The RRR will be different for every individual
and every company depending on their risk tolerance, investment goals and
other unique factors.
Definition of 'Economic Value Added - EVA'
A measure of a company's financial performance based on the residual wealth
calculated by deducting cost of capital from its operating profit (adjusted for
taxes on a cash basis). (Also referred to as "economic profit".)
The formula for calculating EVA is as follows:
= Net Operating Profit After Taxes (NOPAT) - (Capital * Cost of Capital)
This measure was devised by Stern Stewart & Co. Economic value added
attempts to capture the true economic profit of a company.
Definition of 'Profitability Index'
An index that attempts to identify the relationship between the costs and
benefits of a proposed project through the use of a ratio calculated as:
A ratio of 1.0 is logically the lowest acceptable measure on the index. Any
value lower than 1.0 would indicate that the project's PV is less than the
initial investment. As values on the profitability index increase, so does the
financial attractiveness of the proposed project.
Definition of 'Return On Investment - ROI'
A performance measure used to evaluate the efficiency of an investment or to
compare the efficiency of a number of different investments. To calculate
ROI, the benefit (return) of an investment is divided by the cost of the
investment; the result is expressed as a percentage or a ratio.
The return on investment formula:
In the above formula "gains from investment", refers to the proceeds
obtained from selling the investment of interest. Return on investment is a
very popular metric because of its versatility and simplicity. That is, if an
investment does not have a positive ROI, or if there are other opportunities
with a higher ROI, then the investment should be not be undertaken.
Definition of 'Payback Period'
The length of time required to recover the cost of an investment. The
payback period of a given investment or project is an important determinant
of whether to undertake the position or project, as longer payback periods
are typically not desirable for investment positions.
Calculated as:
Payback Period = Cost of Project / Annual Cash Inflows
Definition of 'Earnings Before Interest & Tax - EBIT'
An indicator of a company's profitability, calculated as revenue minus
expenses, excluding tax and interest. EBIT is also referred to as "operating
earnings", "operating profit" and "operating income", as you can re-arrange
the formula to be calculated as follows:
EBIT = Revenue - COGS- Operating Expenses
Also known as Profit Before Interest & Taxes (PBIT), EBIT equals Net Income
with interest and taxes added back to it.
Definition of 'Cost Of Goods Sold - COGS'
The direct costs attributable to the production of the goods sold by a
company. This amount includes the cost of the materials used in creating the
good along with the direct labor costs used to produce the good. It excludes
indirect expenses such as distribution costs and sales force costs. COGS
appears on the income statement and can be deducted from revenue to
calculate a company's gross margin. Also referred to as "cost of sales."
Definition of 'Capital Asset Pricing Model - CAPM'
A model that describes the relationship between risk and expected return and
that is used in the pricing of risky securities.
The general idea behind CAPM is that investors need to be compensated in
two ways: time value of money and risk. The time value of money is
represented by the risk-free (rf) rate in the formula and compensates the
investors for placing money in any investment over a period of time. The
other half of the formula represents risk and calculates the amount of
compensation the investor needs for taking on additional risk. This is
calculated by taking a risk measure (beta) that compares the returns of the
asset to the market over a period of time and to the market premium (Rm-
rf).
Definition of ‘Depreciation Tax Shield’ – DTS A means of reducing income tax payments by deducting depreciation from the taxable income. Depreciation tax shield is computed as the amount of depreciation multiplied by the tax rate. Example, if the annual depreciation is $1,000 and the tax rate is 10%; the corresponding tax shield will be $100. The amount of depreciation will depend on the depreciation method, using accelerated depreciation allows for faster depreciation during the early life of the asset and slows down as the asset ages, hence, it provides for higher tax savings during its early stages of the asset's life.
Formulas Financial Accounting
Break even point (p67) BEP
o o With b being the number of units of output at the BEP
Contribution margin CM o Contribution margin = Sales – Variable costs
Contribution margin per unit(p69) CM p/u o Total contribution margin = Total sales – Total variable costs
Contribution margin Ratio(p70) CM ratio o Contribution margin ratio = Total contribution margin / Total sales
or o Contribution margin ratio = Contribution margin per unit / Sales price per unit
Total contribution margin total CM o Total contribution margin = Total sales – Total variable costs
Margin of safety (p70) o Excess of planned volume of activity over break even point
Achieving target profit (p73)
o o With t being the required number of unit of output to achieve the target profit
Cost per unit (p134) Cpu
o Batch Costing
o
Accounting rate of return (p278) ARR
o Payback Period (p283) PP
o Payback Period = Cost of Project / Annual Cash Inflows
Net Present Value (p287 or p364) NPV o
Present Value (p291) PV
o Internal Rate of Return (P297) IRR
o See book
Economic Value added (p371) EVA
o Shareholder value analysis (p364) SVA
o The value delivered to shareholders because of management's ability to grow
earnings, dividends and share price. In other words, shareholder value is the
sum of all strategic decisions that affect the firm's ability to efficiently increase
the amount of free cash flow over time.
Return of Investment (p398) ROI o A performance measure used to evaluate the efficiency of an investment or to
compare the efficiency of a number of different investments. To calculate ROI, the benefit (return) of an investment is divided by the cost of the investment; the result is expressed as a percentage or a ratio. The return on investment formula:
o
o
Residual Income(p400) RI o RI = Net income – charge for capital invested
Economic Value added 2.0 (p405) EVA
Average inventory turnover period (p440)
o
Economic Order Quantity (p445) EOQ
o
Average settlement period for trade receivables (p457)
o
Operating Cash Cycle (p465) OCC o OCC = Average inventories turnover period + Average settlement for trade
receivables – average payment period for trade payables
Average settlement period for trade payables (p471)
o
Basic Information Corporate Finance 1. Gross Profit Margin
The gross profit margin tells us the profit a company makes on its cost of
sales or cost of goods sold. In other words, it indicates how efficiently
management uses labor and supplies in the production process.
Gross Profit Margin = (Sales - Cost of Goods Sold)/Sales
Suppose that a company has $1 million in sales and the cost of its labor and
materials amounts to $600,000. Its gross margin rate would be 40% ($1
million - $600,000/$1 million).
The gross profit margin is used to analyze how efficiently a company is using
its raw materials, labor and manufacturing-related fixed assets to generate
profits. A higher margin percentage is a favorable profit indicator.
Gross profit margins can vary drastically from business to business and from
industry to industry. For instance, the airline industry has a gross margin of about 5%, while the software industry has a gross margin of about 90%.
2. Operating Profit Margin
By comparing earnings before interest and taxes (EBIT) to sales, operating profit margins show how successful a company's management has been at
generating income from the operation of the business:
Operating Profit Margin = EBIT/Sales
If EBIT amounted to $200,000 and sales equaled $1 million, the operating
profit margin would be 20%.
This ratio is a rough measure of the operating leverage a company can achieve in the conduct of the operational part of its business. It indicates how
much EBIT is generated per dollar of sales. High operating profits can mean the company has effective control of costs, or that sales are increasing faster
than operating costs. Positive and negative trends in this ratio are, for the most part, directly attributable to management decisions.
Because the operating profit margin accounts for not only costs of materials
and labor, but also administration and selling costs, it should be a much smaller figure than the gross margin.
3. Net Profit Margin
Net profit margins are those generated from all phases of a business,
including taxes. In other words, this ratio compares net income with sales. It
comes as close as possible to summing up in a single figure how effectively managers run the business:
Net Profit Margins = Net Profits after Taxes/Sales
If a company generates after-tax earnings of $100,000 on its $1 million of
sales, then its net margin amounts to 10%.
Often referred to simply as a company's profit margin, the so-called bottom
line is the most often mentioned when discussing a company's profitability.
Again, just like gross and operating profit margins, net margins vary between
industries. By comparing a company's gross and net margins, we can get a
good sense of its non-production and non-direct costs like administration,
finance and marketing costs.
For example, the international airline industry has a gross margin of just 5%.
Its net margin is just a tad lower, at about 4%. On the other hand, discount
airline companies have much higher gross and net margin numbers. These
differences provide some insight into these industries' distinct cost
structures: compared to its bigger, international cousins, the discount airline
industry spends proportionately more on things like finance, administration
and marketing, and proportionately less on items such as fuel and flight crew
salaries.
In the software business, gross margins are very high, while net profit
margins are considerably lower. This shows that marketing and
administration costs in this industry are very high, while cost of sales and
operating costs are relatively low.
When a company has a high profit margin, it usually means that it also has
one or more advantages over its competition. Companies with high net profit
margins have a bigger cushion to protect themselves during the hard times.
Companies with low profit margins can get wiped out in a downturn. And
companies with profit margins reflecting a competitive advantage are able to
improve their market share during the hard times, leaving them even better
positioned when things improve again.
Like all ratios, margin ratios never offer perfect information. They are only as
good as the timeliness and accuracy of the financial data that gets fed into
them, and analyzing them also depends on a consideration of the company's
industry and its position in the business cycle. Margins tell us a lot about a
company's prospects, but not the whole story.
Cash Flow And Relationships Between Financial Statement - Free Cash Flow
By establishing how much cash a company has after paying its bills for ongoing activities and growth,
FCF is a measure that aims to cut through the arbitrariness and "guesstimations" involved in reported
earnings. Regardless of whether a cash outlay is counted as an expense in the calculation of income
or turned into an asset on the balance sheet, free cash flow tracks the money.
To calculate FCF, make a beeline for the company's cash flow statement and balance sheet. There
you will find the item cash flow from operations (also referred to as "operating cash"). From this
number, subtract estimated capital expenditure required for current operations:
Cash Flow From Operations (Operating Cash)
- Capital Expenditure
----------------------------
= Free Cash Flow
To do it another way, grab the income statement and balance sheet. Start with net incomeand add
back charges for depreciation and amortization. Make an additional adjustment for changes
in working capital, which is done by subtracting current liabilities from current assets. Then subtract
capital expenditure (or spending on plants and equipment):
Net income
+ Depreciation/Amortization
- Change in Working Capital
- Capital Expenditure
----------------------------
= Free Cash Flow
It might seem odd to add back depreciation/amortization since it accounts for capital spending. The
reasoning behind the adjustment is that free cash flow is meant to measure money being spent right
now, not transactions that happened in the past. This makes FCF a useful instrument for identifying
growing companies with high up-front costs, which may eat into earnings now but have the potential
to pay off later.
Definition of 'Cost Of Equity'
In financial theory, the return that stockholders require for a company. The traditional formula for
cost of equity (COE) is the dividend capitalization model:
A firm's cost of equity represents the compensation that the market demands in exchange for
owning the asset and bearing the risk of ownership.
Let's look at a very simple example: let's say you require a rate of return of 10% on an investment in
TSJ Sports. The stock is currently trading at $10 and will pay a dividend of $0.30. Through a
combination of dividends and share appreciation you require a $1.00 return on your $10.00
investment. Therefore the stock will have to appreciate by $0.70, which, combined with the $0.30
from dividends, gives you your 10% cost of equity.
The capital asset pricing model (CAPM) is another method used to determine cost of equity.
Definition of 'Cost Of Debt'
The effective rate that a company pays on its current debt. This can be measured in either before- or
after-tax returns; however, because interest expense is deductible, the after-tax cost is seen most
often. This is one part of the company's capital structure, which also includes the cost of equity.
A company will use various bonds, loans and other forms of debt, so this measure is useful for giving
an idea as to the overall rate being paid by the company to use debt financing. The measure can also
give investors an idea as to the riskiness of the company compared to others, because riskier
companies generally have a higher cost of debt.
To get the after-tax rate, you simply multiply the before-tax rate by one minus the marginal tax rate
(before-tax rate x (1-marginal tax)). If a company's only debt were a single bond in which it paid 5%,
the before-tax cost of debt would simply be 5%. If, however, the company's marginal tax rate were
40%, the company's after-tax cost of debt would be only 3% (5% x (1-40%)).
Future Value
here are two ways to calculate Future Value (FV):
1) For an asset with simple annual interest: = Original Investment x (1+(interest rate*number of
years))
2) For an asset with interest compounded annually: = Original Investment x ((1+interest
rate)^number of years) Consider the following examples:
1) $1000 invested for five years with simple annual interest of 10% would have a future value of
$1,500.00.
2) $1000 invested for five years at 10%, compounded annually has a future value of $1,610.51.
When planning investment strategy, it's useful to be able to predict what an investment is likely to be
worth in the future, taking the impact of compound interest into account. This formula allows you (or
your calculator) to do just that:
Pn = P0(1+r)n
Pnis future value of P0
P0 is original amount invested
r is the rate of interest
n is the number of compounding periods (years,
months, etc.)
Note in the example below that when you increase the frequency of compounding, you also increase
the future value of your investment.
P0 = $10,000
Pn is the future value of P0
n = 10 years
r = 9%
Example 1- If interest is compounded annually, the future value (Pn) is $23,674.
Pn = $10,000(1 + .09)10 = $23,674
Example 2 - If interest is compounded monthly, the future value (Pn) is $24,514.
Pn = $10,000(1 + .09/12)120
= $24,514
Present Value
Present value, also called "discounted value," is the current worth of a future sum of money or
stream of cash flow given a specified rate of return. Future cash flows are discounted at the discount
rate; the higher the discount rate, the lower the present value of the future cash flows. Determining
the appropriate discount rate is the key to properly valuing future cash flows, whether they are
earnings or obligations. If you received $10,000 today, the present value would be $10,000 because
present value is what your investment gives you if you were to spend it today. If you received
$10,000 in a year, the present value of the amount would not be $10,000 because you do not have it
in your hand now, in the present. To find the present value of the $10,000 you will receive in the
future, you need to pretend that the $10,000 is the total future value of an amount that you invested
today. In other words, to find the present value of the future $10,000, we need to find out how much
we would have to invest today in order to receive that $10,000 in the future.
To calculate present value, or the amount that we would have to invest today, you must subtract the
(hypothetical) accumulated interest from the $10,000. To achieve this, we can discount the future
payment amount ($10,000) by the interest rate for the period. In essence, all you are doing is
rearranging the future value equation above so that you may solve for P. The above future value
equation can be rewritten by replacing the P variable with present value (PV) and manipulating the
equation as follows:
Let's walk backwards from the $10,000 offered in Option B. Remember, the $10,000 to be received in
three years is really the same as the future value of an investment. If today we were at the two-year
mark, we would discount the payment back one year. At the two-year mark, the present value of the
$10,000 to be received in one year is represented as the following:
Present value of future payment of $10,000 at end of
year two:
Note that if we were at the one-year mark today, the above $9,569.38 would be considered the
future value of our investment one year from now.
At the end of the first year we would be expecting to receive the payment of $10,000 in two years. At
an interest rate of 4.5%, the calculation for the present value of a $10,000 payment expected in two
years would be the following:
Present value of $10,000 in one year:
Of course, because of the rule of exponents, we don't have to calculate the future value of the
investment every year counting back from the $10,000 investment at the third year. We could put
the equation more concisely and use the $10,000 as the future value. So, here is how you can
calculate today's present value of the $10,000 expected from a three-year investment earning 4.5%:
The present value of a future payment of $10,000 is worth $8,762.97 today if interest rates are 4.5%
per year. In other words, choosing Option B is like taking $8,762.97 now and then investing it for
three years. The equations above illustrate that Option A is better not only because it offers you
money right now but because it offers you $1,237.03 ($10,000 - $8,762.97) more in cash!
Furthermore, if you invest the $10,000 that you receive from Option A, your choice gives you a future
value that is $1,411.66 ($11,411.66 - $10,000) greater than the future value of Option B.
Present Value of a Future Payment
Let's add a little spice to our investment knowledge. What if the payment in three years is more than
the amount you'd receive today? Say you could receive either $15,000 today or $18,000 in four
years. Which would you choose? The decision is now more difficult. If you choose to receive $15,000
today and invest the entire amount, you may actually end up with an amount of cash in four years
that is less than $18,000. You could find the future value of $15,000, but since we are always living in
the present, let's find the present value of $18,000 if interest rates are currently 4%. Remember that
the equation for present value is the following:
In the equation above, all we are doing is discounting the future value of an investment. Using the
numbers above, the present value of an $18,000 payment in four years would be calculated as the
following:
Present Value
From the above calculation we now know our choice is between receiving $15,000 or $15,386.48
today. Of course we should choose to postpone payment for four years! (For related reading,
see Anything But Ordinary: Calculating The Present And Future Value Of Annuities.)
These calculations demonstrate that time literally is money - the value of the money you have now is
not the same as it will be in the future and vice versa. It is important to know how to calculate the
time value of money so that you can distinguish between the worth of investments that offer you
returns at different times.
Examples
Discounted Cash Flow Valuation - Perpetuities
A perpetuity is a constant stream of identical cash flows with no end. The formula for determining
the present value of a perpetuity is as follows:
A delayed perpetuity is perpetual stream of cash flows that starts at a predetermined date in the
future. For example, preferred fixed dividend paying shares are often valued using a perpetuity
formula. If the dividends are going to originate (start) five years from now, rather than next year, the
stream of cash flows would be considered a delayed perpetuity.
Although it may seem a bit illogical, an infinite series of cash flows can have a finite present value.
Because of the time value of money, each payment is only a fraction of the last.
The net present value (NPV) of a delayed perpetuity is less than a comparable ordinary perpetuity
because, based on time value of money principles, the payments have to be discounted to account
for the delay. Retirement products are often structured as delayed perpetuities.
Net Present Value And Internal Rate Of Return - Introduction To Net Present Value And
Internal Rate Of Return
Net present value (NPV) is the difference between the present value of cash inflows and the present
value of cash outflows. NPV compares the value of a dollar today to the value of that same dollar in
the future, taking inflation and returns into account. NPV analysis is sensitive to the reliability of
future cash inflows that an investment or project will yield and is used in capital budgeting to assess
the profitability of an investment or project.
NPV is calculated using the following formula:
If the NPV of a prospective project is positive, the project should be accepted. However, if NPV is
negative, the project should probably be rejected because cash flows will also be negative.
For example, if a retail clothing business wants to purchase an existing store, it would first estimate
the future cash flows that store would generate, then discount those cash flows into one lump-sum
present value amount, say $565,000. If the owner of the store was willing to sell his business for less
than $565,000, the purchasing company would likely accept the offer as it presents a positive NPV
investment. Conversely, if the owner would not sell for less than $565,000, the purchaser would not
buy the store, as the investment would present a negative NPV. (Sometimes losing investments
aren't what they seem. Learn more in How To Profit From Investment "Losers".)
Internal rate of return (IRR) is the discount rate often used in capital budgeting that makes the net
present value of all cash flows from a particular project equal to zero. Generally speaking, the higher
a project's internal rate of return, the more desirable it is to undertake the project. As such, IRR can
be used to rank several prospective projects a firm is considering. Assuming all other factors are
equal among the various projects, the project with the highest IRR would probably be considered the
best and undertaken first.
You can think of IRR as the rate of growth a project is expected to generate. While the actual rate of
return that a given project ends up generating will often differ from its estimated IRR rate, a project
with a substantially higher IRR value than other available options would still provide a much better
chance of strong growth.
IRRs can also be compared against prevailing rates of return in the securities market. If a firm can't
find any projects with IRRs greater than the returns that can be generated in the financial markets, it
may simply choose to invest its retained earnings into the market. (For related reading, see The Top
New Investment: Doing Nothing.)
Net Present Value And Internal Rate Of Return - Profitability Index
A profitability index attempts to identify the relationship between the costs and benefits of a
proposed project. The profitability index is calculated by dividing the present value of the project's
future cash flows by the initial investment. A PI greater than 1.0 indicates that profitability is positive,
while a PI of less than 1.0 indicates that the project will lose money. As values on the profitability
index increase, so does the financial attractiveness of the proposed project.
The PI ratio is calculated as follows:
PV of Future Cash Flows
Initial Investment
A ratio of 1.0 is logically the lowest acceptable measure for the index. Any value lower than 1.0
would indicate that the project's PV is less than the initial investment, and the project should be
rejected or abandoned. The profitability index rule states that the ratio must be greater than 1.0 for
the project to proceed.
For example, a project with an initial investment of $1 million and present value of future cash flows
of $1.2 million would have a profitability index of 1.2. Based on the profitability index rule, the
project would proceed. Essentially, the PI tells us how much value we receive per dollar invested. In
this example, each dollar invested yields $1.20.
The profitability index rule is a variation of the net present value (NPV) rule. In general, if NPV is
positive, the profitability index would be greater than 1; if NPV is negative, the profitability index
would be below 1. Thus, calculations of PI and NPV would both lead to the same decision regarding
whether to proceed with or abandon a project.
However, the profitability index differs from NPV in one important respect: being a ratio, it ignores
the scale of investment and provides no indication of the size of the actual cash flows.
The PI can also be thought of as turning a project's NPV into a percentage rate.
Calculating the Cost of Equity
The cost of equity can be a bit tricky to calculate as share capital carries no "explicit" cost. Unlike
debt, which the company must pay in the form of predetermined interest, equity does not have a
concrete price that the company must pay, but that doesn't mean no cost of equity exists.
Common shareholders expect to obtain a certain return on their equity investment in a company.
The equity holders' required rate of return is a cost from the company's perspective because if the
company does not deliver this expected return, shareholders will simply sell their shares, causing the
price to drop. The cost of equity is basically what it costs the company to maintain a share price that
is theoretically satisfactory to investors. (For further reading on share price, see Top 5 Stocks Back
From The Dead and The Highest Priced Stocks In America.)
On this basis, the most commonly accepted method for calculating cost of equity comes from the
Nobel Prize-winning capital asset pricing model (CAPM): The cost of equity is expressed formulaically
below:
Re = rf + (rm – rf) * β
Where:
Re = the required rate of return on equity
rf = the risk free rate
rm – rf = the market risk premium
β = beta coefficient = unsystematic risk
But what does this mean?
Rf – Risk-free rate - This is the amount obtained from investing in securities considered free from
credit risk, such as government bonds from developed countries. The interest rate of U.S. Treasury
Bills is frequently used as a proxy for the risk-free rate.
ß – Beta - This measures how much a company's share price reacts against the market as a whole. A
beta of one, for instance, indicates that the company moves in line with the market. If the beta is in
excess of one, the share is exaggerating the market's movements; less than one means the share is
more stable. Occasionally, a company may have a negative beta (e.g. a gold-mining company), which
means the share price moves in the opposite direction to the broader market. (Learn more inBeta:
Know The Risk.)
For public companies, you can find database services that publish betas. Few services do a better job
of estimating betas than BARRA. While you might not be able to afford to subscribe to the beta
estimation service, this site describes the process by which they come up with "fundamental" betas.
Bloomberg and Ibbotson are other valuable sources of industry betas.
(Rm – Rf) = Equity Market Risk Premium (EMRP) - The equity market risk premium (EMRP)
represents the returns investors expect to compensate them for taking extra risk by investing in the
stock market over and above the risk-free rate. In other words, it is the difference between the risk-
free rate and the market rate. It is a highly contentious figure. Many commentators argue that it has
gone up due to the notion that holding shares has become more risky.
The EMRP frequently cited is based on the historical average annual excess returnobtained from
investing in the stock market above the risk-free rate. The average may either be calculated using an
arithmetic mean or a geometric mean. The geometric mean provides an annually compounded rate
of excess return and will in most cases be lower than the arithmetic mean. Both methods are
popular, but the arithmetic average has gained widespread acceptance.
Once the cost of equity is calculated, adjustments can be made to take account of risk factors specific
to the company, which may increase or decrease a company's risk profile. Such factors include the
size of the company, pending lawsuits, concentration of customer base and dependence on key
employees. Adjustments are entirely a matter of investor judgment, and they vary from company to
company. (Learn more in The Capital Asset Pricing Model: An Overview.)
Cost of Newly Issued Stock
Cost of newly issued stock (Rc) is the cost of external equity, and it is based on the cost of retained
earnings increased for flotation costs (cost of issuing common stock). For a constant-growth
company, this can be calculated as follows:
Rc = D1__ + g
P0 (1-F)
where:
F = the percentage flotation cost, or (current stock price
- funds going to company) / current stock price
Example: Cost of Newly Issued Stock
Assume Newco's stock is selling for $40, its expected ROE is 10%, next year's dividend is $2 and the
company expects to pay out 30% of its earnings. Additionally, assume the company has a flotation
cost of 5%. What is Newco's cost of new equity?
Answer:
Rc = 2 + 0.07 = 0.123, or 12.3%
40(1-0.05)
It is important to note that the cost of newly issued stock is higher than the company's cost of
retained earnings. This is due to the flotation costs. (For more on newly issued stock, see Why
Investors Can't Get Enough Of Social Media IPOs and 5 Signs That Social Media Is The Next Bubble.)
Weighted Average Cost of Equity
Weighted average cost of equity (WACE) is a way to calculate the cost of a company's equity that
gives different weight to different aspects of the equities. Instead of lumping retained earnings,
common stock and preferred stock together, WACE provides a more accurate idea of a company's
total cost of equity.
Here is an example of how to calculate WACE:
First, calculate the cost of new common stock, the cost of preferred stock and the cost ofretained
earnings. Let's assume we have already done this and the cost of common stock, preferred stock and
retained earnings are 24%, 10% and 20% respectively.
Now, calculate the portion of total equity that is occupied by each form of equity. Again, let's assume
this is 50%, 25% and 25%, for common stock, preferred stock and retained earnings, respectively.
Finally, multiply the cost of each form of equity by its respective portion of total equity, and sum of
the values to get WACE. Our example results in a WACE of 19.5%.
WACE = (.24*.50) + (.10*.25) + (.20*.25) = 0.195 or 19.5%
Determining an accurate cost of equity for a firm is integral in order to be able to calculate the firm's
cost of capital. In turn, an accurate measure of the cost of capital is essential when a firm is trying to
decide if a future project will be profitable or not.
Cost Of Capital - Cost Of Debt And Preferred Stock Recall from Section 5 that companies sometimes finance their operations through debt in the form of
bonds because bonds provide more flexible borrowing terms than banks. How much do companies
pay for this debt?
Compared to cost of equity, cost of debt is fairly straightforward to calculate. The rate applied to
determine the cost of debt (Rd) should be the current market rate the company is paying on its debt.
If the company is not paying market rates, an appropriate market rate payable by the company
should be estimated.
Calculating the Cost of Debt
Because companies benefit from the tax deductions available on interest paid, the net cost of the
debt is actually the interest paid less the tax savings resulting from the tax-deductible interest
payment.
The after-tax cost of debt can be calculated as follows:
After-tax cost of debt = Rd (1-
tc)
Note: Rd represents the cost to issue new
debt, not the cost of the firm\'s existing debt.
Example: Cost of Debt
Newco plans to issue debt at a 7% interest rate. Newco's total (both federal and state) tax rate is
40%. What is Newco's cost of debt?
Answer:
Rd (1-tc) = 7% (1-0.40) = 4.2%
Calculating the Cost of Preferred Stock
As we discussed in section 6 of this walkthrough, preferred stocks straddle the line between stocks
and bonds. Technically, they are equity securities, but they share many characteristics with debt
instruments. Preferreds are issued with a fixed par value and pay dividends based on a percentage of
that par at a fixed rate.
Cost of preferred stock (Rps) can be calculated as follows:
Rps = Dps/Pnet
where:
Dps = preferred
dividends
Pnet = net issuing
price
Example: Cost of Preferred Stock
Assume Newco's preferred stock pays a dividend of $2 per share and sells for $100 per share. If the
cost to Newco to issue new shares is 4%, what is Newco's cost of preferred stock?
Answer:
Rps = Dps/Pnet = $2/$100(1-0.04) = 2.1%
For more on this subject, read Prefer Dividends? Why Not Look At Preferred Stock?
Next, we'll take a look at the weighted average cost of capital, a calculation that will put our formulas
for both the cost of equity and the cost of debt to work.
Financial Leverage And Capital Structure Policy
Capital structure, the mixture of a firm's debt and equity, is important because it costs a company
money to borrow. Capital structure also matters because of the different tax implications of debt vs.
equity and the impact of corporate taxes on a firm's profitability. Firms must be prudent in their
borrowing activities to avoid excessive risk and the possibility of financial distress or even
bankruptcy.
A firm's debt-to-equity ratio also impacts the firm's borrowing costs and its value to shareholders.
The debt-to-equity ratio is a measure of a company's financial leverage calculated by dividing its total
liabilities by stockholders' equity. It indicates what proportion of equity and debt the company is
using to finance its assets.
A high debt/equity ratio generally means that a company has been aggressive in financing its growth
with debt. This can result in volatile earnings as a result of the additional interest expense.
If a lot of debt is used to finance increased operations (high debt to equity), the company could
potentially generate more earnings than it would have without this outside financing. If this financing
increases earnings by a greater amount than the debt cost (interest), then the shareholders benefit
as more earnings are being spread among the same amount of shareholders. However, the cost of
this debt financing may outweigh the return that the company generates on the debt through
investment and business activities and become too much for the company to handle. Insufficient
returns can lead to bankruptcy and leave shareholders with nothing.
Financial Leverage And Capital Structure Policy - Financial Leverage
Financial leverage is the degree to which a company uses fixed-income securities such as debt and
preferred equity. The more debt financing a company uses, the higher its financial leverage. A high
degree of financial leverage means high interest payments, which negatively affect the company's
bottom-line earnings per share.
Financial risk is the risk to the stockholders that is caused by an increase in debt and preferred
equities in a company's capital structure. As a company increases debt and preferred equities,
interest payments increase, reducing EPS. As a result, risk to stockholder return is increased. A
company should keep its optimal capital structure in mind when making financing decisions to
ensure any increases in debt and preferred equity increase the value of the company. (Learn more
about leverage in ETFs: Losing At Leverage and 5 Ways Debt Can Make You Money.)
Degree of Financial Leverage
The formula for calculating a company's degree of financial leverage (DFL) measures the percentage
change in earnings per share over the percentage change in EBIT. DFL is the measure of the
sensitivity of EPS to changes in EBIT as a result of changes in debt.
Formula:
DFL = percentage change in EPS or EBIT
percentage change in EBIT EBIT-interest
A shortcut to keep in mind with DFL is that if interest is 0, then the DLF will be equal to 1.
Example: Degree of Financial Leverage
With Newco's current production, its sales are $7 million annually. The company's variable costs of
sales are 40% of sales, and its fixed costs are $2.4 million. The company's annual interest expense is
$100,000. If we increase Newco's EBIT by 20%, how much will the company's EPS increase?
Calculation and Answer:
The company's DFL is calculated as follows:
DFL = ($7,000,000-$2,800,000-$2,400,000)/($7,000,000-$2,800,000-$2,400,000-$100,000)
DFL = $1,800,000/$1,700,000 = 1.058
Given the company's 20% increase in EBIT, the DFL indicates EPS will increase 21.2%.
