Summary Corporate Finance Berk Demarzo

8/18/2019 Summary Corporate Finance Berk Demarzo

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Summary Corporate Finance (Berk & DeMarzo)

Financial Markets (Maastricht University)

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Summary Corporate Finance (Berk & DeMarzo)

Chapter 1: The corporation

Theoretisch Chapter.

1.1 four types of firms

Tax implications for corporate entities:

Classical system First, the corporation pays tax on its profits. Then the remaining

profits are distributed to the shareholders who pay their own personal income tax on

this income.

S corporations(in US) alternative system, that is not subject to double taxation.

- the shareholders must be U.S. citizens

- no more than 100 of them.C corporations Companies which are subject to corporate taxes (>100 shareholders)

Shareholders: owners of the company

Control:

Board of directors: a group of people who have the ultimate decision-making authority in

corporations. Shareholders are able to elect the board of directors.

Chief executive officer (CEO): is charged with running the corporation by instituting the

rules and policies set by the board of directors.

Chief financial officer (CFO): most senior financial manager, who often reports directly to

the CEO. Financial managers are responsible for the three main tasks: making investment

decisions, making financing decisions and managing the firm’s cash flows.

1.2 Ownership versus control of corporations

Goal of the firm: The shareholders will agree that they are better off if management makes

decisions that increase the value of their shares.

Many people claim that because of the separation of ownership and control in a

corporation, managers have little incentive to work in the interests of the shareholderswhen this means working against their own self-interest. Agency problem = when managers,

despite being hired as the agents of shareholders, put their own self-interest ahead of the

interests of shareholders.

This agency problem is commonly addressed in practice by minimizing the number of

decisions managers must make for which their own self-interest substantially differs from

the interests of the shareholders (Beloning met: opties, bonussen, aandelen). There is a

limitation to this strategy. By tying compensation too closely to performance, the

shareholders might be asking managers to take on more risk than they are comfortable

taking.


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Share price of the corporation is a barometer for corporate leaders that continuously gives

them feedback on their shareholders’ opinion of their performance.

When shareholders are dissatisfied, they can replace the board of directors or just the CEO.

Hostile takeover, an individual or organization -sometimes known as a corporate raider –

can purchase a large fraction of the equity and acquire enough votes to replace the board ofdirectors and the CEO. With a better management team, the shares would have a price rise

and this results in profit for the corporate raider (and other shareholders).

When a corporation borrows money, the holders of the firm’s debt also become investors in

the corporation. While the debt holders do not normally exercise control over the firm, if the

corporation fails to repay its debts the debt holders are entitled to seize the assets of the

corporation in compensation for the default. When a firm fails to repay its debts, the end

result is a change in ownership of the firm, with control passing from equity holders to debt

holders. Importantly, bankruptcy need not result in a liquidation of the firm. Even if controlof the firm passes to the debt holders, it is in the debt holders’ interest to run the firm in the

most profitable way possible.

The value of the shares of private companies(sole proprietorship, (limited) partnership and

private limited companies) can be difficult to determine, because they have a limited set of

shareholders and they are not generally traded.

Shares of public companies (Public limited companies and corporations) are traded on a

stock market. These markets provide liquidity(=it is possible to sell it quickly and easily for a

price very close to the price at which you could contemporaneously buy it) and determine a

market price for the company’s shares.

Primary market = when a listed company issues

1.3 the stock market

new shares and sells them to investors, they

do so on the primary market.

Secondary market = the trade of shares between investors without the involvement of the

corporation.

Market makers (specialists) = match the buyers and the sellers of shares (makelaars).

Bid price = de biedprijs, the price the market makers stand willing to buy the stock atAsk price = de verkoop/vraagprijs, the price they stand willing to sell the stock for.

Bid-ask spread= the difference between the bid and ask price. The customers always buy at

the ask (the higher price) and sell at the bid (the lower price). The bid-ask spread is a

transaction cost

investors have to pay in order to trade.


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Chapter 2: Introduction to financial statement analysis

Theoretisch Chapter.

Publicly listed companies around the world are required to file their financial statementswith the relevant listing authorities periodically. They must also send an annual

report(jaarverslag) with their financial statements to their shareholders each year. Financial

statements are important tools through which investors, financial analysts and other

interested outside parties (such as creditors) obtain information about a corporation.

2.1 Firms’ disclosure of financial information

Investors need some assurance that the financial statements are prepared accurately.

Corporations are required to hire a neutral third party, known as an auditor, to check the

annual financial statements, to ensure that the annual financial statements are reliable and

prepared according to GAAP.

The balance sheet equation: Assets = Liabilities + Shareholders’ Equity.

Depreciation(afschrijving gebouwen en gereedschap) is not an actual cash expense.

Book value(or carrying amount) of an asset is equal to its

2.2 The Balance Sheet

acquisition cost less accumulateddepreciation

intangible assets (zijn ontastbaarheden zoals): brand names and trademarks, patents,

customer relationships and employees.

.

Goodwill: When a firm acquires another company, the difference between the price paid for

the company and the book value assigned to its intangible assets

Amortization (or impairment charge): If the firm assesses that the

is recorded separately as

Goodwill.

value of these intangibleassets declined over time, it will reduce the amount listed on the balance sheet by an

amortization (or impairment charge) that captures the change in value

Net working capital: The difference between current assets and current liabilities, the

capital available in the short term to run the business (=current assets – current liabilities).

of the acquired

assets. Like depreciation, amortization is not an actual cash outflow.

book value of equity: The difference between the firm’s assets and liabilities is the

shareholders’ equity. Many of the assets listed on the balance sheet are valued based on

their historical cost rather than their true value today. The true value today of an asset may


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be very different from its book value. Also many of the firm’s valuable assets are not

captured on the balance sheet.

The total market value of a firm’s equity equals the market price per share x the number of

shares, referred to as the company’s market capitalization. It depends on what investors

expect those assets to produce in the future.

The book value of a firm’s equity is not a good estimate of the liquidation value of the firm

(sell assets – pay off debts = liquidation value). We could better use the market value

(market capitalization) to determine it.

2.3 Balance sheet analysis

Market-to-book ratio (also called the price-to-book or P/B ratio), which is the ratio of afirm’s market capitalization to the book value of shareholders’ equity.

Market-to-Book Ratio = Market value of equity / Book value of equity

This ratio is one way a company’s share price provides feedback to its managers on the

market’s assessment of their decisions. Analysts often classify firms with low market-to-book

ratios as value stocks, and those with high market-to-book

ratios as growth stocks.

Low High

Market-to-Book Value stocks Growth stocks(market hoog)

Book-to-market Growth stocks(market hoog) Value stocks

Debt-Equity Ratio = Total debt / total equity

Laat zien hoe het bedrijf is gefinancierd.

We can calculate this ratio using either book or market values for equity and debt.

Market

Enterprise value =

debt-equity ratio has important conseqences for the risk and return of its

shares.(h12)

Market

Current ratio = current assets / current liabilities

Quick ratio = (Current assets –

value of equity(=market capitalization) + debt - cash

The enterprise value can be interpreted as the cost to take over the business.

inventory) / current liabilities

Creditors often compare a firm’s current assets and current liabilities to assess whether the

firm has sufficient working capital to meet its short-term needs. This can be done with the

current or quick ratio. A higher current or quick ratio implies less risk of the firm

experiencing a cash shortfall in the near future.


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Depreciation and amortization, expenses on the income statement, are not actual cash

expenses but they represent an estimate of the costs that arise from wear and tear to

obsolescence of the firm’s assets.

2.4 the income statement

EPS = Earnings per share = Net Income / Shares outstanding

If the stock options are “exercised” the company issues new shares and the number of

shares outstanding will grow. The number of shares may also grow if the firm issues

convertible bonds, a form of debt that can be converted to shares. Because there will be

more shares in total to divide into the same earnings, this growth in the number of shares is

referred to as dilution. Firms disclose the potential for dilution by reporting diluted EPS,

which represents earnings per share for the company calculated as though share options

had been exercised or convertible debt had been converted

.

Gross margin = Gross Profit / Sales

A firm’s gross margin reflects its

2.5 Income statement analysis

ability to sell a product for more than the cost of producing

it.

Operating margin = Operating profit / sales

EBIT margin = EBIT / Sales.

Net profit margin = Net income / total sales

The net profit margin shows the fraction of each dollar in sales that is available to equity

holders after the firm pays its expenses plus interest and taxes.

Working capital ratios: shows us how efficiently the firm is managing its net working capital:

-Accounts receivable days = accounts receivable / average DAILY sales(=sales/365)

This ratio shows how many days it takes to collect payment from customers.

-Accounts payable days = accounts payable / average DAILY purchases

-Inventory days = inventory / average DAILY Cost of Goods Sold

Analysts and financial managers often evaluate the firm’s return on investment by

comparing its income to its investment using ratios such as the firm’s return on equity.

Return on Equity (ROE) = Net income / Book value of equity

A high ROE may indicate the firm is able to find investment opportunities that are very

profitable. Another common measure is return on assets (ROA), which is:

Return on Assets = Net income / total assets

The DuPont Identity= (Net Income/Sales) x (Sales/Total Assets) x (Total Assets/ Total Equity)

=ROE = Net profit margin x Asset Turnover x Equity Multiplier

= Return on Assets x Equity Multiplier


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Equity multiplier = indicates the value of assets held per euro or dollar of shareholders

equity. The equity multiplier will be greater the firm’s reliance on debt financing

Analysts and investors use a number of

.

ratios to gauge the market value of the firm.

The most common is the firm’s price-earnings ratio (P/E)

P/E ratio = Market Capitalization/ Net income = Share price / Earnings per share

= P x N / Net income = P / EPS

The P/E ratio is a simple measure that is used to assess whether a share is over- or under-

valued based on the idea that the value of a share should be proportional to the level of

earnings it can generate for its shareholders.

Retained Earnings = Net income – Dividends (staat niet in de Cashflow)

It tend to be higher for industries with higher

expected growth rates. The P/E ratio is not meaningful when the firm’s earnings are

negative. In this case, it is common to look at the firm’s enterprise value relative to sales.

There are two reasons that net income does not correspond to cash earned. First, there are

non-cash entries on the income statement, such as depreciation and amortization. Second,

certain uses of cash, such as the purchase of a building or expenditures on inventory, are not

reported on the income statement.

The statement of cash flows is divided into three sections: operating activities, investment

activities and financing activities. The first section, operating activity,

2.6 The statement of cash flows (Most important for investors.)

starts with net income

from the income statement. It then adjusts this number by adding back all non-cash entries

related to the firm’s operating activities. The next section, investment activity, lists the cash

used for investment. The third section, financing activity,

Operating activity

1. Depreciation is not an actual cash

outflow. Thus, we

shows the flow of cash between

the firm and its investors.

add it back to the net

income when determining the amount of

cash the firm has generated.

2. Next, we adjust for changes to net

working capital (=current assets – current

liabilities) that arises from changes to

accounts receivable, accounts payable or

inventory. Deduct increases in NWC.

1. Accounts receivable: asset -> deduct

2. Accounts Payable: liability -> add

3. Inventory: asset -> deduct


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Investment activity

Purchases of new property, plant and equipment are referred to as capital expenditures.

They do not appear immediately as expenses on the income statement. We subtract the

actual capital expenditure that the firm made

Financing activity

.

Dividends paid to shareholders are a cash outflow. Also listed under financing activity is any

cash the company received from the sale of its own shares, or cash spent buying

(repurchasing) its own shares. The last items to include in this section result from changes to

short-term and long-term borrowing.

Management discussion and analysis (MD&A) or business and operating review =

company’s management reviews the recent year’s performance. Management may also

discuss the coming year, and outline goals and new projects. Management should also

discuss any risks and uncertainties that the firm faces or issues that may affect the firm’s

liquidity or resources.

Management is also required to disclose any off-balance sheet transactions, which are

transactions or arrangements that can have a material impact on the firm’s future

performance yet do not appear on the balance sheet.

2.7 other financial statement information

Chapter 3: Arbitrage and financial decision makingTheoretisch Chapter.

The first step in decision making is to identify the costs and benefits of a decision. The next

step is to quantify these costs and benefits. In order to compare the costs and benefits, we

need to evaluate them in the same terms – cash today.

3.1 Valuing decisions

Competitive market: a market in which a good can be bought and sold at the same price –

that price determines the cash value of the good.


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By evaluating costs and benefits using competitive market prices, we can determine whether

a decision will make the firm and its investors wealthier.

Valuation Principle= The value of an asset to the firm or its investors is determined by its

competitive market price. The benefits and costs of a decision should be evaluated using

these market prices, and when the value of the benefits exceeds the value of the costs, thedecision will increase the market value of the firm.

We call the difference in value between money today and money in the future the time

value of money.

r

3.2 interest rates and the time value of money

f = Risk-free interest rate the risk-free interest rate depends on supply and demand.

Present value(PV) = the value in terms of dollars todayFuture value (FV) = in terms of dollars in the future.

Discount factor = 1/1+r one year discount factor.

Discount rate = the risk-free interest rate is also referred to as the discount rate for a risk-

free investment

.

Net Present Value = PV (Benefits) – PV (costs)

The NPV is the total of the present values of all project cash flows.

3.3 Present value and the NPV decision rule

A positive NPV increases

the value of the firm.

NPV Decision Rule = when making an investment decision, take the alternative with the

highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.

Regardless of our preferences for cash today versus cash in the future, we should

Accept all NPV with value 0 or higher when you’re able to.

always

maximize NPV first. We can then borrow or lend to shift cash flows

through time and find

our most preferred pattern of cash flows.

The practice of

3.4 Arbitrage and the Law of One Price

buying and selling equivalent goods in different markets to take advantage of

a price difference is known as arbitrage. An arbitrage opportunity has a positive NPV. Once

they are spotted, they will quickly disappear. Thus, the normal state of affairs in markets

should be that no arbitrage opportunities exist.


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We call a competitive market in which there are no arbitrage opportunities a normal

market.

If the prices in the two markets differ, investors will profit immediately by buying in the

market where it is cheap and selling in the market where it is expensive. In doing so, they

will equalize the prices. As a result, prices will not differ (at least not for long). This importantproperty is the Law of One Price(onderhevig aan assumpties): If equivalent investment

opportunities trade simultaneously in different competitive markets, then they must trade

for the same price in both markets.

(financial) security (bonds, stocks) = An investment opportunity that trades in a financial

market.In financial markets it is possible to sell a security you do not own by doing a short sale.

In a short-sale, the person who intends to sell the

3.5 No-arbitrage and Security Prices

security first borrows it from someone

who already owns it. Later, that person must either return the security by buying it back or

pay the owner the cash flows he or she would have received. By executing a short sale, it is

possible to exploit the arbitrage opportunity when the bond is overpriced even if you do not

own it.

Note that the

No-arbitrage price = the price in all markets when there’s no arbitrage opportunity.

No-arbitrage price of a security => Price security = PV(all cash flows paid by the security)

risk-free interest rate equals the percentage gain that you earn from investing

in the bond, which is called the bond return.

Bond Return = Gain at end of year / initial cost = (nieuw – oud) / oud =rf

When securities trade at no-arbitrage prices, the cost and benefit are equal in a normal

market and so he NPV of buying a security is zero. (obligatie is risicoloos, is de risicoloze

rente, dus NPV is 0, zie het als een bedrag op de bank zetten).

In a competitive market, if a trade offers a positive NPV to one party, it must give a negativeNPV to the other party. Because all trades are voluntary, they must occur at prices at which

neither party is losing value, and therefore for which the trade of zero NPV(no value

created). Instead, value is created by the real investment projects in which a firm engages,

such as developing new products, opening new stores or creating more efficient production

methods.

Separation Principle = security transactions in a normal market neither create nor destroy

value on their own. Therefore, we can evaluate the NPV of an investment decision

separately from the decision the firm makes regarding how to finance(borrowing or add

stocks) the investment or any other security transactions the firm is considering.


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Portfolio = collection of securities. Because security C is equivalent to the portfolio of A and

B, by the Law of One Price, they must have the same price. This idea leads to the relationship

known as value additivity: that is, the price of C must equal the price of the portfolio, which

is the combined price of A and B.

Value additivity has an important consequence for the value of an entire firm. The cashflows of the firm are equal to the total cash flows of all projects and investments within the

firm. Therefore, by value additivity, the price or value of the entire firm is equal to the sum

of the values of all projects and investments within it.

To maximize the value of the entire

firm, managers should make decisions that maximize NPV.

The price of risk

To eliminate any arbitrage opportunity, the highest bid-price (biedprijs van makelaar voor

jouw aandeel) should be

The risk premium of a security represents the additional return that investors expect to earn

to compensate them for the security’s risk. Because investors are risk averse, the price of a

risky security cannot be calculated by simply discounting its expected cashflow at the risk-

free interest rate, they want their risk premium. Rather, when a cash flow is risky, to

compute its present value we must discount the cash flow we expect on average at a rate

that equals the risk-free interest rate plus an appropriate risk premium.

lower

.

than the lowest ask price(vraagprijs van de andere makelaar

voor zijn aandeel)

Chapter 4: The time value of money

Veel sommen oefenen bij dit Chapter. Praktisch Chapter.

Always draw a timeline with a stream of cash flows!

4.1 The timeline

Rule 1:

It is only possible

4.2 The three rules of time travel

to compare or combine values at the same point in time

Rule 2:

This can be done with compounding = moving a value or cash flow forward in time.

C x (1+r)n= FV The effect of earning “interest on interest” is known as compound interest

Rule 3:

The process of moving a value or cash flow backward in time is known as discounting.PV = C / (1+r)

nn=number of years.


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General formula for a cash flow stream:

4.3 Valuing a stream of cash flows

Present value of a cash flow stream is the summation of the discounted values: ∑ Cn/(1+r)n

Now that we have established the rules of time travel, and determined how to compute

present and future values, we are ready to address our central goal: calculating the NPV of

future cash flows to evaluate an investment decision.

4.4 Calculating the Net Present Value

NPV = PV (benefits) – PV (Costs)

The NPV of an investment opportunity is also the present value of the stream of cash flows.

Perpetuity = A stream of

4.5 perpetuities, annuities and other special cases

equal cash flows (bv1000,1000,1000) that occur at regular

intervals(elk jaar, 2 maanden, etc) and last forever.

The present value formula for the perpetuity already discounts the cash flows to one

period prior to the first cash flow!!

Voldoet een stroom van cashflows niet aan al deze eisen, dan moet je elke stroom een voor

een disconteren/compounden!

Growing Perpetuity = a stream of cash flows that occur at regular intervals and grow at a

constant rate

--------------------------------

forever. The first payment does not grow!

Annuity = A stream of N equal cash flows paid at regular intervals. The difference between

an annuity and a perpetuity is that an annuity ends after some fixed number of payments.

Voldoet een stroom van cashflows niet aan al deze eisen, dan moet je elke stroom een voor

een disconteren/compounden!


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Formules Present Value Future Value

Perpetuity

Growing Perpetuity

Annuity

Growing Annuity

Sometimes, we know the present value or future value but do not know one of the variables

we have previously been given as an input. In such situations, we use the present and/or

future values as inputs, and solve for the variable we are interested in.

4.7 Solving for variables other than Present Value or Future Value

Internal rate of return (IRR) = the interest rate that sets the net present value of the cash

flows equal to zero.

In a few cases it is possible to solve the IRR directly. One other approach is to use trial and

error to find the IRR or other variables than the IRR.


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Chapter 5: Interest Rates

When evaluating cash flows, however, we must use a discount rate that matches the time

period of our cash flows this discount rate should reflect the actual return we could earn

over that time period.

5.1 Interest Rate Quotes and Adjustments

Effective annual rate: indicates the actual amount of interest that will be earned at the end

of one year.

It is convenient to adjust the discount rate to match the time period of the cash flows

Adjusting the discount rate to different time periods:

In general, we can convert a discount rate of r for one period to an equivalent discount rate

for n periods using the following formula:

Equivalent n-Period Discount Rate = (1 + r)

. This is

necessary to apply the perpetuity or annuity formulas.

n

– 1

N can be larger than 1 (to compute a rate over more than one period) or smaller than 1 (to

compute a rate over a fraction of a period).

Annual percentage rate (APR): the amount of interest earned without the effect ofcompounding.

To compute the actual amount that you will earn in one year, we must first convert the APR

to an EAR. We cannot use the APR itself as a discount rate!

Converting an APR to an EAR: 1 + EAR = (1 + APR/k)k

where k reflects the compounding periods per year.

The EAR increases with the frequency of compounding because the ability to earn interest

on interest (compounding interest) sooner.

Amortizing loans: each month you pay interest on the loans plus some part of the loan

balance.

5.2 Application: Discount Rates and Loans

When the compounding interval for the APR is not stated explicitly, it is equal to the

interval between the payments. Than we do not need to convert the APR to EAR, because

there are no more compounding intervals than payment intervals!


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The outstanding balance on a loan, also called the outstanding principal, is equal to the

present value of the remaining future loan payments, again evaluated using the loan interest

rate.

Interest rates are determined in the market based on individuals’ willingness to borrow and

lend.

Nominal interest rates: the rate at which your money will grow if invested for a certain

period.

Real interest rate r

5.3 The Determinants of Interest Rates

r: The rate of growth of your purchasing power, after adjusting for

inflation.

Growth in purchasing power = 1 + rr = (1+r)/(1+i) = Growth of money/growth of priceswhere r is the nominal interest rate, I is the rate of inflation

Real Interest Rate = rr

The real interest rate should

= (r–i)/(1+i) =ongeveer r-i

not be used as a discount rate for future cash flows. It can only

be used if the cash flows have been adjusted to remove the effect of inflation (in that case,

we say the cash flows are in real terms). This approach is error prone however, so

throughout

Interest rates also effect firm’s incentive to raise capital and invest. Investments are negative

dependent of interest rates: high interest rates -> lower investment, low interest rates ->

higher investment.

The central bank is able to lower interest rates to stimulate investment if the economy is

slowing or in recession.

this book we will always forecast actual cash flows including any growth due to

inflation, and discount using nominal interest rates.

Term structure of interest rates: The relationship between the investment term(termijn) and

the interest rate.

Yield curve: the plot of this relationship (term structure)

A risk-free cashflow received in two years should be discounted at the two-year interestrate, and a cashflow received in ten years should be discounted at the ten-year interest rate.

This is because of the fact that we could also have this return instead of investing in the

investment, so it’s the opportunity cost of capital. This makes it more difficult to use annuity

and perpetuity formula’s because every cashflow in future has its own discount rate.

If interest rates are expected to rise, long-term interest rates will tend to be higher than

short-term rates to attract investors. Also the reversed is possible. The yield curve tends to

be decreasing (inverted) as the economy comes in of a recession and the interest rates are

expected to decrease. The yield curve tends to be steep(increasing) as the economy comesout of a recession and interest rates are expected to rise.


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Risk and interest rates:

when we refer to the “risk-free interest rate”, we mean the rate on U.S. Treasuries. All other

borrowers have some risk of default. To compensate for the risk that they will receive less if

the firm defaults, investors demand a higher interest rate than the rate on U.S. Treasuries.

The right discount rate for a cash flow is the rate of return available in the market on other

investments of comparable risk and return.

After-Tax Interest Rates:

After-tax interest rate: taxes reduce the amount of interest the investor can keep, and we

refer to this reduced amount as the after-tax interest rate.

= r (1 – t) where t=tax rate.

In some cases, the interest on loans is tax deductible. In that case, the cost of paying intereston the loan is offset by the benefit of the tax deduction. The net effect is that when interest

on a loan is tax deductible, the effective after-tax interest rate is r(1-t).

5.4 Risk and Taxes

5.5 The Opportunity Cost of Capital

Opportunity cost of capital (Cost of Capital): the best available expected return offered in

the market on an investment of comparable risk and term to the cash flow being discounted.

We will use the Cost of Capital as discount rate.

Because any fund invested in a new project could be returned to shareholders to invest

elsewhere, the new project should be taken only if it offers a better return than

shareholders’ other opportunities.


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Chapter 6: Investment Decision Rules

Remember NPV Rule: when making an investment decision, take the alternative with the

highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.

6.1 NPV and Stand-Alone Projects

The NPV of the project depends on the appropriate cost of capital. Often, there may be

some uncertainty regarding the project’s cost of capital. In that case, it is helpful to compute

an:

NPV profile: this graphs the project’s NPV over a range of discount rates.

The Internal rate of return (IRR) of an investment is the discount rate that sets the NPV of

the project’s cash flow equal to zero. The IRR of a project provides useful information

regarding the sensitivity of the project’s NPV to errors in the estimate of its cost of capital.

The difference between the cost of capital and the IRR is the maximum estimation error in

the cost of capital that can exist without altering the original decision

With respect to the other investment rules, the NPV is the most secure investment rule.

.

The Internal Rate of Return (IRR) investment rule: Take any investment opportunity where

the IRR exceeds the opportunity cost of capital. Turn down any opportunity whose IRR is less

than the opportunity cost of capital.

6.2 The Internal Rate of Return Rule

Pitfall #1: Delayed investments

The IRR rule is only guaranteed

Even though the IRR rule fails to give the correct answer in this case, the IRR itself still

provides useful information in conjunction with the NPV rule. As mentioned earlier, IRR

indicates how sensitive the investment decision is to uncertainty in the cost of capital

estimate.

to work for a stand-alone project if ALL of the project’s

negative cash flows precede its positive cash flows.

Pitfall #2: Multiple IRRs

When there is more than one IRR, we cannot apply the IRR rule. Our only choice is to rely on

the NPV rule.

Even though the IRR rule fails in this case, the two IRRs are still useful as bounds on the cost

of capital.


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Pitfall #3: Nonexistent IRR

No IRR exists; that is, there is no discount rate that makes the NPV equal to zero. However,

the NPV can be always positive as always negative as well.

The Payback Investment Rule: you should only accept a project if its cash flows pay back its

initial investment within a pre-specified period. You accept the project if the payback period

is less than a pre-specified length of time.

6.3 The Payback Rule

It is useful as a shortcut to get a quick sense of the project before calculating NPV.

It is typically used for small investment decisions.

When the payback period is short, then most projects that satisfy the payback rule will have

a positive NPV.

Payback Rule pitfalls

The payback rule is not as reliable as the NPV rule because it:

(1) ignores the project’s cost of capital and the time value of money,

(2) ignores cash flows after the payback period and

(3) relies on an ad hoc decision criterion (what Is the right number of years to require for the

payback period?).

NPV Rule: Pick the project(s) with the highest NPV.

IRR rule:

6.4 Choose between projects

When we have IRRs which we can use correctly (no pitfalls), we can use them to

choose between projects. The project with the largest IRR is the best project. Picking one

project over another simply because it has a larger IRR can lead to mistakes. When projects

differ in their scale of investment, the timing of their cash flows or their riskiness, then their

IRRs cannot be meaningfully compared!Difference in Scale: Because the IRR is a return, you can’t tell how much value will

actually be created without knowing the scale of the investment.

Differences in Timing: Even when projects have the same scale, the IRR may lead you

to rank them incorrectly due to differences in the timing of the cash flows.

This is because earning a high annual return is much more valuable if you earn it

for several years than if you earn it for only a few days.

Differences in Risk: To know whether the IRR of a project is attractive, we must

compare it to the project’s cost of capital, which is determined by the project risk.

Ranking projects by their IRRs ignores risk differences.


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-> the NPV Rule is the solution

An alternative for comparing projects is to compute the:

The incremental IRR: the IRR of the incremental cash flows that would result from replacing

one project with the other.

The incremental IRR identifies the discount rate at which the optimal decision changes.

However, when using the incremental IRR to choose between projects, we encounter all of

the same problems that arose with the IRR Rule:

-Even if the

The incremental IRR tells us the discount rate at which it become

profitable to switch from one project to the other.

negative cash flows precede the positive ones for the individual projects,

it need not to be true for the incremental cash flows.

-The incremental IRR can indicate whether it is profitable to switch from one project

to another, but it does not indicate whether either project has a positive NPV.

-When the individual projects have different costs of capital, it is not obvious what

cost of capital the incremental IRR should be compared to

. In this case only the NPV

rule will give a reliable answer.

In practice, there are often limitations(budget or other constraints) on the number of

projects the firm can undertake.

The firm must choose the best set of investments it can make given the resources it has

available.

6.5 Project selection with resource constraints

Sometimes it is not efficient to choose the project with the highest NPV, because of its use of

the resources. It can be better to invest in other projects with a higher total NPV.

The Profitability index = an index that identifies the optimal combination of projects

Two conditions must be satisfied:

1. The set of projects taken following the profitability index ranking

to

undertake. “bang for the buck”

= NPV / Resource Consumed

Starting with the project with the highest index, we move down the ranking, taking allprojects until the resource is consumed.

completely exhausts the

available resource.

2. There is only a single relevant resource constraint.

In many cases, the firm may face multiple resource constraints. For instance, there may be a

budget limit as well as a headcount constraint. If more than one resource constraint is

binding, then there is no simple index that can be used to rank projects.


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Chapter 7: Fundamentals of Capital Budgeting (cal. Free Cash Flows)

Capital budget = lists the projects and investments that a company plans to undertake

during the coming year.

Capital budgeting = a process in which firms analyse alternative projects and decide which

ones to accept.

This process begins with forecast of the project’s future consequences for the firm.

7.1 Forecasting Earnings

First-> Incremental earnings forecast

Given the revenue and cost estimates, we can forecast the incremental earnings.

Capital expenditures=> not directly listed as expenses

Depreciation => not actual cash outflows

Interest expense -> we do not include interest expense by forecasting

the incremental earnings. We evaluate the project on its

own, separate from the financing decision.

Marginal corporate tax rate => the tax rate it will pay on an incremental dollar of

pre-tax income.

EBIT x t

Earnings are not actual cash flows. However, to derive the forecasted cash flows of a project,

financial managers often begin by forecasting earnings:

Incremental earnings of a project = the amount by which the firm’s earnings are expected to

change as a result of the investment decision.

c

Even when the EBIT is negative taxes are relevant. They are deductible.

Unlevered net income => because we didn’t include the interest costs.

EBIT x (1-tc)

=(Revenues – Costs – Depreciation) x (1 – tc)

Revenues = sales and other gains, costs = c.o.g.s etc.


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Indirect Effects on Incremental Earnings

Project externalities

Project externalities are indirect effects of the project that may increase or decrease the

profits of other business activities of the firm.Cannibalization = when sales of a new product displace sales of an existing product.

Cannibalization leads to

When computing the incremental earnings of an investment decision, we should include all

changes between the firm’s earnings with the project versus without the project.

Opportunity CostsThe opportunity cost of using a resource is the value it could have provided in its best

alternative use. Because this value is lost when the resource is used by another project, we

should include the opportunity cost as an incremental cost of the project!

A common mistake is to conclude that if an asset is idle, its opportunity cost is zero. We

could sell or rent the asset.

lower sales but also to lower cost of goods sold

Sunk Costs and Incremental Earnings

Sunk Cost = any unrecoverable cost for which the firm is already liable. Sunk costs have been

or will be paid regardless of the decision about the project. Therefore, they should not be

included in the incremental earning analysis.

!

Some sunk costs are;

-Overhead expenses = associated with activities that are not directly attributable to a single

business activity but instead affect many different areas of the corporation (accounting for

example). Only include as incremental expense the additional overhead expenses that arise

because of the decision to take on the project!

-Past research and development expenditures. Money that has already been spent.

For a real project, the estimates are much more complicated.

-> differences in sales, differences in price over time and reduce of profit margins due to

competition.


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7.2 Second -> Determining Free Cash Flow and NPV

Free Cash Flow = The incremental effect of a project on the firm’s available cash.

Calculating Free Cash Flow from Earnings

Earnings include non-cash charges, such as depreciation, but do not include the cost of

capital investment. To determine the free cash flow from the incremental earnings, we must

adjust for these differences.

-We must add back to earnings the depreciation expense

-We must deduct the actual capital expenditures

-We must deduct increases in Net Working Capital

Net Working Capital = Current Assets – Current Liabilities

= Cash + Inventory + Receivables – Payables

trade credit= The difference between receivables and payables

Free Cash Flow = (Revenues – Cost – Depreciation) x (1 – tc)

+ Depreciation +CapEx - ΔNWC

Free Cash Flow = (Revenues – Cost) x (1 – t c) – CapEx – ΔNWC + tc x Depreciation

Depreciation tax shield = tc

Third -> calculating the NPV

To calculate the NPV, we must discount its free cash flow at the appropriate cost of capital

(return of best alternative investment).

x Depreciation. It is the tax savings that results from the ability

to deduct depreciation.

Firms often report a different depreciation expense for accounting and for tax purposes.

Because only the tax consequences of depreciation are relevant for free cash flow, we

should use the depreciation expense that the firm will use for tax purposes in our forecast.


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7.3 Choosing among alternatives

Choose alternative with the highest NPV.

When comparing alternatives, we need to compare only those cash flows that differ

between them. We can ignore any cash flows that are the same under either scenario.

Houd rekening met dat uitbestede kosten ook belasting aftrekbaar zijn!

7.4 Further adjustments to Free Cash Flow

-Other non-cash items (like patents, brandnames) that appear as part of incremental

earnings should not be included in the project’s free cash flow.

-Because depreciation contributes positively to the firm’s cash flow through the depreciation

tax shield, it is in the firm’s best interest to use the most accelerated method of

depreciation that is allowable for tax purposes (this increases their present value)

-liquidation value = in calculation of free cash flow, we include the liquidation value of any

assets that may be disposed of (sometimes negative value due to remove costs).

Gain on Sale = Sale Price – Book Value

After-Tax Cash Flow from Asset Sale = Sale Price - (tc

-Sometimes the firm explicitly forecasts free cash flow over a shorter horizon than the fullhorizon of the project or investment. This is necessarily true for investments with an

indefinite life. We estimate the value of the remaining free cash flow beyond the forecast

horizon called the-

terminal or continuation value = represents the market value of the free cash flow from the

project at all future dates.

x Gain on Sale)

when an asset is fully depreciated when it’s sold, the entire Sale Price is taxable.

-Tax loss carryforwards and carrybacks = allow corporations to take losses during a current

year and offset them against gains in nearby years. Carry back -> 2 years. Carry forward -> 20

years.

7.5 Analyzing the project

Estimates of the cash flows and cost of capital are subject to significant uncertainty.

Break-even= the level for which the investment has an NPV of zero. (For example – IRR).

Break-even analysis = we calculate for each parameter the value at which the NPV of the

project is zero.

EBIT break-even = the level of sales for which the project’s EBIT is zero.


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Sensitivity analysis = breaks the NPV

calculation into its component

assumptions and shows how the NPV

varies as the underlying assumptions

change. It shows us the effects oferrors in our NPV estimates for the

project. Such an analysis also reveals

which aspects of the project are most

critical.

Scenario analysis= Considers the effect on the NPV of changing multiple project parameters

Chapter 8: Valuing Bonds

The prices of risk-free government bonds can be used to determine the risk-free interest

rates that produce the yield curve.

Also firms often issue bonds to fund their own investments, and the returns investors

receive on those bonds is one factor determining a firm’s cost of capital.

8.1 Bond Cash flows, Prices and Yields

Bond certificate = indicates the amounts and dates of all payments to be made.

Maturity date = the final repayment date.

Term = the time remaining until the repayment date

Coupons = the promised interest payments of the bond

Face value = the notional amount we use to compute the interest payments. Usually, theface value is repaid at maturity.

Coupon rate = is expressed as an APR, so the amount of each coupon payment (CPN) is ->

Coupon Payment (CPN) = (Coupon Rate x Face Value) / (Number of Coupon

Payments per Year)

Zero-coupon bond = a bond that does not make coupon payments. The only cash payment

the investor receives is the face value of the bond on the maturity date.

Prior to its maturity date, the price of a zero-coupon bond is less than its face value!

Treasury bills = U.S. bonds, with maturity up to one year, are zero coupon bonds.

Zero-coupon bonds trade at a discount (lower price than face value), so they are also calledpure discount bonds.


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Yield to maturity (YTM) or just Yield = The IRR of an investment in a bond. The yield to

maturity of a bond is the discount rate that sets the present value of the promised bond

payments equal to the current market price of the bond. (Remember: a security has NPV =

0!!). The IRR of an investment(YTM) in a zero-coupon bond is the rate of return that

investors will earn on their money if they buy the bond at its current price and hold it tomaturity!!

By the Law of One Price -> the YTM is the risk-free interest rate. In a competitive market all

risk-free security will have the same return(YTM), otherwise there is an arbitrage

opportunity. Rf n = YTMn

Zero-coupon bond -> P = FV/(1+YTM

Spot interest rates = default-free, zero-coupon yield

n)n n = periods, FV = face value

YTMn = (FV/P)1/n

-1 n=Periods, FV = face value

A negative YTM on a Treasury bill implies that investors have an arbitrage opportunity -> sell

the bill and holding the proceeds in cash.

We used FV as Future value before, but the Face Value is the Future Value of a zero-c-bond.

Yield curve = plots the risk-free interest rate for different maturities(eindjaren). Wd also

refer to it as the zero-coupon yield curve.

Coupon bonds = pay investors their face value at maturity, but in addition, these bondsmake regular coupon interest payments!

Treasury notes = original maturities from one to 10 years

Treasury bonds = which have original maturities of more than 10 years.

Because the coupon payments represent an annuity, the YTM is the interest rate y from ->

Yield to Maturity Or the Price of a Coupon Bond -> Solving Equation

We need to use either trial-and-error or annuity spreadsheet for solving y.

We need the coupon rate only for calculating the CPN.

When we calculate a bond’s yield to maturity, the yield we compute will be a rate per

coupon interval. This yield is typically stated as an annual rate by multiplying it by the

number of coupons per year. -> y x (n coupons per year) = YTM

Bond traders generally quote bond yields rather than bond prices, because it is independent

of the Face Value of the bond.


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8.2 Dynamic Behavior of Bond Prices

Zero coupon bonds -> trade at a discount

Coupon bonds -> trade at discount, or at premium (higher price than Face value) or at par

(price equal to face value)

Bond price is Greater than FV Equal to FV Less than FV

Then the bond

trades -

‘at a premium’ or

‘above par’

‘at par’ ‘at a discount’ or

‘below par’

This occurs when - Coupon rate > YTM Coupon Rate = YTM Coupon Rate < YTM

The market price of a bond changes over time for two reasons ->

1. The bond gets closer to its maturity date

2. Changes in market interest rates affect the bond’s yield to maturity and its price

(PV of the remaining cash flows).

General property for bonds = If a bond’s yield to maturity has not changed, then the IRR of

an investment in the bond equals its yield to maturity even if you sell the bond early!

Yield to maturity -> return (the IRR) for whole term.

IRR -> return for a part of the term.

Coupon bonds -> a bit more complicated, because as time passes most of the cash

flows get closer but some of the cash flows disappear (CPNs)

Between to CPNs -> the prices of al coupon

bonds rise (but still equal to the YTM).

Coupon is paid -> the price drops by the

amount of the coupon.

Note -> the higher the coupon rate and

especially for bonds that are trading at

premium -> the higher the pricedifferences.

Bonds at premium -> price drops

exceeds the price increase, so the price will fall if maturity

comes closer.

Bonds at discount -> price increases exceeds the price drops, so the price will rise if

maturity comes closer

Zero coupon bonds -> no price jumps.


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If interest rates in the economy fluctuate, the yields that investors demand to invest in

bonds will also change.

Higher YTM -> As interest rates and bond yields rise, bond prices will fall, and vice versa.

Shorter-maturity zero-coupon bonds are less sensitive to changes in interest rates than are

longer-term zero-coupon bonds.Bond with higher coupon rates, because they pay higher cash flows upfront, are less

sensitive to interest rate changes than otherwise identical bonds with lower coupon rates.

Duration = The sensitivity of a bond’s price to changes in interest rates is measured by the

bond’s duration. Bonds with high durations are highly sensitive to interest changes.

Note that the bond price tends to converge to the face value as the bond approaches to

maturity date, but also moves higher when its yield falls and lower when its yield rises.

Bonds are risky too because of the risk of changing interest rates!! -> Changes IRR if the

bond is sold earlier.

8.3 The Yield curve and Bond Arbitrage

Because it is possible to replicate the cash flows of a coupon bond using zero-coupon bonds

(due to the Law of One Price), we can use the Law of One Price to compute the price of a

coupon bond from the prices of zero-coupon bonds.

The Law of One Price states that the price of the portfolio of zero-coupon bonds(with face

values equal to the CPNs and FV of the coupon bond) must be the same as the price of the

coupon bond

If there is a difference between the price of a portfolio of zero-coupon bonds and the price

of the coupon bond, there would be an arbitrage opportunity!

Instead of using the prices of the zero-coupon bonds to derive the price of the coupon bond,

we can use the zero-coupon bond yields too!

The yield of a zero-coupon bond is the competitive market interest rate for a risk-free

investment for a term equal to the term of the zero-coupon bond.

-> Therefore, the price of a coupon bond must equal the present value of its CPNs

and face value discounted at the competitive market interest rates.

The information in the zero-coupon yield curve is sufficient to price all other risk-free bonds.

2

1 2

(Bond Cash Flows)

V 1 (1 ) (1 )

=

+= + + +

+ + +

n

n

PV PV

CPN CPN CPN F

YTM YTM YTM

2 3

100 100 100 1000 $1153

1.035 1.04 1.045

+= + + =P


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Above we have used the YTM of zero-coupon bonds for determining the Price of a Coupon

Bond. But earlier we have seen another method calculating the YTM of Coupon Bonds.

Like ->

This is a weighted average of the yields of the zero-coupon bonds of equal and shorter

maturities (because according the Law of One Price it can’t be different from the zero-

coupon YTM).

It is possible that (zero-coupon)bonds have different yields while they have same maturity

depending on their coupon rates!!

This depends on the yield curve! When the yield curve rises, the YTM of bonds with

late cashflows (zero-coupon bonds, all value at the end) are higher than bonds withhigh coupon rates (CPN’s earlier in time when the YTM’s are respectively lower).

The reverse is also possible, and when the yield curve is flat (no differences in time),

all the average YTM’s are the same regardless their CPNs.

Below -> yield curve with rising YTM’s in time.

Coupon-paying yield curve = The plot of the yields of coupon bonds of different maturities.

As we saw, two coupon-paying bonds with the same maturity may have different yields By

convention, practioners always plot the yield of the most recently issued bonds, termed the

on-the-run bonds.

By the Law of One Price, it is also possible to determine the zero-coupon bond yields using

the coupon-paying yield curve. Either type of yield curve provides enough information to

value all other risk-free bonds.

8.4 Corporate Bonds

Corporate bonds = bonds issued by corporations. The issuer may default (not pay back the

full amount).Credit risk = the risk of default.

2 3100 100 100 1000 $1153

1.0444 1.0444 1.0444+= + + =P


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The cash flows that a purchaser of a bond with credit risk expects to receive may be less

than that amount. As a result, investors pay less for bonds with credit risk than they would

for an otherwise identical default-free (US) bond.

Because the yield to maturity for a bond is calculated using the promised cash flows, the

YTM with credit risk will be higher than that of otherwise identical default-free bonds.

Note that the yield to maturity of a defaultable bond is not equal to the expected return of

investing in the bond!

Investors will demand a risk premium to invest in risky bonds.

Note that bond’s price decreases and its yield to maturity increases, with a greater likelihood

of default. Controversely, the bond’s expected return, which is equal to the firm’s debt cost

of capital, is less than the yield to maturity if there is a risk of default. Moreover, a higher

yield to maturity does not necessarily imply that a bond’s expected return is higher!

Several companies rate the creditworthiness of bonds and make this information available toinvestors (AAA, AA, A, BBB, BB, B, CCC, CC, C)

Investment-grade bonds = Bonds in the top four categories. They have low default risk.

Speculative bonds, junk bonds or high-yield bonds = Bonds in the bottom five categories

because of their likelihood of default is high.

Corporate Yield Curves

Default spread or credit spread = thedifference between the yields of

corporate bonds and the Treasury

yields.


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Chapter 9: Valuing Stocks – only theorie – Pricing of stocks

9.1 The Dividend-Discount Model

The Law of One Price implies that to value any security, we must determine the expected

cash flows an investor will receive from owning it.

If investors have the same beliefs, their valuation of the stock will not depend on their

investment horizon.

Two sources of cash flows: Dividend payments and selling shares.

The future dividends and price are not known at t=0, but the investor has someexpectations about them.

According to The Law of One Price => Given these expectations, the investor will be willing

to pay a price today up to the point that these transactions have minimal NPV=0 (NPV>0 =

arbitrage opportunity). In a competitive market buying or selling a share of stock must be a

zero-NPV investment opportunity.

Stocks are risky -> not possible to use the Risk-free interest rate -> We discount them based

on The equity cost of capital rE = the expected return of other investments available in the

market with equivalent risk

If the Price is lower than P

.

0, than the NPV > 0 -> buy the stock (Price will rise till NPV = 0)

Price more than P0

, than the NPV < 0 -> sell the stock (Price will drop till NPV = 0)

The expected total return of the stock should equal the expected return of other

investments available in the market with equivalent risk.

9.2 Applying the Dividend-Discount Model

Money Spent on investment cannot be used to pay dividends

Firms can increase its dividend in three ways ->

1. Increase it earnings 2. Increase dividend payout rate

3. Decrease shares outstanding

Dividend-Discount Model can only deal with options 1 and 2.

Cutting the firm’s dividend to increase investment will raise the stock price if, and only if, the

new investments have positive NPV.


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Limitations dividend-Discount model ->

-Uncertainty associated with forecasting a firm’s dividend growth rate and future dividends.

-Small changes in the assumed dividend growth rate can lead to large changes in the

estimated stock price.

9.3 Total Payout and Free Cash Flow Valuation Models

Total Payout Model

In our discussion of the dividend-discount model, we implicitly assumed that any cash paid

out by the firm to shareholders takes the form of a dividend.

Using the Total Payout Model, we can work with share repurchases!

The total payout model = values all of the firm’s equity, rather than a single share.

We can apply the same simplifications that we obtained by assuming constant growth in the

dividend-discount model. The only change is that we discount total dividends and share

repurchases and use the growth rate of earnings (rather than earnings per share) when

forecasting the growth of the firm’s total payouts.

This method can be more reliable and easier to apply when the firm uses share

repurchases.

The Discounted Free Cash Flow Model

Enterprise Value = Market Value of Equity - Debt + CashThe Discounted Free Cash Flow Model determines the value of the firm to all investors

(both equity and debt holders)

Advantage -> we can value the firm without forecasting dividends, share repurchases

or use of debt!!

Dividend Discount model -> firms cash and debt are indirectly included through the effect of

interest income and expenses on earnings.

Discounted Free Cash Flow -> ignore interest and expenses (FCFs are based on Unlevered

Net Income), but then adjust for cash and debt directly.

Big difference!! Since we are discounting cash flows to both equity holders and debt

holders, the free cash flows should be discounted at the firm’s weighted average cost of

capital rwacc!! Firm no debt -> rwacc = r

Enterprise value and Free Cash Flows (capital budgeting)

-The firm’s free cash flow is equal to the sum of the free cash flows from the firm’s current

and future investments.

-The NPV of any individual project represents its contribution to the firm’s enterprise value.

E


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Present Value of……. Determines the…….

Dividend Payments Stock Price

Total Payouts (dividends and repurchases.) Equity Value

Free Cash Flow (cash available to pay all

security holders)

Enterprise Value

9.4 Valuation Based on Comparable Firms

Estimate the value of the firm based on the value of other comparable firms or investments

that we expect will generate very similar cash flows in the future.

Identical companies do not exist!

This is possible because according to the Law of One Price securities with the same amountof risk must have the same value, cause otherwise there is an arbitrage possibility.

1. P/E ratio

2. Enterprise Value Multiples -> is advantageous if we want to compare firms with different

amounts of leverage.

Limitations of multiples ->

1. No clear guidance about how to adjust for differences in expected future growth rates,

risk, or differences in accounting policies.

2. Comparables only provide information regarding the value of a firm relative to other firms

in the comparison set.

3. Using multiples will not help us determine if an entire industry is overvalued.

Advantages Multiples ->

1. Simplicity 2. Based on actual prices of real firms

Advantages Discounted CF’s (Dividend-Discount Model, Discounted Free Cashflow Model,

Total Payout Model) ->

More accurate & insightful because the true driver of values for firms is the ability to

generate CF’s for investors.

No single technique provides a final answer regarding a stock’s true value. All approaches

require assumptions or forecasts that are too uncertain to provide a definitive assessment of

the firm’s value. Real-world practioners use combinations of approaches regarding stock

pricing.


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9.5 information, competition and stock prices

Given accurate information about any two of these variables, a valuation model allows us to

make inferences about the third variable.

For a publicly traded firm, its current stock

price should already provide very accurate

information, aggregated from a multitude of

investors, regarding the true value of its

shares.

Only in the relatively rare case in which we have some superior information that other

investors lack regarding the firm’s cash flows and cost of capital would it make sense to

second-guess the stock prices (and get possibly an arbitrage opportunity NPV > 0).

Efficient Markets Hypothesis = securities will be fairly priced, based on their future cashflows, given all information that is available to investors.

The degree of competition, and therefore the accuracy of the efficient markets hypothesis,

will depend on the number of investors who possess(bezitten) this information.

Public, Easily Interpretable information -> All investors can determine the effect of this

information on the firm’s value -> the accuracy of the Efficient Market Hypothesis is narrow.

-> stock prices react nearly instantaneously to such news. (Only NPV > 0 for fast boys)

Private or Difficult-to-Interpret information -> Private information will be held by a

relatively small number of investors. These investors may be able to profit by trading on

their information (NPV > 0, arbitrage opportunities for specialist who’ll have information

first) ->Efficient markets hypothesis will not hold in strict sense.

In the long run, we should expect that the degree of “inefficiency” in the market will be

limited by the costs of obtaining the private information.

Though there are hardly any arbitrage opportunities, investing in stocks is attractive due to

the future cash flows (cost of capital).

Corporate managers should ->1. Focus on positive NPVs and free cash flow -> increases stock prices.

2. Avoid accounting illusions

3. Use financial transactions to support investment -> with efficient markets the firm can sell

its shares at a fair price to new investors. Thus, the firm should not be constrained from

raising capital to fund positive NPV investments opportunities.

The efficient markets hypothesis states ->

Securities with equivalent risk should have the same expected return

An arbitrage opportunity is a situation in which two securities with identical cash flowshave different prices


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Chapter 10: Capital Markets and the Pricing of Risk – Cost of Capital

10.1 A first Look at Risk and Return

While small stock portfolio performed the best in the long run, its value also experienced the

largest fluctuations.

10.2 Common Measures of Risk and Return

When an investment is risky, there are different returns it may earn.

Each possible return has some likelihood of occurring.

This information is summarized with a probability distribution.

-> expectations!

Expected return = E[R] = PR x R (probability x return)

Variance Var (R) = PR x (R – E[R])2

Standard Deviation = Volatility = measures of the risk

If we don’t know the explicit probability distribution, we can estimate and compare risk and

return from historical data, which is a sensible strategy if we are in a stable environment and

believe that the distribution of future returns should mirror that of past returns.

10.3 Historical Returns of Stocks and Bonds

Realized Return R = Dividend Yield + Capital Gain Rate =rE

To focus on the returns of a single security, let’s assume that you reinvest all dividends

immediately and use them to purchase additional shares of the same stock or security. In

this case, we can use the next formula to compute the stock’s return between dividend

payments, and then compound the returns from each dividend interval to compute the

return over a longer horizon ->

Historical Return Rannual = (1 + RQ1)(1 + RQ2)(1 + RQ3)(1 + RQ4)

Where Q’s are quartiles.

Empirical Distribution -> probability distribution using historical data

Avarage Annual Returns Rbar = 1 / T (R1 + R2 + R……)

Var (R) = (1 / (T – 1 )) ∑ (Rt – Rbar)2

Standard Deviation = Volatility = Square root (variance)

We can use a security’s historical average return to estimate its actual expected returnTwo difficulties with determining future expected returns with historical returns ->


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1. We do not know what investors expected in the past (optimistic, pessimistic?)

2. The average return is just an estimate of the true expected return and is subject

to estimation error.

Standard Error = a statistical measure of the degree of estimation error

Standard Deviation / � − −

Because the average return will be within two standard errors of the true expected return

approximately 95% of the time, we can use the standard error to determine a reasonable

range for the true expected value.

95% Confidence Interval= Historical Average Return +/- (2x Standard Error)

10.4 The Historical Trade-Off between Risk and Return

Excess Returns = the difference between the average return for an investment and the

average return for T-Bills -> measures the risk premium -> Average Return – r f

Positief lineair verband bij

portfolio’s tussen AverageReturn en Volatiliteit.

-Maar niet bij losse

aandelen

-Larger stocks tend to have

lower volatility than smaller

stocks

-All stocks tend to have

higher risk and lower

returns than largeportfolio’s.

Higher risk requires higher returns!

10.5 Common Versus Independent Risk


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Common Risk = Risk that is perfectly correlated. Risk that affects all securities.

Independent Risk = Risk that is uncorrelated. Risk that affects a particular security.

Diversification = the averaging out of the independent risk in a large portfolio.

When risks are independent and identical, the standard deviation of the average is

known as the standard error -> SD (individual risk) = SD/� Diversification reduces risk.

10.6 Diversification in Stock Portfolios

Firm Specific news = good or bad news about an individual company

Market-Wide news = News that affects all stocks (about the economy).

Independent Risks -> Due to firm-specific news.Other names -> Idiosyncratic Risk, unique risk, unsystematic risk, diversifiable risk.

Common Risks -> Due to market-wide news

Other names -> Systematic Risk, Undiversifiable Risk, Market Risk.

When many stocks are combined in large portfolio’s, the firm specific risks for each stock

will average out and be diversified.

The systematic risk, however, will affect all firms and cannot be diversified.

Actual firms are affected by both market-wide risks and firm-specific risks.

When firms carry both types of risk, only the unsystematic risk will be diversified in a largeportfolio.

The Volatility will therefore decline until only the systematic risk remains

The Risk premium for diversifiable risk is zero, so investors are NOT compensated for holding

firm-specific risk. Otherwise they get return for risk without taking the risk.

Because investors can eliminate firm-specific risk “for free” by diversifying their portfolios,

they will not require or earn a reward or risk premium for holding it.

The risk premium of a security is determined by its systematic risk (not depend on

diversifiable risk) -> otherwise there’s an arbitrage opportunity.

Stock’s volatility = a measure of total risk (systematic + diversifiable risk)

it’s not useful in determining the risk premium on individual stocks. There’s no clear

relationship between volatility and average returns for individual securities

-> Volatility might be a reasonable measure of risk for well-diversified portfolio’s

10.7 Measuring systematic Risk


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Efficient Portfolio = contains only systematic risk (no way to reduce volatility without

lowering its expected return).

Market Portfolio = an Efficient portfolio that contains all shares and securities in the market.

Beta = Sensitivity to systematic Risk -> The expected percent change in the excess return of

a security for a 1% change in the excess return of the market portfolio. = Δstock/Δmarket

When the stock return moves independently of the market -> Beta = 0 (no syst. Risk)

Beta differs from volatility

Volatility measures total risk - Beta is a measure of only systematic risk

Stocks in cyclical industries are likely to be more sensitive to systematic risk and have higher

betas than stocks in less sensitive industries. Drug and food companies are very insentitive.

10.8 Beta and the Cost of Capital

We have emphasized that financial managers should evaluate an investment opportunity

based on its cost of capital, which is the expected return available on alternative

investments in the market with comparable risk and term. For risky investments, this cost of

capital corresponds to the risk-free interest rate plus an appropriate risk premium.

Market Risk Premium = E[Rmkt] – rf

Reward investors expect to earn for holding portfolio with beta 1.

Negative Beta -> negative risk premium -> note that stock with a negative beta will tend to

do well when times are bad, so owning it will provide insurance against the systematic risk ofother stocks in the portfolio.

Security’s Cost of Capital = E [R] = rf + B x (E[Rmkt] - rf

= Capital Asset Pricing Model (CAPM).

= One of most important method for estimating cost of capital

We need (market) portfolio’s for determining the risk premium of individual

stocks! With that Risk Premium we can determine the Cost of Capital.

Chapter 11: Optimal Portfolio Choice and the Capital Asset Pricing

Model – Cost of Capital


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Financial managers are also investors, investing money on behalf of their shareholders.

When a company makes a new investment, financial managers must ensure that the

investment has a positive NPV. Doing so requires knowing the cost of capital of the

investment opportunity and, as we shall see in the next chapter, the CAPM is the mainmethod used by most major corporations to calculate the cost of capital!

11.1 The Expected Return of a Portfolio

To find an optimal portfolio, we need a method to define a portfolio and analyse its return.

Portfolio weights x i = Value of investment i (n.o.sh. x P)/ Total value of portfolio

(Historical) Return of a portfolio Rp= ∑x iR i

R i = historical Returns individual investments

Expected return of a portfolio E[Rp] = ∑x iE[R i

11.2 The Volatility of a Two-Stock Portfolio

]

In this section, we describe the statistical tools that we can use to quantify the risk stocks

have in common and determine the volatility of a portfolio.

Covariance(R

-By combining stocks into a portfolio, we reduce risk through diversification. Because theprices of the stocks do not move identically, some of the risk is averaged out in a portfolio. -

As a result, both portfolios have lower risk than the individual stocks.

-The amount of risk that is eliminated in a portfolio depends on the degree to which the

stocks face common risks and their prices move together.

To find the risk of a portfolio, we need to know the degree to which the stocks face common

risks and their returns move together. -> covariance and correlation allow us to measure the

co-movements of returns.

i, R j) =

Covariance(Ri, R j) from Historical Data =

Covariance > 0 = Stocks both above or below their averages

Covariance < 0 = Stocks move in the opposite direction (one above average, one below)

The magnitude of the Covariance is difficult to interpret -> therefore we have the correlation


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Correlation Coëfficient =

The correlation is a barometer of the degree to which the returns share common risk

and tend to move together.

When the correlation (and

thus the covariance) equals

0, the returns are

uncorrelated, they have no

tendency to move either

together or in opposition of

one another. Independent

risks are uncorrelated (corr/cov = 0).

Stock returns will tend to move together if they are affected similarly by economic events.Thus, stocks in the same industry tend to have more highly correlated returns than stocks in

different industries.

Computing a portfolio’s variance and volatility

For a two-stock portfolio ->

Thus ->

Note that -> Cov (R1, R2) = Corr (R1, R2) x SD(R1) x SD(R2

)

This shows that with a positive amount invested in each

stock, the more the stocks move together and the higher their covariance or correlation, the

more variable the portfolio will be. The portfolio will have the greatest variance if the stocks

have a perfect positive correlation of +1!

11.3 The Volatility of a Large Portfolio

For a large portfolio ->

This expression reveals that

the risk of a portfolio depends on how each stock’s return moves in relation to it.

More general ->


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This formula says that the variance of a portfolio is equal to the sum of the covariances of

the returns of all pairs of stocks in the portfolio multiplied by each of their portfolio weights.

For an equally weighted portfolio ->

This equation demonstrates that as the number of stocks, n, grows large, the variance of the

portfolio is determined primarily by the average covariance among the stocks.

Almost all of the benefit

of diversification can be

achieved with about 30stocks. Even for very

large portfolio, we

cannot eliminate all of

risk.

The variance of the portfolio is at least (maximum diversification)

� ( )

In general, the effect of diversification ->

Each security contributes to the

volatility of the portfolio

according to its volatility, or

total risk, scaled by its

correlation with the portfolio,

which adjust for the fraction of

the total risk that is common to

the portfolio. Therefore, when combining stocks into a portfolio that puts positive weights

on each stock, unless all of the stocks have a perfect positive correlation of +1 with the

portfolio, the risk of the portfolio will be lower than the weighted average volatility of the

individual stocks ->


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The Expected Return of the portfolio is equal to the weighted average expected return, but

the volatility of a portfol

Summary Corporate Finance Berk Demarzo

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