Overview

The Balance Sheet

Definition Financial statements that show the value of the firms

assets and liabilities at a particular point in time (from an accounting perspective).

Copyright 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

The Balance Sheet

3

The Main Balance Sheet Items Current Assets Cash & Securities Receivables Inventories

+ Fixed Assets Tangible Assets Intangible Assets

} Current Liabilities Payables Short-term Debt

+ Long-term Liabilities

+ Shareholders Equity

{=


Market Value vs. Book Value

Book Values are determined by GAAP Market Values are determined by current values Equity and Asset Market Values are usually higher than their

Book Values


The Income Statement

Definition Financial statement that shows the revenues,

expenses, and net income of a firm over a period of time (from an accounting perspective).


The Income Statement

Earnings Before Income & Taxes (EBIT) EBIT = - total Revenues - costs - deprecation


The Statement of Cash Flows

Definition Financial statement that shows the firms cash

receipts and cash payments over a period of time.


Taxes

Taxes have a major impact on financial decisions Marginal Tax Rate is the tax that the individual pays on each

extra dollar of income. Average Tax Rate is the total tax bill divided by total income.


Future Values

Future Value - Amount to which an investment will grow after earning interest.

Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original

investment.


Future Values

Future Value of $100 = FV

FV r t= +$100 ( )1


Present Values

Present Value

Value today of a future cash

flow.

Discount Rate

Interest rate used to compute

present values of future cash flows.

Discount Factor

Present value of a $1 future payment.


Present Values

Present Value = PV

PV = Future Value after t periods (1+r) t


Present Values

Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of

any cash flow.

DFr t

=+1

1( )


Time Value of Money (applications)

The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable.

PV FVr t

= +1

1( )


PV of Multiple Cash Flows

PVs can be added together to evaluate multiple cash flows.

PV Cr

Cr

= + ++ +

11

221 1( ) ( )

....


Perpetuities & Annuities

Perpetuity A stream of level cash payments that never ends.

Annuity

Equally spaced level stream of cash flows for a limited period of time.



PV of Perpetuity Formula C = cash payment r = interest rate

PV Cr=



PV of Annuity Formula C = cash payment r = interest rate t = Number of years cash payment is received

[ ]PV C r r r t= +1 11( )



PV Annuity Factor (PVAF) - The present value of $1 a year for each of t years.

[ ]PVAF r r r t= +1 11( )



Applications Value of payments Implied interest rate for an annuity Calculation of periodic payments

Mortgage payment Annual income from an investment payout Future Value of annual payments

[ ]FV C PVAF r t= +( )1


Inflation

Inflation - Rate at which prices as a whole are increasing.

Nominal Interest Rate - Rate at which money invested grows.

Real Interest Rate - Rate at which the purchasing power of an investment increases.


Inflation

1 + real interest rate = 1+nominal interest rate1+inflation rate

approximation formula

Real int. rate nominal int. rate - inflation rate


Effective Interest Rates

Annual Percentage Rate - Interest rate that is annualized using simple interest.

Effective Annual Interest Rate - Interest rate that is annualized using compound interest.


Bonds

Terminology Bond - Security that obligates the issuer to make specified

payments to the bondholder. Coupon - The interest payments made to the bondholder. Face Value (Par Value or Principal Value) - Payment at the

maturity of the bond. Coupon Rate - Annual interest payment, as a percentage of face

value.


Bond Pricing The price of a bond is the Present Value of all cash flows

generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

PV cpnr

cpnr

cpn parr t

=+

++

+ +++( ) ( )

.... ( )( )1 1 11 2


Bond Cash Flows


Bond Pricing Example (continued) Q: How did the calculation change, given semi-annual coupons

versus annual coupon payments?

Time Periods

Paying coupons twice a year, instead of once

doubles the total number of cash flows to be discounted

in the PV formula.

Discount Rate

Since the time periods are now half years, the discount rate is also

changed from the annual rate to the half year rate.


Bond Yields Current Yield - Annual coupon payments divided by bond

price. Yield To Maturity - Interest rate for which the present value

of the bonds payments equal the price.


Bond Yields Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate,

the yield to maturity can be found by solving for r.

PV cpnr

cpnr

cpn parr t

=+

++

+ +++( ) ( )

.... ( )( )1 1 11 2


Bond Yields Rate of Return - Earnings per period per dollar invested.

Rate of return = total incomeinvestment

Rate of return = Coupon income + price changeinvestment


Nominal and Real rates

0

2

4

6

8

10

12

14

85 86 87 88 89 90 91 92 93 94 95 96 97 98 9920

0020

0120

0220

0320

0420

05

Year

Perc

ent

Yield on UK nominal bonds

Yield on UK indexed bonds


Default Risk Credit risk Default premium Investment grade Junk bonds


Corporate Bonds Zero coupons Floating rate bonds Convertible bonds


Stocks & Stock Market Primary Market - Place where the sale of new stock first

occurs. Initial Public Offering (IPO) - First offering of stock to the

general public. Seasoned Issue - Sale of new shares by a firm that has

already been through an IPO


Stocks & Stock Market Common Stock - Ownership shares in a publicly held

corporation. Secondary Market - market in which already issued securities

are traded by investors. Dividend - Periodic cash distribution from the firm to the

shareholders. P/E Ratio - Price per share divided by earnings per share.


Stocks & Stock Market Book Value - Net worth of the firm according to the balance

sheet. Liquidation Value - Net proceeds that would be realized by

selling the firms assets and paying off its creditors. Market Value Balance Sheet - Financial statement that uses

market value of assets and liabilities.


Valuing Common Stocks Expected Return - The percentage yield that an investor

forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR).

Expected Return = = + r Div P PP

1 1 0

0


Valuing Common Stocks The formula can be broken into two parts.

Dividend Yield + Capital Appreciation

Expected Return = = + r DivP

P PP

1

0

1 0

0


Valuing Common Stocks Dividend Discount Model - Computation of todays stock

price which states that share value equals the present value of all expected future dividends.

H - Time horizon for your investment.

P Divr

Divr

Div Pr

H HH0

11

221 1 1

=+

++

+ ++

+( ) ( )...

( )


Valuing Common Stocks If we forecast no growth, and plan to hold out stock

indefinitely, we will then value the stock as a PERPETUITY.

Perpetuity P Divr

or EPSr

= =01 1

Assumes all earnings are paid to shareholders.


Valuing Common Stocks Constant Growth DDM - A version of the dividend growth

model in which dividends grow at a constant rate (Gordon Growth Model).

P Divr g0

1=

Given any combination of variables in the equation, you can solve for the unknown variable.


Valuing Common Stocks If a firm elects to pay a lower dividend, and reinvest the

funds, the stock price may increase because future dividends may be higher.

Payout Ratio - Fraction of earnings paid out as dividends Plowback Ratio - Fraction of earnings retained by the firm.


Valuing Common Stocks Growth can be derived from applying the return on equity to

the percentage of earnings plowed back into operations. g = return on equity X plowback ratio


Valuing Common Stocks Present Value of Growth Opportunities (PVGO) - Net present

value of a firms future investments. Sustainable Growth Rate - Steady rate at which a firm can

grow: plowback ratio X return on equity.


Random Walk Theory The movement of stock prices from day to day DO NOT

reflect any pattern. Statistically speaking, the movement of stock prices is

random (skewed positive over the long term).


Another Tool Fundamental Analysts Research the value of stocks using NPV and other

measurements of cash flow


Efficient Market Theory Weak Form Efficiency

Market prices reflect all historical information

Semi-Strong Form Efficiency Market prices reflect all publicly available information

Strong Form Efficiency Market prices reflect all information, both public and private


Net Present Value

Net Present Value - Present value of cash flows minus initial investments.

Opportunity Cost of Capital - Expected rate of return given up by investing in a project


Net Present Value NPV = PV - required investment

NPV C Crt

t= + +0 1( )

NPV C Cr

Cr

Crt

t= + ++

++ +

+01

12

21 1 1( ) ( )...

( )


Net Present Value Terminology C = Cash Flow t = time period of the investment r = opportunity cost of capital

The Cash Flow could be positive or negative at any time period.


Net Present Value Net Present Value Rule Managers increase shareholders wealth by accepting all

projects that are worth more than they cost. Therefore, they should accept all projects with a positive net

present value.


Payback Method

Payback Period - Time until cash flows recover the initial investment of the project.

The payback rule specifies that a project be accepted if its

payback period is less than the specified cutoff period.


Other Investment Criteria Internal Rate of Return (IRR) - Discount rate at

which NPV = 0. Rate of Return Rule - Invest in any project offering a

rate of return that is higher than the opportunity cost of capital.

Rate of Return = C - investmentinvestment

1


Equivalent Annual Annuity

Equivalent Annual Cost - The cash flow per period with the same present value as the cost of buying and operating a machine.

factorannuity flowscash of luepresent va=annuity annual Equivalent


Annuity Factor

trt, r)(11

r1=FactorAnnuity

+


Profitability Index

ProfitabilityProject PV Investment NPV Index

J 4 3 1 1/3 = .33K 6 5 1 1/5 = .20L 10 7 3 3/7 = .43M 8 6 2 2/6 = .33N 5 4 1 1/4 = .25


Capital Budgeting Techniques


Capital Budgeting Process Capital Budget - The list of planned investment projects. The Decision Process 1 - Develop and rank all investment projects 2 - Authorize projects based on:

Outlays required by law of company policy Maintenance of cost reduction Capacity expansion in existing business Investment for new products


How To Handle Uncertainty Sensitivity Analysis - Analysis of the effects of changes in sales,

costs, etc. on a project. Scenario Analysis - Project analysis given a particular

combination of assumptions. Simulation Analysis - Estimation of the probabilities of different

possible outcomes. Break Even Analysis - Analysis of the level of sales (or other

variable) at which the company breaks even.


Operating Leverage Operating Leverage- The degree to which costs are fixed.

Degree of Operating Leverage (DOL) - Percentage change in profits given a 1 percent change in sales.

salesin change %profitsin change %=DOL


Operating Leverage The percentage of fixed costs in a company's cost

structure. Generally, the higher the operating leverage, the more a company's income is affected by fluctuation in sales volume.

The higher income vs. sales ratio results from a smaller portion of variable costs, which means the company does not have to pay as much additional money for each unit produced or sold.

The more significant the volume of sales, the more beneficial the investment in fixed costs becomes.


Rates of Return

20.2%or .202=

31.12.825.47 =Return Percentage +

Percentage Return = Capital Gain + Dividend Initial Share Price


Rates of Return

Dividend Yield = Dividend Initial Share Price

Capital Gain Yield = Capital GainInitial Share Price


Rates of Return

Nominal vs. Real

1+ real ror = 1 + nominal ror1 + inflation rate

%4.16ror real 164.1=ror real+1 .033 + 1 .202 + 1

=

=


Market Indexes

Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms.

Standard & Poors Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues.


Rate of Return


Measuring Risk

Variance - Average value of squared deviations from mean. A measure of volatility.

Standard Deviation - Average value of squared

deviations from mean. A measure of volatility.


Risk and Diversification

Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.

Unique Risk - Risk factors affecting only that firm. Also called diversifiable risk.

Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called systematic risk.



Portfolio rateof return

=fraction of portfolioin first asset

xrate of returnon first asset

+fraction of portfolioin second asset

xrate of returnon second asset

((

((

))

))



05 10 15

Number of Securities

Port

folio

sta

ndar

d de

viat

ion


05 10 15

Number of Securities

Port

folio

sta

ndar

d de

viat

ion

Market risk

Uniquerisk



Topics Covered Measuring Market Risk

Beta

Risk and Return CAPM

Capital Budgeting and Project Risk


Measuring Market Risk Market Portfolio - Portfolio of all assets in the economy. In

practice a broad stock market index is used to represent the market.

Beta - Sensitivity of a stocks return to the return on the market

portfolio.


Portfolio Betas Diversification decreases variability from unique risk, but not

from market risk. The beta of your portfolio will be an average of the betas of

the securities in the portfolio.

If you owned all of the S&P Composite Index stocks, you would have an average beta of 1.0


Risk and Return


Measuring Market Risk Market Risk Premium - Risk premium of market

portfolio. Difference between market return and return on risk-free Treasury bills.

0

2

4

6

8

10

12

14

0 0,2 0,4 0,6 0,8 1

Beta

Expe

cted

Ret

urn

(%) .

Market Portfolio


Measuring Market Risk CAPM - Theory of the relationship between risk and

return which states that the expected risk premium on any security equals its beta times the market risk premium.

Market risk premium = r - rRisk premium on any asset = r - r

Expected Return = r + B(r - r )

m f

f

f m f


Measuring Market Risk Security Market Line - The graphic representation of

the CAPM.

Beta

Expe

cted

Ret

urn

(%) .

Rf

Rm

Security Market Line

1.0


Security Market Line Return

BETA

rf 1.0

SML

SML Equation = rf + B ( rm - rf )


Capital Asset Pricing Model

R = rf + B ( rm - rf )

CAPM


Testing the CAPM Avg Risk Premium 1931-2002

Portfolio Beta 1.0

SML 30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium


Capital Budgeting & Project Risk The project cost of capital depends on the use to which the

capital is being put. Therefore, it depends on the risk of the project and not the risk of the company.


Cost of Capital Cost of Capital - The return the firms investors could expect

to earn if they invested in securities with comparable degrees of risk.

Capital Structure - The firms mix of long term financing

and equity financing.


WACC Weighted Average Cost of Capital (WACC) - The expected

rate of return on a portfolio of all the firms securities.

Company cost of capital = Weighted average of debt and equity returns.


WACC

V)r x (E+)r x (D

assetsequitydebtr =

( ) ( )equityVEdebtVDassets rx rx r +=

sinvestment of valueincome total

assets =r


WACC Taxes are an important consideration in the company

cost of capital because interest payments are deducted from income before tax is calculated.


WACC Weighted -average cost of capital=

[ ] [ ]WACC = x (1 - Tc)r + x rDV debt EV equity


WACC Three Steps to Calculating Cost of Capital 1. Calculate the value of each security as a proportion of the

firms market value. 2. Determine the required rate of return on each security. 3. Calculate a weighted average of these required returns.


WACC Issues in Using WACC Debt has two costs. 1)return on debt and 2)increased cost of equity

demanded due to the increase in risk

Betas may change with capital structure

Corporate taxes complicate the analysis and may change our decision

[ ] [ ]B = x B + x Bassets DV debt EV equity


Measuring Capital Structure In estimating WACC, do not use the Book Value of securities. In estimating WACC, use the Market Value of the securities. Book Values often do not represent the true market value of a

firms securities.


Measuring Capital Structure

Market Value of Bonds - PV of all coupons and par value discounted at the current interest rate.


Measuring Capital Structure

Market Value of Bonds - PV of all coupons and par value discounted at the current interest rate.

Market Value of Equity - Market price per share multiplied by the number of outstanding shares.


Required Rates of Return Bonds

r = YTMd

r = CAPM= r + B(r - r )

e

f m f

Common Stock


Required Rates of Return Dividend Discount Model Cost of Equity

Perpetuity Growth Model = solve for re

P = Divr - g0

1

e

r = DivP

+ ge 10


Required Rates of Return Expected Return on Preferred Stock

Price of Preferred Stock = solve for preferred

P = Divr0

1

preferred

r = DivPpreferred

1

0


Free Cash Flows Treat the whole company as one big project and discount the

companys cash flows by the weighted-average cost of capital. The operating cash flow less investment expenditures is the

free cash flow, which is the amount of cash that the business can pay out to investors after paying for all investments necessary for growth.


* FCF and PV * Free Cash Flows (FCF) should be the theoretical basis for all

PV calculations. FCF is a more accurate measurement of PV than either Div

or EPS. The market price does not always reflect the PV of FCF. When valuing a business for purchase, always use FCF.


Capital Budgeting Valuing a Business

The value of a business or project is usually computed as the discounted value of FCF out to a valuation horizon (H).

The valuation horizon is sometimes called the terminal value and is calculated like PVGO.

HH

HH

rPV

rFCF

rFCF

rFCFPV

)1()1(...

)1()1( 22

11

++

+++

++

+=


Capital Budgeting Valuing a Business or Project

HH

HH

rPV

rFCF

rFCF

rFCFPV

)1()1(...

)1()1( 22

11

++

+++

++

+=

PV (free cash flows) PV (horizon value)

Slide Number 1The Balance SheetThe Balance SheetMarket Value vs. Book ValueThe Income StatementThe Income StatementThe Statement of Cash FlowsTaxesFuture ValuesFuture ValuesPresent ValuesPresent ValuesPresent ValuesTime Value of Money(applications)PV of Multiple Cash FlowsPerpetuities & AnnuitiesPerpetuities & AnnuitiesPerpetuities & AnnuitiesPerpetuities & AnnuitiesPerpetuities & AnnuitiesInflationInflationEffective Interest RatesBondsBond PricingBond Cash FlowsBond PricingBond YieldsBond YieldsBond YieldsNominal and Real ratesDefault RiskCorporate BondsStocks & Stock MarketStocks & Stock MarketStocks & Stock MarketValuing Common StocksValuing Common StocksValuing Common StocksValuing Common StocksValuing Common StocksValuing Common StocksValuing Common StocksValuing Common StocksRandom Walk TheoryAnother ToolEfficient Market TheoryNet Present ValueNet Present ValueNet Present ValueNet Present ValuePayback MethodOther Investment CriteriaEquivalent Annual AnnuityAnnuity FactorProfitability IndexCapital Budgeting TechniquesCapital Budgeting ProcessCapital Budgeting ProcessHow To Handle UncertaintyOperating LeverageOperating LeverageRates of ReturnRates of ReturnRates of ReturnMarket IndexesRate of ReturnMeasuring RiskRisk and DiversificationRisk and DiversificationRisk and DiversificationRisk and DiversificationTopics CoveredMeasuring Market RiskPortfolio BetasRisk and ReturnRisk and ReturnMeasuring Market RiskMeasuring Market RiskMeasuring Market RiskSecurity Market LineCapital Asset Pricing ModelTesting the CAPMCapital Budgeting & Project RiskCost of CapitalWACCWACCWACCWACCWACCWACCMeasuring Capital StructureMeasuring Capital StructureMeasuring Capital StructureRequired Rates of ReturnRequired Rates of ReturnRequired Rates of ReturnFree Cash Flows* FCF and PV *Capital BudgetingCapital Budgeting

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Overview