Finance IBy: Andrew Iu

1

Table of Contents

Reminders 4Chapter 4 4Chapter 5 4Chapter 6 4Chapter 10 & 11 4Chapter 7 4

Questions to Review 5Chapter 9 5Chapter 22 5Chapter 11 5

Week 1, Class 1 61.1 What is Corporate Finance? 61.2 Corporate Securities as Contingent Claims on Total Firm Value 61.3 The Corporate Firm 61.4 Goals of the Corporate Firm 81.5 Financial Institutions, Financial Markets and the Corporation 81.6 Trends in Financial Markets and Management 8

Week 1, Class 2 104.1 The Financial Market Economy 104.2 Making Consumption Choices Over Time 104.3 The Competitive Market 104.4 The Basic Principle 114.5 Practicing the Principle 114.6 Illustrating the Principle 114.7 Corporate Investment Decision Making 11

Week 2, Class 1 135.1 The One-Period Case 135.2 The Multiperiod Case 135.3 Compounding Periods 135.4 Simplifications 135.5. What is a Firm Worth? 14

Week 3, Class 1 156.2 How to Value Bonds 156.3 Bond Concepts 15

Week 3, Class 2 16The Term Structure of Interest Rates 16The Expectations Hypothesis 16The Liquidity Preference Theory 16

Week 4, Class 2 176.4 The Present Value of Common Stocks 176.5 Estimates of Parameters in the Dividend Discount Model 176.6 Growth Opportunities 176.7 The Dividend Growth Model and the NPVGO Model (Advanced) 186.7 Price-Earnings Ratio 18

1

Week 5, Class 1 1915.1 Common Stock 1915.2 Corporate Long-Term Debt: The Basics 1915.3 Preferred Shares 2015.4 Income Trusts 2115.5 Pattens of Long-Term Financing 21

Week 6, Class 1 2210.1 Returns 2210.2 Holding Period Returns 2210.3 Return Statistics 2210.4 Average Stock Returns and Risk-Free Returns 2210.5 Risk Statistics 2210.6 More on Average Returns 22

Week 6, Class 2 2311.1 Individual Securities 2311.2 Expected Return, Variance, and Covariance 2311.3 Risk and Return for Portfolios 2311.4 The Efficient Set for Two Assets 2311.5 The Efficient Set for Many Securities 2411.6 Diversification: an Example 25

Week 8, Class 1 2611.7 Riskless Borrowing and Lending 2611.8 Market Equilibrium 2711.9 Relationship between Risk and Expected Return (CAPM) 28

Week 8, Class 1 (cont’d) 3012.1 Factor Models: Announcements, Surprises and Expected Returns 3012.2 Risk: Systematic and Unsystematic 3012.3 Systematic Risk and Betas 3012.4 Portfolios and Factor Models 3012.5 Betas and Expected Returns 3112.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory 3112.7 Parametric Approaches to Asset Pricing 31

Week 8, Class 1 3213.1 The Cost of Equity Capital 3213.2 Estimation of Beta 3213.3 Determinants of Beta 3213.4 Extensions of the Basic Model 3313.6 Reducing the Cost of Capital 33

Week 8, Class 2 3414.1 Can Financing Decision Create Value? 3414.2 A Description of Efficient Capital Markets 3414.3 & 14.4 The Different Types of Efficiency and the Evidence for Each 3414.5 The Behavioural Challenge to Market Efficiency 3614.6 Empirical Challenges to Market Efficiency 3614.7 Reviewing the Differences 3614.8 Implications for Corporate Finance 36

Week 9, Class 1 377.1 Why Use NPV? 377.2 The Payback Period Rule 377.3 The Discounted Payback Period Rule 377.4 The Average Accounting Return 377.5 The Internal Rate of Return 377.6 Problems with the IRR Approach 387.7 Profitability Index (PI) 40

W9,C2 - W10,C2 41

2

8.1 Incremental Cash Flows 418.2 The Majestic Mulch and Compost Company: An Example 418.3 Inflation and Capital Budgeting 418.4 Alternative Definitions of Operating Cash Flow 418.5 Applying the Tax Shield Approach to the Majestic Mulch and Compost Company Pro-ject 428.6 Investments of Unequal Lives: The Equivalent Annual cost method 42Appendix 8A - Capital Cost Allowance 43

Week 11, Class 1 4422.1 Types of Leases 4422.2 Accounting and Leasing 4422.3 Taxes and Leases 4422.4 The Cash Flows of Financial Leasing 4422.4 A Detour on Discounting and Debt Capacity with Corporate Taxes 4522.5 NPV Analysis of the Lease-Versus-Buy Decision 4522.8 Does Leasing Ever Pay? The Base Case 4522.9 Reasons for Leasing 4522.9 Some Unanswered Questions 45

Week 11, Class 2 469.1 Decision Trees 469.2 Sensitivity Analysis, Scenario Analysis and Break-Even Analysis 469.3 Monte Carlo Simulation 46

3

Reminders Chapter 4• The change in x resulting from an investment project is the NPV. It is NOT the change in Y.

The change in Y is NPV(1+r)

Chapter 5• LOOK FOR ANNUITY’S IN ADVANCE/ARREARS.

Chapter 6• The YTM is always given at an annual rate, but is compounded semi-annually or to match

the payment increments. Do NOT discount without converting to EAR. • YTM = APR • When applying spot rates (to bond pricing) apply the one-year spot rate to the first coupon

payment, the two-year spot rate to the second, and so on. • Remember that spot rates are cumulative and future rates are not cumulative. • (6A.12 - liquidity premiums apply only to the given time horizon). • To calculate the value of a share in x periods, compound the growth of the dividend forward

to that period and apply the perpetuity formula. Do not simply perform a future value calcu-lation (this does not account for the growth rate).

• In a dividend pricing question, where this is a finite growing annuity and a terminal perpetu-ity, remember to grow the first dividend of the perpetuity by the correct amount

Chapter 10 & 11• Variance is the sum of the squared residuals divided by N - 1 NOT SIMPLY N • WHEN CALCULATING THE VALUE OF THE SD FOR A PORTFOLIO, REMEMBER TO SQUARE ROOT

THE VARIANCE • When calculating covariance, remember that the SIGNS MATTER. It is not like variance,

where the signs are irrelevant. The formula is (observation - average), not (average - obser-vation).

• Read the question carefully• The expected return on a portfolio is the weighted expected return on the securities • The formula for the variance of a portfolio is (Xa)²(Var(a)) + 2(Xa)(Xb)Cov(a,b)...

• NOT -2(Xa)(Xb)Cov(a,b) • The portfolio with the least risk is called the minimum variance portfolio • Get the variance on a portfolio calculation right! MULTIPLY the weights by the SDs.

Chapter 7• In the AAR calculation, the value of the denominator is the average book value

• This implies that you actually need to add up each year’s book value and divide by the number of years!

• Do not simply take the average of the first and last years’ book values

4

Questions to Review Chapter 9• 9.1 - remember to look carefully at the time periods. • 9.12 - remember to multiply by 1-t when performing break-even sales questions • 9.7, part 2 - remember to add depreciation to fixed costs for the numerator in the break-

even formula

Chapter 22• 22.11

• lease payments are after tax• if a company receives no tax shield, use the before-tax interest rate as the discount rate

Chapter 11• 11.1 - Remember to when calculating the weighted expected returns to calculate the %

weight correctly • 11.3 - Read the question carefully • 11.7 - When calculating a portfolio variance/SD under varying probabilities, remember that

you must first determine the portfolio return under each scenario and then calculate the portfolio’s variance from there

5

Week 1, Class 11.1 What is Corporate Finance?

• The firm is financed with debt and equity. • Shareholders’ equity equals the asset value of the firm less debt. • Finance answers three questions:

A. In what long-term assets should the firm be invested? (capital budgeting)B. How can the firm raise the cash for these investments? (capital structure) C. How should short-term operating cash flows be managed? (net working capital)

• Net Working Capital = Current Assets - Current Liabilities.

• The value of the firm is equal to the debt plus the equity; the mixture of capital can alter the value of the firm. If this is the case, the capital mixture generating the most value must be chosen.

• Value creation depends upon cash flows. Retained cash flows, in excess of the cash flows paid to credi-tors (debt holders) and shareholders, increase the value of the firm.

• The treasurer is responsible for handling cash flows, analyzing capital expenditures, and making financ-ing plans. The controller handles the accounting function, which includes taxes, costs and financial accounting, and information systems.

1.2 Corporate Securities as Contingent Claims on Total Firm Value

• Since debt and equity securities depend on the value of the firm, these securities are said to be contin-gent claims on the total firm value.

1.3 The Corporate Firm

Finance I Notes 6

Sole Proprietorship Partnership Corporation

Definition

Complexity of Set-Up

Liquidity and Market-ability

Voting Rights

Taxation

Reinvestment and Divi-dend Payout

Liability

Continuity of Existence

Business owned by one person.

Business owned by two or more people. There are two types: 1) general partnership

- each partner agrees to share some management work and liability.

2) limited partnership - one partner is a general partner and the limited partners do not participate in managing the business.

Business entity created a distinct ‘legal person’ composed of one or more actual individuals or legal entities.

No formal charter re-quired (and therefore the cheapest).

Some written docu-ments required, de-pending of partnership complexity.

Incorporators must prepare articles of in-corporation and a set of bylaws.

Equity investment is limited to sole proprie-tor’s personal wealth.

Units subject to restric-tions on transferability. There is no market for trading units.

Common stock can be listed on exchange.

Complete control by owner.

Some voting control by limited partners; gen-eral partners manage firm.

Each share typically has one vote; shareholders elect a board of direc-tors who, in turn, se-lect senior manage-ment.

All business income is taxed at personal in-come tax rate.

Partnership income is taxed.

Both corporate profits and dividends are taxed (though a dividend tax credit exists).

Broad latitude on rein-vestment and dividend payout.

Partnerships are gener-ally prohibited from reinvesting partnership cash flow. All net cash flow is distributed to partners.

Broad latitude on rein-vestment and dividend payout.

Unlimited liability. No distinction is made between personal and business assets.

Limited partners are not liable; general partners may have un-limited liability.

Shareholders are not personally liable for obligations of the cor-poration.

Limited life. Limited life. Perpetual life.

• Income trusts hold the debt and equity of an underlying business and distribute income to unitholders. • Since it is not a corporation, unitholders originally did not enjoy limited liability; however, limited

liability was extended to trust holders later as the structure grew in importance. • For the same reason, distributions are taxed only in the hands of the unitholders.

Finance I Notes 7

• The corporation is a company form used to solve the problem of raising large amounts of cash. Because sole proprietorships and partnerships have limited lives, limited transferability of issues and unlimited liability for owners, raising capital is very difficult for these forms of business organization.

1.4 Goals of the Corporate Firm

• Set-of-Contracts Viewpoint: view of the corporation as a set of contracting relationships among indi-viduals who have conflicting objectives, such as shareholders and mangers. This view point suggests that the corporate firm will attempt to maximize the shareholders’ wealth by taking actions that in-crease the current value per share of existing stock in the firm.

• There are three distinct sets of corporate interests: shareholders, directors and executives. • It is assumed that these two groups will behave in a self-interested manner. • Shareholders (the principals) hire managers (the agents) to act on their behalf. • The costs of aligning managers’ goals with shareholders’ goals are called agency costs. These include:

• Monitoring costs; and • Incentive costs.

• Residual losses are the lost wealth to shareholders due to divergent behaviour of managers. • Williamson proposes the notion of expense preference: that managers prefer certain types of expenses

(office furniture, company cars, etc.) • Donaldson argued that the basic financial objective of managers is the maximization of corporate

wealth, which is the amount of wealth over which management has control. This is not the same as shareholder wealth.

• The diffusion of ownerships generates an ownership-control dichotomy.

• Shareholders align managerial interests with their own through several mediums: • They control the election of the board of directors; • Contracts with management and compensation arrangements (such as stock option plans); and • The dropping of share price leaves a company vulnerable to takeovers (by other firms, for in-

stance).

• Stakeholders include shareholders, management, employees, customers, suppliers and the public.

1.5 Financial Institutions, Financial Markets and the Corporation

• Financial institutions serve as intermediaries between fund suppliers (investors) and fund raisers (corpo-rations, governments, etc.).

• Indirect finance refers to the use of an intermediary to match lenders and borrowers of funds. The spread on the interest rates rendered to each party is the intermediary’s profit-making mechanism.

• Direct finance refers to the circumventing to the intermediary by the lender and borrower.

• Short term debt securities trade in money markets; these are often called money-market instruments.• Capital markets are forums for raising long-term debt or equity. • The money market is a dealer market (dealers buy and sell securities are their own risk), as opposed to

an auction market (where buyers and sellers trade directly with one another).

• Primary markets are those markets where securities are initially issued. • Placements of new issues can be either:

• Private - sold to buy-side financial institutions like pension funds and mutual funds. • Public - sold to retail investors.

• In this case, underwriting is often conducted by a banker or group of bankers (called a syndicate). This process involves the bankers purchasing the issue and reselling it; profit is made on the spread between the purchase price and the sale price.

• Secondary markets are markets where securities are traded after they are issued. • There are two kinds of secondary markets

• Auction markets - buyers and sellers interact directly to exchange securities. • Dealer markets - a collection of dealers buy and sell securities (called over-the-counter mar-

ket). • Stocks that trade on an organized exchange (i.e., an auction market) are said to be listed. • The foreign exchange market is the world’s largest over-the-counter (dealer) market.

1.6 Trends in Financial Markets and Management

Finance I Notes 8

• Financial engineering involves the designing of new securities and new financial processes. Successful financial engineering:

• Controls risk; and • Reduces tax

Finance I Notes 9

Week 1, Class 2 4.1 The Financial Market Economy

• Financial markets develop to facilitate borrowing and lending between individuals. • Financial markets permit varying inter-temporal consumption preferences

• Financial instruments are byproducts of financing arrangements between those who require funds and those who are willing to invest funds.

• Bearer instruments are a type of financial instrument which convey interest payments. • Financial intermediaries match borrowers (issuers of financial instruments) and lenders (buyers of fi-

nancial instruments). • The interest rate where the funds demanded equals the funds supplied is called the equilibrium rate of

interest. • It is the intersection between the supply and demand curves for fund where the ‘price’ of the funds

is the interest rate. • Market clearing refers to a condition where the supply of funds (generated by lenders) exactly equals

the demand for funds (generated by borrowers). • In market disequilibrium, funds can be rationed. For instance, if supply exceeds demand (because

the interest rate is unreasonably high), the amount lenders can provide may be restricted by the intermediary. This condition, however, will not last long as transactions beyond the intermediary place downward pressure on the interest rate.

4.2 Making Consumption Choices Over Time

4.3 The Competitive Market

• We assume perfectly competitive financial markets in which all agents are price takers. This results from three conditions:

• Trading is costless; market access is free; • Information on borrowing and lending is readily available; and• There are many traders and no single trader can influence the market.

10

Consumption Now

Consumption in One Year

A

B

Maximum possible consumption in one year

Maximum possible consumption now

C

X

Y

Point of zero borrowing

X + Y/(1+r)

*the interest rate is considered risk-free since we assume default cannot occur.

**the line is straight because we assume the individual does not influence the market rate of interest (r). This is a con-dition of a perfectively competitive financial market.

The red line represents the result of a shift in the interest rate.

slope = -(1+r) Y + X(1+r)

• If the possibility exists of borrowing and lending at different interest rates (assuming the same level of risk), arbitrage will occur to close the interest rate spread.

4.4 The Basic Principle

• The financial markets provide a benchmark for testing investments. • An investment project is only desirable if it expands the range of consumption choices (shifts the con-

sumption mix curve out). This is called the first principle of investment decision making.

4.5 Practicing the Principle

• Not only are financial markets a benchmark, they are also mechanisms for enabling investments. • Note that as long as an investment project has a positive NPV, the consumption mix curve is shifted

outward (the individual does not necessarily have to sacrifice current consumption, regardless of the size of the investment).

• The separation theorem states that the regardless of consumption preference, if an investment in-strument has a positive NPV, it should be purchased. The value of an investment to an individual does not depend on consumption preferences.

4.6 Illustrating the Principle

• Net present value = present value of the cash flow [ CF / (1+r) ] less the outlay (cost of the invest-ment).

• NPV is a measure of the amount of cash an investor would require today to substitute for the invest-ment.

• If NPV > 0, the consumption mix curve shifts outward and the investment should be undertaken; if NPV < 0, the investment should not be undertaken. This is called the NPV rule.

4.7 Corporate Investment Decision Making

11

Consumption Now

Consumption in One Year

A

B

C

X

Y

X + Y/(1+r)

Y + X(1+r)

∆Y = investment cost • (r1 - r)

• Assume investment instrument 1 has a return (r1) greater than the market rate (r). It shifts the budget line up by ∆Y.

• ∆X is called the NPV of the investment. It is equal to ∆Y divided by (1+r).

• ∆Y = ∆X • (1+r)

Y + X(1+r) + ∆Y

∆X = investment cost • (r1 - r) / (1+r)

slope = -(1+r)

• Shareholders in a firm will be unanimous in accepting positive NPV projects (since they will always in-crease the value of the firm).

• One difference between the firm and the individual is that the firm has no consumption endowment. • Regardless of the consumption preferences (patient or impatient) of individual shareholders, positive

NPV will always be accepted. • If an individual investor wishes to consume today, his shares will increase by his ownership portion

of the NPV; if an investor wishes to consume in one year, his shares will increase by his ownership portion of the NPV times (1+r).

• As long as managers follow the NPV rule, they will be acting in the best interest of shareholders.

12

Consumption Now

Consumption in One Year

NPV Quantity

Starting point: consumption now = 0, consumption in one year = 0

Week 2, Class 15.1 The One-Period Case

• The relationship between present and future value is: • FV = PV(1+r)^t.

• T represents the number of periods • r represents the interest in a single period

• When analyzing investment alternatives, present and future value analyses will always lead to the same decision.

• Net present value is the present value of the cash flows minus the present value of the cost of the in-vestment.

• The discount rate will vary depending upon the risk associated with the investment.

5.2 The Multiperiod Case

• Compounding is the process of interest accruing upon interest. • In a two-period case where the principal is $1, the future value = $1 • (1 + r) • (1 + r) = 1 + 2r + r^2.

• 2r represents the simple interest (without accruing interest). • r^2 represents the compound interest (interest upon interest).

• The process of calculating the present value of a future cash flow is called discounting.

• The present value factor is the element multiplied by the future cash flow to determine its present value.

• The present value of a set of cash flows is simply the sum of the present values of the individual cash flows.

• The NPV is equal to the sum of the present values of all the future cash less the outlay

5.3 Compounding Periods

• The stated annual interest rate is the annual interest rate without consideration for compounding (also called annual percentage rate).

• The effective annual rate (EAR) is the annual rate when a consideration is made for compounding. • The conversion formula (to determine EAR) is (1 + r/m)^m -1, m is the number of compounding

periods per year.• Therefore, the future value calculation changes to:

• FV = PV(1+r/m)^(m•n)• If interest is compounded continuously (that is, m is infinite in the above equation), then the future

value calculation is: • FV = PV • e^(r•t) • Because interest accrues continually upon interest, continuous compounding generates the highest

FV of any compounding period.

5.4 Simplifications

• There are four types of cash flow series: • Perpetuity; • Growing perpetuity; • Annuity; and• Growing Annuity.

• The present value of each of the above has a finite value (including the perpetual cash flow streams). • It is important to apply the correct discount rate to calculate the present value of each.

• In the case of mortgages, the stated annual interest rate is always compounded semi-annually. • Therefore, to determine the monthly payment on a mortgage with r stated rate and a value of PV:

• First, convert r to an effective annual rate figure; • Second, determine the monthly rate which, when compounded, yields the effective annual

rate; and

13

• Last, apply the annuity formula (below) where the discount rate is the monthly rate (deter-mined in the second step) and the number of compounding periods is the total number of months the mortgage will exist for.

Growing Cash Flow Stagnant Cash Flow

Perpetual

Finite

Growing Perpetuity

PV = C / (r-g)

Perpetuity

PV = C / r

Growing Annuity

PV = (C/(r-g)) [1 - (1+g)^t/(1+r)^t ]

Annuity

PV = (C/R) [ 1 - 1/(1+r)^t ]; orPV = (C) [ 1/r - 1/(r(1+r)^t) ]

Note that the element [ 1/r - 1/(r(1+r)^t) ] is called the annuity factor

Annuity Tricks I. Delay annuity

• If an annuity begins more than one period from the present (at the end of period x), to determine the present value of the annuity:

• Calculate the PV of the annuity at the end of period x-1 (normal calculation); and• Discount the above quantity to the present (PV / (1+r)^(x-1)).

II. Annuity in advance• The above annuity formula assumes the annuity begins payment in one period (called an annuity in

arrears). • If the annuity begins payment immediately (annuity in advance), with t payments in total, then to

calculate the PV of this annuity: • Calculate the annuity’s PV with the above formula but with payments t-1; and • Add the first payment to this quantity.

III. Infrequent annuity • If an annuity has payments less frequently than every year (every x years), then to determine the

PV of this annuity: • Adjust the discount rate by compounding the EAR x times; and• Using this discount rate, apply the above formula.

IV. Equating Present Value of Two Annuities • In the case of two separate annuities (typically where one is a cash inflow and one is an outflow),

to determine the coupon (payment amount) on the outflow annuity, equate the present value of this annuity with the present value of the inflow annuity and solve for C.

5.5. What is a Firm Worth?

• A firm is akin to any investment project: it is worth the sum of the present values of all its future cash flows.

14

Week 3, Class 16.2 How to Value Bonds • In a pure discount bond, or a zero-coupon bond, the holder receives no cash payment until maturity. • The date when the issuer makes the last payment is called the maturity date or simply maturity. The

bond expires on this date. • Level coupon bonds make regular payments to the holder (coupons) as well as the principal in the final

period. • The principal is sometimes called the face value or the denomination. • Bonds issued in Canada typically have $1,000 face values.

Present value of a bond = present value of an annuity (where C is the coupon payment) + the present value of the principal

• The stated price (clean price) is calculated by removing the effect of accrued interest; the dirty price is the sum which is actually paid

• Clauses which allow the issuer to repurchase bonds are called call provisions. • A fixed-rate preferred stock that provides the holder with a fixed dividend is a perpetuity.

6.3 Bond Concepts • A bond will trade:

• At face value if the coupon rate equals the market rate of interest• At a discount if the coupon rate is less than the market rate of interest• At a premium if the coupon rate is greater than the market rate of interest

• The yield to maturity (called the yield for short) is the discount rate (r) required to equate the bond’s trading price (clean price) with the present value of its future cash flows.

• Holding period return = (ending price - beginning price + FV of interest payment)/(beginning price)

15

Week 3, Class 2The Term Structure of Interest Rates • A spot rate is the cumulative rate of interest over a given period.

• r1 (spot rate 1) over period 1• r2 (spot rate 2) over period 1 and period 2 (cumulative element)

• The yield to maturity on a multi-period bond yields an average (of sorts) on the spot rates over the bond’s periods.

• The forward rate is the expected rate over a given interval (past period 1). It is a non-cumulative rate. • (1+r2)^2 = (1+r1)•(1+f2), where f2 = forward rate in period 2. • The forward rate over period 1 is equal to the spot rate over period 1.

• The value of a zero-coupon bond after period 1 is given by F / (1+r)^2, where F = the face value and r is the spot rate for one year, beginning at the end of period 1. The question becomes how do we deter-mine r.

The Expectations Hypothesis • The expectations hypothesis states that the forward rate (f2) is equal to the one-year spot rate, begin-

ning at the end of period 1. • However, this hypothesis assumes that investors are risk neutral (not risk averse).

The Liquidity Preference Theory • If an investor has a one-year time horizon, and there are two investment instruments available:

• Invest in a one-year instrument.• Invest in a two-year instrument and sell at the end of year one.

• Since the investor cannot sell the second instrument at end of year one with certainty, risk is involved. The market therefore sets the forward rate on instrument two (for year two) higher than the expected spot rate for year two to compensate for risk. • Hence, f2 > spot rate expected over year 2

• If an investor has a two-year time horizon, and there are two investment instruments available:• Invest in a two-year instrument. • Invest in a one-year instrument and then purchase another one-year instrument.

• Since the investor cannot sell the second instrument at the end year one with certainty, risk is involved. The market prices the two-year instrument with a lower forward rate than the expected spot-rate in year two to compensate for risk. • Hence, f2 < spot rate expected over year 2

• These conclusions are contradictory. The true pricing of f2 depends on time-horizon sought by most investors. Economists have concluded that this time horizon is typically shorter rather than longer. • Hence, f2 > spot rate expected over year 2 is true most of the time. • This is called the liquidity premium.

• A flat yield curve implies stable or declining future spot rates (since the liquidity premium is offset by falling spot rates).

16

Week 4, Class 26.4 The Present Value of Common Stocks • There are two ways to value a stock:

A. The present value of all future dividends; or B. The present value of a finite stream of dividends plus the present value of the future share sale

price. • The second method is actually identical to the first since the future share price is a function of the pre-

sent value of the dividends received after the sale of the shares. • There are three growth rate adjustments

A. Zero growth 1. Share price = DIV / r

B. Constant growth 1. Share price = DIV / (r-g)

C. Differential growth 1. Growth rate changes over time 2. Compute the share price manually (calculate present values over different interest rate in-

tervals and discount and sum all of these in the present).

6.5 Estimates of Parameters in the Dividend Discount Model • Net investment equals gross investment less depreciation • Net investment can only be positive if some earnings are retained (and not paid out as dividends).

Deriving the Growth RateEarnings next year = earnings this year + retained earnings • return on retained earnings

Dividing each side by earnings this year:

1 + g = 1 + retention rate • return on retained earnings g = retention rate • return on retained earnings

Return on equity serves as a proxy for return on retained earnings.

Deriving the Discount Rate r = DIV / Po + gTherefore, r = dividend yield + growth rate r = dividend yield + retention rate • ROE

• Note that the growth is derived under the assumption that future return on retained earnings and the retention rate are equal to their past values.

• G cannot exceed r; if it does, the analyst has likely made projections for the next few years, but not ad infinitum

6.6 Growth Opportunities • When a company pays out all its earnings (DPS = EPS), the company is called cash cow. • When a firm is a cash cow, P = EPS/r = DIV/r • NPVGO stands for the net present value (per share) of growth opportunities • P = EPS/r + NPVGO • Two conditions must be met:

• Earnings must be retained so that the projects can be funded • The projects must have a positive NPV

• A policy of investing in projects with negative NPVs rather than paying out earnings as dividends will lead to growth in dividends and earnings, but will reduce value

• Firms with no dividends have positive share prices because: • Investors believe they will receive dividends eventually• The firm will be acquired in a merger

17

6.7 The Dividend Growth Model and the NPVGO Model (Advanced) • A steady growth in dividends results from a continual investment in growth opportunities, not just an

investment in a single opportunity. Therefore, it is worthwhile to compare the dividend growth model with the NPVGO model when growth occurs through continual investing.

• Under the dividend discount model, we divide the dividend by the discount rate less the growth (which is calculated as the retention rate times the return on retained earnings)

• Under the NPVGO model, we calculate the value of a stock in three parts: • First, we calculate the present value of the NPVs of each year’s investment

• Since each year’s NPV grows by a constant rate (the growth rate) and each year’s NPV is dis-counted at the discount rate (to the power of the year number), the NPVGO is simply a perpe-tuity where,

• The numerator is the NPV in year 1 • The denominator is the difference between the discount rate and the growth rate

• Second, we calculate the value of the share as a cash cow (EPS / r). • Last, we sum these two quantities together

• These approaches will yield the same current share prices

6.7 Price-Earnings Ratio • Under the NPVGO model: Price per share = EPS/r + NPVGO • The price-to-earnings multiple implies: P/EPS = 1/r + NPVGO / EPS. Hence, three variables influence

the P/E: • Growth opportunities: two companies have the same EPS, the company with the higher NPVGO

(access to superior growth opportunities) will trade a higher multiple. • Risk: Also, the P/E ratio is negatively related to r. Hence, the higher the risk, the lower the multi-

ple. • Accounting convention: Accounting convention also influences the P/E ratio (when revenue and

depreciation are recognized, for example).

18

Week 5, Class 115.1 Common Stock • Common stock (or common shares) stock has no special preference either in dividends or in bank-

ruptcy • Some stock have a stated value called the par value • Common shareholders are protected by limited liability

• Authorized shares specify the maximum number of shares a corporation can issue

• Book value of equity = retained earnings + contributed surplus + share capital + adjustments to equity • The market value of shares is typically higher than book-value per share • Replacement value refers to the current cost of replacing the assets of the firm • Market value, book value and replacement value are all equal when a firm purchases an asset • The following ratios measure the performance of the firm’s asset purchases

• Market-to-book value ratio of common stock • Tobin’s Q ratio (market value of assets to replacement value of assets)

• Shareholders elect directors who, in turn, appoint management • Shareholders have the following rights

• The right to vote • The right to share proportionally in dividends paid • The right to share proportionally in assets remaining after liabilities have been paid in a liquidation • The right to vote on matters of great importance to shareholders (ex: merger) • The right to share proportionally in any new sock when approved by the board of directors

• Voting can occur in two ways• Cumulative Voting: each shareholder is given a number of votes (typically, the number of shares

held times the number of directors to be elected). These most votes may distributing to one or more candidate

• If there are N directors up for election, then 1/(N+1) percent of the stock will guarantee elec-tion

• Permits participation of minority shareholders • Straight Voting: each shareholder may cast his number of votes for each candidate

• Excludes participation of minority shareholders • To elect a director, 50% of shares + one are required

• Staggering involves permitting a fraction of the board to be elected at any one time. It has two effects: • Makes it more difficult for a minority to elect a director when there is cumulative voting • Makes successful takeover attempts less likely

• A proxy is the legal grant of authority by a shareholder to someone else to vote his or her shares • An outside group of shareholders can attempt to obtain as many votes as possible via proxy

• Dividends • Unless a dividend is declared by the board of directors, it is not a liability • Dividends are not tax-deductible • Dividends received by individual shareholders are partially sheltered; Canadian corporations that

own shares in other companies are 100% tax protected

• Classes of Shares• Share classes often have different voting rights • Nonvoting shares must receive dividends no lower than dividends on voting shares • Nonvoting shares allow management to retain control • US stocks with superior voting rights typically trade at 5% higher than their nonvoting counterparts • Coattail provisions give nonvoting shareholders the right to vote or to convert their shares into vot-

ing shares in the case of a takeover bid

15.2 Corporate Long-Term Debt: The Basics • Securities issued by firms can be classified as equity or debt

19

• Corporations can legally default at any time on its liability (this can be a valuable option) • The main differences between debt and equity include:

• Debt is not an ownership interest• The device used by creditors to protect themselves is the loan contract (indenture)

• The payment of interest is a cost of doing business and is therefore tax deductible • The government effectively a tax-subsidy on the use of debt

• Unpaid debt is a liability. • If not paid, creditors can claim the firm’s assets. This may result in liquidation or bankruptcy

• When corporations try to create a debt security that is really equity, they are trying to obtain the tax benefits of debt while eliminating its bankruptcy costs

Types of debt • Debenture: unsecured corporate debt • Bond: secured by a mortgage on the corporate property • Note: short-term obligation (less than 7 years) • Long-term debt is any debt longer than one-year from the date is originally issued and is sometimes

called funded debt

• A sinking fund is an account managed on behalf of the issuer by a bond trustee for the purpose of retir-ing all or part of the bond prior to the stated maturity.

• Sinking funds reduce the risk of the company repaying the principal and also enhance liquidity • Call provisions give the firm the right to pay a specific amount (call price) to retire (extinguish) the

debt before the stated maturity date • Canada plus calls have a dynamic call price which are designed such that the call premium compen-

sates investors for the difference in interest between the original bond and new debt issued to replace it.

• Seniority indicates preference in position over other lenders. Some debt is subordinated. • Debt cannot be subordinated to equity

• Security is a form of attachment to property; it provides that the property can be sold in the event of default to satisfy the debt for which security is given.

• A mortgage is used for security on tangible property • Holders of such debt have prior claim on mortgaged assets

• An indenture is the written agreement between the corporate debt issuer and the lender, setting forth maturity date, interest rate and all other terms.

• Restrictive covenants: • Restrictions on further indebtedness• A maximum on the amount of dividends that can be paid • A minimum level of working capital

15.3 Preferred Shares • Preferred shares have preference over commons share holders in the payment of dividends and the

case of liquidation • Preference means preferred shareholders must receive a dividend before common shareholders

• Failure to pay a dividend on preferred shares cannot result in bankruptcy • Dividends paid on preferred shares are either cumulative or noncumulative

• Cumulative shares require that missed dividends be carried forward in arrearage • Preferred shareholders must be paid their dividends (cumulative and current) before common

shareholders receive dividends • Dividends in arrears:

• Prevent common shareholders from receiving dividends • Grant preferred shareholders voting rights if the dividends are not paid within a given amount

of time • Preferred shares can be:

• Convertible into common shares • Callable by the issuer• Bestowed with the right to sell back to the issuer a given price (redeemable)

• Some preferreds are floating rate • Yields on preferreds are generally lower than bond yields (since they are more tax efficient for compa-

nies to hold)

20

• Hence, most preferreds are held by corporate investors

• Lightly taxed companies (or those protected by tax shelters) benefit from issuing preferreds over debt (since they do no benefit from the tax shield created by the debt but enjoy lowering financing costs on preferred - since yields are lower)

• Other reasons for issuing preferreds (for heavily taxed companies) include: • Regulated public utilities companies can pass the tax advantage of issuing preferred shares on to

their customers because of the way pricing formulas are built • Preferreds do not involve the same bankruptcy threats as debt • Issuance of preferreds does not influence firm control

15.4 Income Trusts • The operating entity pays the income trust interest, royalties, or lease payments, which are typically

tax-deductible, until its operating income is zero. This means that he operating entity does not have to pay tax

• The income trust receiving the payments is not taxed since it is not a corporation (but a partnership). Therefore, payments are taxed only in the hands of unitholders.

15.5 Pattens of Long-Term Financing • Cash flow to finance capital expenditure and net working capital is derived from three sources:

• Internal financing (cash flows generated in the business) represents about two thirds • Internal financing is defined as net income + depreciation - dividends

• Sale of marketable securities • External financing

• Debt (used first) • Equity (used as a last resort)

• There is a financing pecking order with internally generated cash flow used first, followed by debt and equity last

21

Week 6, Class 110.1 Returns • Total earnings = dividend income + capital gain (- capital loss) • Total cash if stock is sold = initial investment + total dollar earnings = proceeds from sale + dividends • Regardless of whether a gain is realized, it must included in returns • Dividend yield = Dividend (in one period) / Price (today) • Capital gains yield = [ Price (in one period) - Price (today) ] / Price (today) • Return (percentage) = dividend yield + capital gains yield

10.2 Holding Period Returns • The holding period returns on the textbook indices (Canadian common stock, US common stock, small

stocks, long bonds, and Canadian treasury bills) are pretax, nominal returns • Calculating cumulative returns on these indices assumes the reinvestment of dividends

10.3 Return Statistics • A frequency distribution depicts the distribution of returns • Average return is the mean of the distribution

10.4 Average Stock Returns and Risk-Free Returns • The yield on a T-bill is called the risk-free return over a short time • The difference between risky returns and risk-free returns is often called the excess return on the

risky asset. It represents a risk premium. • This results from the fact that the standard deviation on T-Bills is much lower than common stocks

10.5 Risk Statistics • The risk of returns is measured by the dispersion of a frequency distribution

• The greater the dispersion (and the wider the distribution), the greater the uncertainty of returns • The variance and its square root, the standard deviation, are the most common measures of variability

or dispersion

• The normal distribution is the bell-shaped, symmetric distribution which any actual distribution will approach as the number of observations approaches infinity

• The standard deviation measures the spread of the normal distribution • 68.26% of observations will fall within one standard deviation of the mean • 95.44% of observations will fall within two standard deviations of the mean• 99.74% of observations will fall within three standard deviations of the mean• Therefore, for instance, if the mean is 11.1% and the SD is 16.03%, there is less than a 5% chance

that an observation (a year’s return) will outside the range -20.90% to 43.16%

• Value at risk (VaR) represents the maximum possible loss at a certain confidence level • In the above example, the probability of an observation falling below -20.90% is 2.28%. • Therefore, the VaR on a 200 million investment is 41.8 million (200 • -20.90%), provided we are

willing accept that there is a 2.28% chance that the return is lower

10.6 More on Average Returns • Geometric average answers the question What was your average compound return per year over a par-

ticular period?• Geometric average return = [(1+r1) • (1+r2) • (1+rt)]^(1/t) - 1

• Arithmetic average answers the question What was your return in an average year over a particular period?

• The geometric average return is approximately equal to the arithmetic average less half the variance (the geometric average will always be smaller)

• In predicting a return over the next T periods (and with historical data of N periods available) apply the following: R(T) = (T-1)/(N-1)•geometric average + (N-T)/(N-1)•arithmetic average

• Notice, geometric averages are less relevant over short time periods and arithmetic average are less relevant over long time period

22

Week 6, Class 211.1 Individual Securities • Covariance is a statistic measuring the interrelationship between two securities. • Alternatively, this relationship can be stated in the correlation between two securities.

11.2 Expected Return, Variance, and Covariance • Var(R) = [ ∑(R - Avg. R)^2 ] / (n-1)• SD(R) = [Var(R)]^0.5• COV(Ra, Rb) = [ ∑(Ra - Avg. Ra)(Rb - Avg. Rb) ] / (n-1)

• Covariance will be negative if observations move in different direction and positive if they move in the same direction

• Covariance is not useful because it gives us an absolute magnitude (instead of a relative magni-tude)

• ρ(a,b) = COV(Ra,Rb) / [SDa • SDb] • Correlations will vary between -1 (for perfectively negatively correlated) and 1 (for perfectively

positively correlated) • This standardization makes correlation a more useful variable

11.3 Risk and Return for Portfolios • expected portfolio returns = Xa(Ra) + Xb(Rb) + Xc(Rc) + ... + Xi(Ri)

• Xi is the proportion of the portfolio allotted to security i and Ri is the expected return on security i • The expected return is simply the historical arithmetic average

• The expected return on a portfolio is simply a weighted average of the expected returns on the individual securities

• portfolio variance (two-security model) = (Xa)²(Var(Ra)) + 2(Xa)(Xb)(COV(a,b)) + (Xb)²(Var(Rb))• The variance of a portfolio depends on both the variances of the individual securities and the co-

variance between the two securities• The lower the covariance between the securities, the lower the portfolio variance

• This is called a hedge

A B

A

B

(Xa)²(Var(Ra)) (Xa)(Xb)(COV(a,b))

(Xa)(Xb)(COV(a,b)) (Xb)²(Var(Rb))

• The variance of the portfolio equals the sum of the elements in the above matrix • The SD of a portfolio will always be less than the weighted average SD of the individual securities when

the correlation between the securities is less than 1 (this applies to discussions of two or more securi-ties)

• This is attributable to the affects of diversification• This explains why the standard deviation of most stocks are lower than the index

11.4 The Efficient Set for Two Assets

23

• We can apply the same logic to international and domestic exposure. Simply make A a domestic portfo-lio and B an international portfolio. Mixing these portfolios together creates a more efficient set (since the correlation coefficient between the two portfolios is less than 1)

• One caution regarding this analysis is that expected returns (as calculated by historical averages) can be unrealistic if they are based upon periods in history which are atypical (ex: during crises or unusual bull markets)

11.5 The Efficient Set for Many Securities

24

A

B

The straight line represents the feasible set under a correlation of 1 between A & B.

It is impossible for an investor to choose any point off the curved lined (the curved line assume the correlation coefficient is below 1). This is called the opportunity set, feasible set or efficient set.

1

This is the point of minimal risk (the lowest possible standard deviation and vari-ance). This is called the minimum variance portfolio.

Expected return on portfolio

Standard deviation on portfolio

A rational investor will never choose a portfolio on the backward bend-ing portion of the feasible set. All portfolios where the securities have ρ <= 0 and even some where ρ >= 0 have backward bending portions. We say that portfolios along this portion of the set are dominated. The smaller ρ, the more bent the curve.

A

B

Expected return on portfolio

Standard deviation on portfolio

C

D

E

F

Any point within this region can be chosen, but no beyond it can.

MV

Any point between MV and F lies on the effi-cient set. A rational investor will choose a point on this line. Any point below this line implies a lower expected return with the same risk.

A B ... N

A

B

...

N

(Xa)²(Var(Ra)) (Xa)(Xb)(COV(a,b)) ... (Xa)(Xn)(COV(a,n))

(Xa)(Xb)(COV(a,b)) (Xb)²(Var(Rb)) ... (Xb)(Xn)(COV(b,n))

... ... ... ...

(Xa)(Xn)(COV(a,n) (Xb)(Xn)(COV(b,n)) ... (Xn)²(Var(Rn))

• Again, the variance of the portfolio is the sum of the elements in this matrix. • Notice that the number of terms containing covariance increases as the matrix grows. • In general,

• The number of terms whose value depends upon individual-security variance (unsystemic risk) is N• The number of terms whose value depends on covariance is N²-N or N(N-1) • Hence, covariance becomes increasingly important as N grows

11.6 Diversification: an Example • Variance of a portfolio = (1/N)(average variance) + (1-(1/N))(average covariance) • Variance of a portfolio = average covariance as N approaches infinity • Hence the floor on portfolio is covariance (or systematic risk or market risk) • Diversifiable, unique or unsystematic risk is that risk can can be diversified away • Total risk of an individual security (variance) = portfolio risk (covariance) + unsystematic or diversible

risk (variance - covariance)

25

Variance of portfolio’s return

Number of securities

Average COV

Average VAR

Portfolio risk, market risk, systematic risk

Diverisfiable risk, nonsystematic risk, unique risk

Week 8, Class 111.7 Riskless Borrowing and Lending • The standard deviation of portfolio (risk) which includes a risky security and a risk-less security is equal

to the weight of the risky security times the standard deviation of the security. This results from the fact that:

• The variance on a risk-less security is zero (since it never deviates from the expected return) • The covariance between the two securities is zero (since every residual of the risk-less security is

zero) • Alternatively, borrowing at the risk-free rate will amplify returns (since the marginal expected return

on the risky security will exceed the cost of borrowing). • However, it will cause the weight of the risky security to exceed 100% (for example, investing

$1,000 and borrowing $200 at the risk-less rate will cause the weight to be 120%). • This will also amplify the standard deviation • This assumes the investor can borrow at the risk-free rate (which is impossible). The borrowing rate

is higher than the risk-less rate, which implies that the marginal standard deviation (SD added via leverage) will exceed the marginal gain in expected return.

• The optimal portfolio: • Any point on the efficient set (from the minimum variance portfolio to a portfolio composed en-

tirely of the highest risk, highest return security), or in the region below the efficient set is feasi-ble

• Choosing any feasible point and then connecting this with the risk-free rate forms a line upon which some mixture of the risky-asset mix (the mix which went into creating the feasible point) and risk-free investments can be used to achieve a given point on the line

• The capital market line is the line which lies tangent to the efficient frontier and is constructed by mixing risk-free assets with the asset-mix which was used to create the point of tangency.

26

Expected portfolio return

Standard deviation of portfolio

Risk-free rate

Mixture of risk-less and risky security

Purely risky secu-rity portfolio

Levered returns under a risk-free borrowing rate

Levered returns under a borrowing rate above the risk-free rate

Higher cost of borrow-ing drives down return/risk ratio.

• A rational investor will only choose portfolios along the capital market line • The separation principle argues that investors make two separate decisions:

• 1) The investor first: • Estimates the expected returns on risky assets• Estimates the variances and covariances of the risky assets • Calculates the efficient frontier (from MV to T to F in the below) • Determines the point of tangency (T in the below)

• 2) The investor, depending on their risk aversion, determines how to mix the risky portfolio T with risk-free assets (representing movement along the capital market line from the risk-free level to above the tangency point)

11.8 Market Equilibrium • Homogenous expectations assumes that all investors have the same expectations for returns, variances

and covariances. • Under this assumption, every investor will calculate the same efficient set and therefore tangency port-

folio (and hence, every investor will create a portfolio along the capital market line depending on the individual’s risk tolerance)

• This portfolio every investor chooses (before risk-free borrowing/investing) is called the market portfo-lio. It is a market-value weighted portfolio, meaning that each security is weighted by security market capitalization divided by total market capitalization.

• Beta measures the responsiveness of a security to movements in the market portfolio. • A negative beta security, when added to a diversified portfolio (ideally, one that represents the

market portfolio well), the portfolio’s risk level falls.

State Type of Economy Return on Market (%) Return on Security (%)

I

II

III

Bull 15 25

Bull 15 15

Bear -5 -5

27

A

B

Expected return on portfolio

Standard deviation on portfolio

C

D

E

F

Tangency point is the ideal mixture of risky assets. At this point, the portfolio contains no borrowing or lending of risk-free assets.

MV

Risk-Free Rate

Capital market line

Any point on the capital market line can be achieved by combining the tangency point portfolio (100% risky assets) with risk-free assets (either borrowing or lending).

Any point on this line is attainable by mixing the portfolio at point x with risk-free assets.

x

T

State Type of Economy Return on Market (%) Return on Security (%)

IV Bear -5 -15

• The formula for beta is the covariance of market portfolio’s return to the security return divided by the market portfolio’s variance.

• Beta = COV(Ri, Rm) / VAR(Rm) • The average beta above all securities in the market is equal to 1

• The variance of an individual security is only important if the investor is looking to hold a portfolio of only one security

• The beta of an individual security is important for decision making when the investor’s portfolio is well diversified (representative of the market portfolio)

• Under the homogenous expectations hypothesis, all investors hold the market portfolio. While most investors do not hold the market portfolio exactly, they do hold portfolios diversified enough to allow beta to serve as a good risk measure.

11.9 Relationship between Risk and Expected Return (CAPM) • Expected market return = risk-free rate + risk premium • Capital Asset Pricing Model (CAPM): Expected return on security = risk-free rate + beta • (expected

market return - risk-free rate)

28

Expected market return

Expected security return

I

II

III

IVSlope of the line of best fit equals beta. A beta above 1 implies a security which is risk-ier than the market; below 1 is the oppo-site.

Single-security portfolio Diversified portfolio

Security variance Security betaSecurity’s variance and covari-ances with portfolio holdings

Partially diversified portfolio

• Beta (since it is a good measure of risk for most investors (since most investors something akin to the market portfolio)) is positively related to return

• Under this model: • If beta = 0, the return on the security equals the risk-free return • If beta = 1, the return on the security equals the expected market return

Three additional important points:

1) Linearity: the SML is a straight line. This follows from the fact that we can artificially create an point on the SML line by mixing a beta 1 security (ie, a market portfolio) with risk-free borrowing or lending. Therefore:

1) if a security is below the line, its price will fall (since no rational investor will purchase it when they can capture a higher return/risk ratio by mixing a market portfolio and risk-free investments). A falling price will drive expected returns higher until the security lies on the SML.

2) if a security lies above the line, investors will push the price of the security higher (because it offers a greater return/risk ratio) and therefore the expected returns lower until the security is positioned on the SML.

2) Portfolios as well as securities: the SML applies to securities as well as portfolios. A portfolio can be positioned on the line by taking its beta (weighting the securities’ betas) and multiplying by the risk premium.

3) Potential confusion: the SML (Security Market Line) and the CML (Capital Market Line) are not the same. The SML determines the expected return of a single security based upon its beta; the CML de-termines the expected return on the optimal portfolio (market portfolio) based upon standard devia-tion (not the same as beta).

29

Beta

Expected security return

Direct relationship between beta (risk) and expected return. Note that the slope of the line equals to the difference between the market return and the risk-free rate.

Beta = 1

Risk-free rate

Expected market return

Security market line (SML) Positive NPV Project

Negative NPV Project

Week 8, Class 1 (cont’d) 12.1 Factor Models: Announcements, Surprises and Expected Returns • Actual return = expected return + uncertain (risky) return

• The uncertain return component results from any news which the market could not anticipate (ex: earnings surprises, key executives leaving, sudden drop in interest rates, etc.)

• Events which the market anticipates are said to be discounted • For instance, a company’s earnings release will often not have a significant influence on the

market since the market discounted this news item (included the news when it calculated ex-pected return)

• An announcement = expected + surprise • If the market anticipates a 0.5% increase in GNP, and the actual figure is 1.5%, the surprise (or

innovation) is 1%. • The expected component drives expected returns • The surprise component drives the uncertain return

• News refers to the surprise component of an announcement; the expected component will have no in-fluence on share price since it will already be discounted

12.2 Risk: Systematic and Unsystematic • The uncertain return component of actual return is the true risk associated with a security • The surprises (drivers of uncertain return) can be divided into two categories:

A. Systematic risk: is any risk that affects a large number of assets, each to a greater or lesser de-gree 1. Uncertainty regarding general economic conditions

B. Unsystematic risk: is a risk that specifically affects a single asset or a small group of assets 1. Also called idiosyncratic risk

• The distinction between these two types of risk is never precise; even a seemingly isolated occur-rence will affect the broader economy in a minor way.

• Therefore, actual return = expected return + systematic risk (m) + unsystematic risk (ε) • CORR(εx, εy) = 0, where εx is the idiosyncratic risk associated with security x and εy is the same

risk of some other security • If a risk is truly unsystematic, it will be uncorrelated with the risk of other securities in the

market

12.3 Systematic Risk and Betas • The beta coefficient captures the influence of systematic risk

• It tells us the response of the stock’s return to a systematic risk • We previously defined beta to be the relationship between a security and one systematic risk - the

market portfolio’s return• We can generalize beta to any type of systematic risk

• For instance, we can define m = βiFi + βGNPFGNP + βrFr

• Where, βi is the beta coefficient for the inflation rate and Fi is surprise for the inflation rate • Likewise for GNP and the interest rate (r)

• This model is called the factor model, and the systematic sources of risk, designated F, are called the factors.

• Therefore, actual return = expected return + β1F1 + β2F2 + β3F3 +...+ βkFk + ε• Where ε is uncorrelated to every other securities’ ε

• In practice, researchers use a one-factor model: • Actual return = expected return + β(Rm - exp. returnm) + ε

• Where Rm is the return on the market portfolio

12.4 Portfolios and Factor Models • The return on a entire portfolio is given by the sum of:

• Weighted average of expected returns: X1R1 + X2R2 + X3R3 + X4R4 +...+ XnRn

• (Weighted average of Betas)F: (X1β1 + X2β2 + X3β3 +...+ Xnβn)F • Weighted average of unsystematic risks: X1ε1 + X2ε2 + X3ε3 + X4ε4 + ...+Xnεn

• The third element in the equation actually zero as diversification approaches the market portfolio (be-cause all the correlations are zero)

30

• Unsystematic risk can be diversified away (third component of the equation) • Systematic risk cannot (second term in the equation)

• In the previous chapter, systematic risk was argued to be the result of positive covariances; in this chapter, this risk is the result of a factor. Since a single factor drives the positive covari-ances, the arguments are analogous

12.5 Betas and Expected Returns • In CAPM, the beta of a security measure the security’s responsiveness to movements in the market port-

folio. • In the one-factor model of the arbitrage pricing theory, the beta of a security measures its responsive-

ness to the factor. • Since market portfolio contains no unsystematic risk (since it has perfect diversification), its expected

returns are perfectly related to the factor through the portfolio’s beta. Hence, after scaling properly, we can treat the market portfolio as the factor itself.

• When the factor is the market portfolio itself, the beta for the market portfolio is one.

• Hence, the APT and CAPM are fundamentally equivalent

12.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory

Pedagogy Application

Capital Asset Pricing Model

Arbitrage Pricing Theory

• The treatment - beginning with the case of two risky assets, moving to the many risky assets, and finishing when a risk-free asset is added to the many risky ones - is of great intuitive value

• The model adds factors until the unsystematic risk of any security is uncorrelated with the unsys-tematic risk of every other secu-rity

• The model can handle multiple factors while CAPM cannot

12.7 Parametric Approaches to Asset Pricing • APT and CAPM are parametric or empirical models in that an overarching theory is constructed where

certain attributes are related to expected returns through parameters (betas in APT), and these pa-rameters are derived through an analysis of actual data

• Consider another model: expected return is related to P/E. Instead of arguing that an inverse relation-ship exists for valuation reasons, one might argue that the P/E is simply a better measure of systematic risk.

• Style portfolios are often defined by stock attributes • High P/Es correspond to growth portfolios • Low P/Es correspond to value portfolios • Fund managers are compared against benchmarks (appropriate indices) and peer groups

31

Week 8, Class 113.1 The Cost of Equity Capital • Firms can pursue two courses of action

if they have extra cash: • Distribute it to shareholders via

dividends• Reinvest in a project

• Firms should pursue the latter if the expected return is superior (assuming the risk is the same on the project as it is on the firm) on the available pro-ject than what investors could achieve elsewhere in the market

• In other words, the IRR on the project must exceed the expected return for the firm overall

• The expected return is the cost of equity:

• E(R) = Rf + B (E(Rm) - Rf)

13.2 Estimation of Beta • Beta = COV(Ri, RM) / VAR (RM) • Beta is also the slope of the line of

best between the returns on the firm when plotted as a function of the mar-ket returns

• This line is called the characteristic line of the firm

• The error in beta-estimation on a sin-gle stock is much higher than the error for a portfolio of securities. This is because of the error which arises from unsystematic returns

13.3 Determinants of Beta • Cyclicality of revenue: different in-

dustries have different sensitivities to the business cycle

• Operating leverage: lower variable costs and higher fixed costs imply higher operating leverage

• The steeper the slope of the TC line, the lower contribution mar-gin and operating leverage are

• Operating leverage can be meas-ured by: % chg. in EBIT / % chg. in Sales

• Operating leverage magnifies the affects of the business cycle

• Operating leverage refers to the fixed costs of production

• Financial leverage: financial leverage refers to the fixed cost of financing

• These fixed costs result from the interest expense which does not vary with the quantity sold

32

Project’s IRR

Beta

Risk-free rate

Positive NPV Projects

Negative NPV Projects

SML

Dollars

Quantity

FC

TC

Dollars

Quantity

FC

TC

Low operating leverage

High operating leverage

• BAsset (1 + (1-t)(D/E)) = BEquity

• BAsset represents the unlevered beta of the security - it is the beta which would exist if the firm was financed by purely equity

• The Bequity will always be greater than or equal to the BAsset

• From the above formula, it is apparent that leverage increases Beta

13.4 Extensions of the Basic Model• Choosing the same discount rate for all projects is incorrect unless they all have the same risk level

(betas) • To value a portion of a business (or a project):

• Unlever the beta of the pure play • Relever the beta based upon the business’s capital structure

• The cost of debt: return that the firm’s long-term creditors demand on new borrowing• The YTM is this required rate of return • The Coupon rate of the firm’s outstanding debt is irrelevant

• The cost of preferred stock: a share of preferred is essentially a perpetuity • rp = D / P,

• rp = the required rate of return on the preferred• D = dividend • P = the market price of the preferred

• The weighted average cost of capital: • Firms may issue debt or equity a single time, thereby upsetting the optimal debt-to-equity ratio • A firm’s total capitalization (enterprise value) = long-term debt and equity • V = S + B + P • The weights for common stock, bonds and preferreds are therefore: S/V, B/V and P/V • We use the market values for stocks, bonds and preferreds • The cost of debt is (1-t)YTM

• The use the after-tax cost of the debt because this is the true cost of the debt to the firm • RWACC = (S/V)• Rs + (B/V) • (1-t) • YTM + (P/V) • Rp • This is the discount rate we would use to evaluate projects with essentially the same risk level as

the entire firm

13.6 Reducing the Cost of Capital • The Expected return and therefore cost of capital are negatively related to liquidity • Liquidity is the cost of buying and selling stock. There are broadly three costs:

• Brokerage fees - costs paid to the broker to execute a trade • Market impact costs - the price drop associated with the sale of a large issue • Bid-ask spread - the wider the bid-ask spread the specialist offers, the higher the cost

• Since trading costs (liquidity) are deduced from return, investors will demand greater returns on securi-ties with higher trading costs

• Hence, expected returns are positively related to both beta and trading costs • The spread a specialist charges (bid-ask spread) is positively related to the ratio of informed investors

to uninformed investors (this is called adverse selection) • This is because the more informed investors there are, the higher the likelihood the specialist will

the exploited (since informed investors have information which enables them to determine the true worth of a share)

• Hence, more informed investors raise the cost of capital (by increasing the bid-ask spread) • Firms can improve the cost of capital

• By lowering the ratio (through, for instance, stock splits, dividend reinvestment programs, etc.) • Supplying more information to many everyone informed

• Greater financial data on corporate segments and management forecasts • Encouraging analysts to follow the company • These actions will reduce information asymmetry

33

Week 8, Class 214.1 Can Financing Decision Create Value?• There are three ways to create value from financing opportunities (earn positive NPVs):

• Fool investors: complex securities can sometimes be sold for more than their fair value (for in-stance, issuing stocks and warrants)

• By the efficient market hypothesis, this should be impossible • Reduce cost or increase subsidies: packaging securities with a strategy to:

• Minimize overall tax; or • Reduce the cost of underwriting/issuance (investment bankers, lawyers, accountants, etc.)

• Create a new security: conducting financial innovation to offer risk/reward trade-offs which are not easily replicable.

• This allows firms to issue securities at higher costs (and hence raise capital more cheaply)

14.2 A Description of Efficient Capital Markets • In an efficient market, security prices adjust immediately and correctly to new information • The efficient market hypothesis (EMH) has implications for investors and firms:

• Prices will adjust before investors have time to exploit any new information • Firms should not expect to be able issue securities at greater than the present value of their cash

flows

Foundations of Market Efficiency 1) Rationality: all investors are rational (price will rise immediately to reflect new information because

no rational investor would wait) 2) Independent Deviations from Rationality: the number and influences of overly-optimistic and overly-

pessimistic irrational investors will cancel one another out, hence making the market collectively ra-tional

1) Opponents of the EMH argue that irrationalities do not perfectly cancel at that, at times, the majority of investors are swept away in either over-optimism of over-pessimism.

3) Arbitrage: Arbitrage is risk-less profit; it is achieved by simultaneously purchasing and selling substi-tute securities

14.3 & 14.4 The Different Types of Efficiency and the Evidence for Each • There are three forms of market efficiency which depend upon classifications of information. • Because the form of efficiency depends upon the availability of information:

• Strong form implies semi-strong form efficiency• Semi-strong form implies weak-form efficiency

34

Form Informa-tion Type

Description Support / Evidence

Weak Form

Semi-Strong Form

Strong Form

Past price data

• A capital market is weak-form efficient if it fully incorporates past information in past stock prices.

• Weak-form efficiency can be expressed mathematically by: Pt = Pt-1 + expected return + random error.

• The random error is due to new information on the stock. This random error creates a “random walk”.

• Historical price information is the easiest type of information to acquire.

• Seasonal share-price trends should not exist under this form of efficiency.

• It is cheap to access information and iden-tify trends (anyone with a computer and some knowledge of programming and sta-tistics can design such an information system)

• Serial correlation - serial correlations near 0 imply there is no cor-relations between re-turns historically (shares follow a ran-dom walk)

Publicly available informa-tion

• A market is semi-strong efficient if it incorpo-rates all publicly available information includ-ing published accounting statements as well as historical price information

• Event studies: the re-lease of information in time t should be re-flected in the abnormal period at time t. There should be no carry-over from past events

• Mutual-fund perform-ance: mutual funds are consistently unable to outperform the market (implying that analyz-ing all publicly avail-able information is futile)

• Growth in ETFs con-firms investors agree it is impossible to regu-larly outperform the market

Private & Public in-formation

• Any information pertinent to the value of a security is fully incorporated (this includes even private information)

• This implies corporate insiders should not be able to profit for private information

• Little supporting evi-dence; insiders are able to consistently earn excess returns

35

Weak form efficiency (price information)

Semi-strong form effi-ciency (publicly avail-able information)

Strong form efficiency (all information - pub-lic and private)

Degree of informa-tion availability

Efficient Markets Misconceptions

• The Efficacy of Dart Throwing: all the EMH says is that manager will not be able to outperform the market for a sustained period of time (or at least that it is highly improbable).

• Price fluctuations: price fluctuations to imply randomness - share prices are constantly reacting to new information

• Shareholder disinterest: because only a portion of outstanding shares are traded each day, it implies markets are inefficient - this is incorrect because many more investors are following a share on a given day than are trading on that day.

14.5 The Behavioural Challenge to Market Efficiency • Rationality: many investors are irrational (investors are likely to sell winners and hold losers ) • Independent Deviations from Rationality: psychologists argue that investors deviate from rationality in

accordance with a set of principles (and therefore do not do so randomly, hence allowing deviations to cancel).

• First principle - representativeness: the belief that positive returns in the past on a security imply a higher probability of positive returns in the future

• Leads to bubbles • Second principle - conservatism: people are too slow to adjust their belief system to new infor-

mation. • Studies report that prices seem to be adjust slowly to information contained in earnings an-

nouncements • Investors are slow to adjust their perceptions of a company

• Arbitrage: arbitrage only functions correctly if the influence amateurs does not exceed the influence of professionals (if amateurs underprice McDonalds in the past, they may continue to do this in the fu-ture).

14.6 Empirical Challenges to Market Efficiency • Limits to arbitrage: engaging in arbitrage can result in large short-term losses if the market remains

irrational. “Markets can say irrational longer that you can stay solvent”. • Earnings surprise: prices adjust slowly to earnings announcement surprises (conservatism evidence) • Size: the return on stocks with small market capitalizations tend to have higher returns (beyond the

compensation for extra risk) • Value versus growth: value stocks (low valuation multiples) tend to outperform growth stocks • Crashes and bubbles: stock market crashes on no significant news indicate market inefficiency (bubble

theory - securities sometimes move wildly above their true values).

14.7 Reviewing the Differences • Representativeness creates overreaction to stock returns which generate bubbles • Conservatism implies investors adjust their beliefs slowly which creates under-reactions

14.8 Implications for Corporate Finance • Accounting: Changes in accounting will not be fool an efficient market (since accounting changes do

not affect the cash flows from a security) • Timing decisions: managers will attempt to issue equity when it is overvalued to earn a positive NPV on

the issuance • Under efficient capital markets, this should be impossible • In reality, it is not and evidence suggests that bankers are indeed successful in this activity

• This may be because bankers are corporate insiders (have access to private information) • Share prices return less than the market after IPOs and SEOs

• Speculation and efficient markets: if markets are efficient, managers should not waste time attempt-ing to determine the direction of currencies or interest rates.

• The same holds for acquisitions• Managers should only buy other companies if synergies can be generated (not because the

company is undervalued) • Information on market prices:

• The shares of the acquirer in a deal often fall, implying that deals often hurt the acquirer • There is a strong negative correlation between managerial turnover and prior share prices

• Stocks tend to fall far before the forced departure of an executive

36

Week 9, Class 17.1 Why Use NPV? • Increases firm value for shareholders (simple decision rule) • Value-additivity - the principle that the value of the firm rises by the NPV of the project • Three key attributes of NPV are:

• NPV uses cash flows - earnings are an artificial construct • NPV uses all the cash flows of the project • NPV discounts the cash flows properly (at the appropriate discount rate)

7.2 The Payback Period Rule • The payback period is the amount of the time it takes to recoup the initial investment outlay • The payback period rule requires a project to repay the outlay within a given amount of time • Problems with the payback period

• Timing of the cash flows within the payback period • The temporal distribution of cash flows is irrelevant• The payback period therefore fails to consider the time value of money

• Payments After the Payback Period • Payback period fails to consider cash flows after the payback date (Despite the fact that these

cash flows could be enormous) • Arbitrary standard for payback period

• Payback period benchmarks are chosen arbitrarily • This is unlike the NPV rule, where the discount rate is not arbitrary but is commensurate

with risk

• Managerial perspective (advantages)• The payback period is simple • The recapturing of cash is often important • Standard academic criticisms are often exaggerated

• With small projects, the payback period rule may be useful; for large projects, NPV is the overriding method

7.3 The Discounted Payback Period Rule • We discount the cash flows and then ask how long it will take these cash flows to equal the initial in-

vestment • The discounted payback period will always be longer than the normal payback period

• Like the normal payback rule, this rule requires us to make some arbitrary choice for the cut-off date • This rule is a poor comprise between NPV and the payback period rule

• If we are going to discount the cash flows and compare them with the initial outlay, why not simply calculate NPV?

7.4 The Average Accounting Return • The AAR = the average project earnings (after tax and depreciation) / average book value

• Problems • AAR uses accounting numbers (earnings & book value) which are somewhat arbitrary • AAR does not take into account timing (no present value calculations involved) • AAR requires an arbitrary cut-off

• Advantage: easy to calculate from numbers already in the accounting system

7.5 The Internal Rate of Return • The IRR is the discount rate which yields a NPV of zero

• Accept if IRR > discount rate • Reject if IRR < discount rate • Indifferent if IRR = discount rate

• The IRR does not depend upon anything external (hence the word internal) • A bond’s IRR is its YTM

37

7.6 Problems with the IRR Approach • An independent project is one whose acceptance or rejection is independent of the acceptance or

rejection of all other projects • Mutually exclusive investments implies can accept A or B but not both.

Two Problems for both independent and mutually exclusive investments • 1 - Investment or financing?

• if the initial cash flow is in and the terminal cash flow is out, then the project is a financing one • if this is the case, the decision rule is reversed:

• If the IRR > the discount rate, reject (expensive financing - we can borrow at the discount rate, so why borrow at a higher IRR?)

• If the IRR < discount rate, accept (cheaper financing)

• 2 - Multiple Rates of Return • If cash flows changes signs N times, there will be N IRRs (hence if there are negative and then posi-

tive and then negative cash flows, there will be 2 IRRs). • No one IRR is superior to another so it illogical to choose one IRR as the correct one

38

NPV

Discount rate

Positive NPV Projects

IRR

Negative NPV Projects

NPV

Discount rate

Positive NPV Projects

IRR

Negative NPV Projects

• Modified IRR (MIRR) handles this problem by combining cash flows into only two cash flows by shifting cash flows along the time line

• By discounting and summing cash flows, there will be only one sign change and hence only one IRR

• However, MIRR employs an discount rate )and this implies the project’s evaluation is not strictly internal)

Flows Number of IRRS IRR Criterion

First cash flow is negative, sec-ond is positive (investing)

1 Accept: IRR > r

Reject: IRR < r

First cash flow is positive, sec-ond is negative (financing)

1 Accept: IRR < r

Reject: IRR > r

Multiple cash flows with differ-ent signs

Many No valid IRR

Problems with Mutually Exclusive Projects

• Scale problem - IRR does not consider the size of the project; hence, it is possible for one project to a higher NPV while the other has a higher IRR

• Solution: calculate the IRR on the incremental cash flows. If this is above the discount rate, accept the larger project.

• Timing problem - because two different projects will have different temporal cash flow distributions, they will have different sensitivities to changes in the discount rate

• The investment with more cash flow distributed in a later time-period will be more sensitive to changes in the discount rate (the slope of the NPV line below is steeper)

• To solve this problem: • Calculate the incremental IRR

• If the discount rate is below this incremental IRR, purchase the investment with heavier cash flows later

• If the discount rate is above, purchase the investment with earlier cash flows

39

NPV

Discount rate

Incremental IRR

IRR IRR

B

A

• Redeeming qualities: • No discount rate is required • The project’s benefits are summarized in one number

7.7 Profitability Index (PI) • Profitability index = PV of CFs subsequent to initial investment / initial investment

Three considerations: • Independent projects

• Accept if PI > 1• Reject if PI < 1

• Mutually exclusive projects • Accept if incremental PI > 1

• Capital rationing • If we do not have enough financing to fund all positive NPV projects:

• Choose the projects with the highest PIs • PI therefore helps to ration capital

40

W9,C2 - W10,C2 8.1 Incremental Cash Flows • In calculating the NPV of a project, only cash flows that are incremental to the project should be used.

Incremental cash flows are the changes in the firm’s cash flows that occur as a direct consequence of accepting the project.

• A sunk cost is a cost which has been incurred in the past; these costs do not enter out analysis • Lost revenues can be viewed as costs. They are called opportunity costs because, by taking the pro-

ject, the firm forgoes other opportunities for using the assets. • Side effects are classified as either

• Erosions - reduction in sales as a result of a project • Synergy - increase in cash flows (more inflows or less outflows) resulting from existing projects by

accepting a new project • Allocated costs should be viewed as a cash outflow of a project only if it is an incremental cost to the

project

8.2 The Majestic Mulch and Compost Company: An Example • Net working capital is defined as the difference between current assets and current liabilities

• An investment in net working capital represents a cash outflow since it represents 1. Accounts receivable not received in cash 2. Inventory (which ties up cash and is hence a cash outflow from the firm) 3. Or a cash a balance (which ties up cash and is hence a cash outflow from the firm)4. Free up cash by deferring payment through accounts payable • **Note that the consideration for net working capital is the same reconciliation process used in

the operating section of the cash flow statement to reconcile net income to operating CF • Net working capital ultimately goes to zero as the project is closed out

• The change in working capital each year is a cash outflow. • Hence an increase in working capital for one year represents an outflow for that year

• Project cash flow: • Operating CF = revenue - operating costs (which exclude deprecation) - taxes • Investment CF = changes in working capital + investment outlays (+ investment returns like salvage

value)

• Which set of books?• There are two sets of books:

• Tax books - where the size of taxes are calculated according CRA rules • Shareholders’ books - where GAAP rules are applied

• Interest expenses are not considered in calculating cash flows since we assume financing is purely equity-based

8.3 Inflation and Capital Budgeting • The real interest rate is the inflation-adjusted rate (it deducts the influence of inflation) while the

nominal interest rate does not • 1 + nominal interest rate = (1 + real interest rate) ( 1 + inflation rate)

• Therefore, real interest rate ≈ nominal interest rate - inflation rate • This approximation fails as the rates get larger

• A cash flow is expressed in nominal terms if the actual dollars to be received are given • Discounting? Which rate do I use?

• Nominal cash flows must be discounted at the nominal rate • Real cash flows must be discounted at the real rate

• The NPVs will be same regardless of whether real or nominal rates are used as long as the discount rate and the cash flow terms are consistent.

• Depreciation is always a nominal quantity (because the straight-line method makes no consideration for inflation)

8.4 Alternative Definitions of Operating Cash Flow • Operating cash flow can be calculated in three ways:

41

• Net income + depreciation (bottom-up approach) • Sales - costs - taxes (top-down approach)• (Sales - costs) * (1 - t) + depreciation * t (tax-shield approach)

• The only cash flow effect of depreciation is to reduce taxes• t * depreciation is the called the depreciation tax shield

8.5 Applying the Tax Shield Approach to the Majestic Mulch and Compost Company Project • The tax shield approach involves disaggregating cash flows into components and taking the present

value of each of these. • The sum of the present values of each of these cash flow series equals the NPV of the project. • The four cash flow series are:

• After tax operating cash flows: (Revenue - operating expenses) * (1 - t) • Changes in NWC, which is composed of

• Required cash balance • Accounts receivable • Accounts payable • Inventory • Other short-term financing mechanisms

• Equipment flows • Investing costs • Salvage returns

• The tax shield benefits • There are two components to the PV of the tax shield

• The incremental cash flow resulting from the CCA • The lost protection after the asset is sold

• There components culminate in the following formula

• There are three advantages to the tax shield approach • Simplifying formula • The ability to discount different types of cash flows at different rates• There is no necessity to make all cash flows nominal or real. We can simply make the present val-

ues of each different stream nominal or real and add these together

8.6 Investments of Unequal Lives: The Equivalent Annual cost method • When two investments have unequal lives (and therefore unequal costs), it is not enough to choose the

machine with the lowest PV for costs • First, convert all terms to real terms • Second, determine the PV of the costs for each machine • Third, standardize the cash outflow by using an annuity formula where n is the number of cash

flows • This standardized cash flow is called the equivalent annual cost

• Note that we can only do this because there is no revenue difference between the two investments

General Decision to Replace (Advanced)

• First, determine the equivalent annual cost of the new machine (the replacement) • Second, determine the PV of the cost for holding the old machine for one additional

• Compound this PV forward one period and compare it with the EAC for the replacement machine• If this quantity exceeds the EAC, purchase the replacement immediately

42

Appendix 8A - Capital Cost Allowance • Since capital cost allowance is deducted in computing taxable income, larger CCA rates reduce taxes

and increase cash flows. • When an asset is sold, the UCC in its asset class (or pool) is reduced by what is realized on the asset or

by its original cost, whichever is less. The amount is called the adjusted cost of disposal (ACD)

Case 1 - Assets remain in class • Cost of all acquisitions - adjust cost of disposal = net acquisitions

• If the net acquisitions is positive, we apply the 50% rule to the net acquisitions • If net acquisitions is negative, the 50% rule does not apply

Case 2 - Asset class closed • Three cases

• ACD < remaining UCC = terminal loss• The UCC left after the ACD deduction results in a tax savings (treat it as depreciation - a tax

deductible item) • ACD > remaining UCC = terminal gain (and asset is sold below original cost)

• Pay ordinary tax rate on this terminal gain as if it were revenue • ACD > remaining UCC = terminal gain (and asset is sold above original cost)

• Pay ordinary tax rate on the the difference between the remaining UCC and the original cost • Pay capital gains tax on the amount by which the asset sale exceeds the original cost

• Remember that only 50% of a capital gain is taxed

43

Week 11, Class 122.1 Types of Leases • A lease is a contactual agreement between a lessee and a lessor. The agreement establishes that the

lessee has the right to use an asset and in return must make periodic payments to the lessor • The lessor owns the asset

• The lessor can be either the original manufacturer or an independent leasing company • If the company is an independent lessor, the lease is called a direct lease • If the company is the manufacturer, the lease is a sales type lease

• The lessee uses the asset• There are two broad types of leases

• Operating (service) leases • Operating leases are not fully amortized - the term of the lease is less than the economic life

of the asset• Lessor must maintain and insure the leased asset (service) • Cancellation option - gives the lessee the right to cancel the lease before the expiration date

• Financial leases • Do not provide maintenance or service • Financial leases are fully amortized • Lessee usually has a right to renew the lease on expiration • Financial leases cannot be cancelled

• The lessee must make all payments are face bankruptcy • There are two specific types of financial leases

• Sale and lease-back back: a company sells assets to another firm and immediately leases • Advantages

• Lessee immediately receives cash while still retaining use of the asset• Lessor make gain a tax advantage over and above purchase cost (when the PV of

the lease payments is included)• Leveraged lease:

• The lessor puts up no more than 40-50% of the asset’s cost • Lenders supply the remaining financing • Lender has two protections:

• First lien on the asset • In the event of loan default, the lender receives the lease payments

22.2 Accounting and Leasing • Off-balance sheet financing a firm could arrange to use an asset without reporting it on the balance

sheet • Capitalization: report the PV of the lease payments as a liability, with the offsetting item as the asset’s

value• Operating leases are not capitalized • Financial leases are capitalized

A lease must be capitalized if one of the following four conditions are met: I. The lease transfers ownership of the property by the end of the term of the lease II. The lease permits the purchase of the asset below fair market value III. The lease is for 75% of the asset’s economic life IV. The PV of the lease payments is above 90% of the asset’s fair market value at the beginning of the

lease

22.3 Taxes and Leases • The lessee gets a tax deduction on the full lease payments

22.4 The Cash Flows of Financial Leasing • There are three important cash flows to consider in leasing:

• The lease payments • Remember lease payments are made at the beginning of a period (annuity in advance)

44

• Remember that lease payments are discounted at the after-tax rate (since they are tax de-ductible)

• The tax shield • The initial investment outlay / salvage value

22.4 A Detour on Discounting and Debt Capacity with Corporate Taxes • In a world with corporate taxes, risk-less cash flows should be discounted at the after-tax risk-free rate • In a world with corporate taxes, one determines the increase in the firm’s optimal debt level by dis-

counting a future guaranteed after-tax inflow at the after-tax risk-less interest rate

22.5 NPV Analysis of the Lease-Versus-Buy Decision • Discount all cash flows at the after-tax interest rate • The lease payment is similar to the interest payment made to service debt

• This implies that lease payments should be discounted approximately equal to the cost of serving debt (the after-tax cost of debt)

• The textbook discounts both cash flows (tax shield and lease payments) at the after-tax cost of debt for the lessee

22.8 Does Leasing Ever Pay? The Base Case • As long as:

• Both parties have identical interest rates and tax rates• Transaction costs are ignored

• No value is created from a lease agreement

22.9 Reasons for Leasing • Taxes may be reduced

• If the lessor’s tax rate exceeds the lessees (or the lessee does not have the income to use the tax shield), and the lessor has the income to utilize the tax shield, value is created from the lease

• Many smaller firms do not have the income to utilize the accelerated tax shield in the early years of an asset acquisition

• The lessor must pass some of the tax savings on to the lessee to create value for both parties • Reservation payments are the payments level at which the lessee or lessor will be indifferent to

the lease• The lease payment must fall between the reservation payments

• Reduction of uncertainty • The true residual value of an asset is not certain• This cash flow is therefore risky • By leasing, the lessee (usually the smaller company) passes this risk onto the lessor (usually the

larger company capable of absorbing this risk with a wider asset base) • Transaction cost

• The transaction cost ownership transfer is typically lower than leasing • Leasing is most beneficial when the transaction cost of purchase and resale outweigh the agency

costs and monitoring cost of a lease

• There are many bad reasons for leasing • Leasing to improve ROA

• Return - leasing payments are often lower than sum of the depreciation and interest expense associated with acquiring an asset

• Assets - because leasing is off-balance-sheeting financing, it reduces the asset base • 100% financing

• Leasing does not free up debt capacity (since intelligent bankers will realize a lease payment is identical in form to an interest payment)

• Other reasons• Circumventing capex (therefore increasing cash flow)

22.9 Some Unanswered Questions • Even though leasing does not free-up debt capacity, the two tend to go hand-in-hand • Leasing for manufacturers v. independent leasers

• Manufacturing companies calculate CCA based on cost • independent leasers calculate CCA based on selling price

• Why are some assets commonly not leased?• The more sensitive an asset is to maintenance/service costs, the less likely that it will be leased

(because ownership encourages responsibility) • Leasing may allow price discrimination

45

Week 11, Class 29.1 Decision Trees • In decision-tree modelling, we break our analysis into branches which are weighted by probability. The

steps are• determine the NPV of each branch• discount the NPV of each branch to t=0 • weight each branch NPV by probability • deduct initial investment costs which are common to all branches

• Often times different parts of the decision trees will have different discount rate - apply the correct rates when moving through time on the tree

9.2 Sensitivity Analysis, Scenario Analysis and Break-Even Analysis

Sensitivity analysis

• In a sensitivity analysis, we create base-case, pessimistic and optimistic case for the variables • Revenue

• Market size • Market share • Price

• Cost • Variable • Fixed

• Investment size• A different NPV is calculated for each projection (each variable’s NPV is calculated under a base-case,

pessimistic and optimistic assumption) • Advantages

• Removes the false sense of security • Reveals which variables are most important (to which variables is NPV most sensitive?) and there-

fore require further research • Disadvantages

• Make unwittingly create a false sense of security (if the ‘pessimistic projections’ are too optimistic) • Sensitivity analysis treats each variable as autonomous when this is not the case (many variables

are related)

Scenario analysis • Scenario analysis removes this last disadvantage of sensitivity analysis but considering a variety of sce-

narios where multiple variables are changes

Break-even analysis

• Accounting break-even refers to level of sales required to set net income = 0 • Financial break-even refers to the level of sales required to set NPV = 0• In financial break even, we apply the following framework:

PV of cash inflows = PV of cash outflows

PV of After-tax revenue + PV of CCA tax shield = PV of after-tax Variable Costs + PV of after-tax Fixed Costs + Initial Investment Cost

9.3 Monte Carlo Simulation

• In a Monte Carlo simulation, we construct probabilities for each variable in a cash flow projection and run the model many times to get a cash flow distribution

• This is divided into a number of steps: • 1 - Specify the basic models

• Break the cash flow model into variables

46

• 2 - Specify a probability distribution for each variable in the model • 3 - The computer draws one outcome • 4 - Repeat the procedure• 5 - Calculate NPV

• Determine a distribution for the cash flows and use this to calculate the NPV

47