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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)
1.2 Ownership versus control of corporations
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.
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 shareholders
when 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 of
directors 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 control
of the firm passes to the debt holders, it is in the debt holders’ interest to run the firm in the
most profitable way possible.
1.3 the stock market
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 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 at
Ask 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.
2.1 Firms’ disclosure of financial information
Publicly listed companies around the world are required to file their financial statements
with 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.
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.
2.2 The Balance Sheet
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 acquisition cost less accumulated
depreciation.
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 is recorded separately as
Goodwill.
Amortization (or impairment charge): If the firm assesses that the value of these intangible
assets 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 of the acquired
assets. Like depreciation, amortization is not an actual cash outflow.
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).
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.
2.3 Balance sheet analysis
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.
Market-to-book ratio (also called the price-to-book or P/B ratio), which is the ratio of a
firm’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.
Market-to-Book
Book-to-market
Low
Value stocks
Growth stocks(market hoog)
High
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 debt-equity ratio has important conseqences for the risk and return of its
shares.(h12)
Enterprise value = Market value of equity(=market capitalization) + debt - cash
The enterprise value can be interpreted as the cost to take over the business.
Current ratio = current assets / current liabilities
Quick ratio = (Current assets – 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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2.4 the income statement
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.
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.
2.5 Income statement analysis
Gross margin = Gross Profit / Sales
A firm’s gross margin reflects its 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 undervalued based on the idea that the value of a share should be proportional to the level of
earnings it can generate for its shareholders. 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.
Retained Earnings = Net income – Dividends (staat niet in de Cashflow)
2.6 The statement of cash flows (Most important for investors.)
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, 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, shows the flow of cash between
the firm and its investors.
Operating activity
1. Depreciation is not an actual cash
outflow. Thus, we 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.
2.7 other financial statement information
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.
Chapter 3: Arbitrage and financial decision making
Theoretisch Chapter.
3.1 Valuing decisions
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.
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, the
decision will increase the market value of the firm.
3.2 interest rates and the time value of money
We call the difference in value between money today and money in the future the time
value of money.
r f = Risk-free interest rate
the risk-free interest rate depends on supply and demand.
Present value(PV) = the value in terms of dollars today
Future 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 riskfree investment.
3.3 Present value and the NPV decision rule
Net Present Value = PV (Benefits) – PV (costs)
The NPV is the total of the present values of all project cash flows. 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.
Accept all NPV with value 0 or higher when you’re able to.
Regardless of our preferences for cash today versus cash in the future, we should 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.
3.4 Arbitrage and the Law of One Price
The practice of 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 important
property 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.
3.5 No-arbitrage and Security Prices
(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 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.
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)
Note that the 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
=r f
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 negative
NPV 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 cash
flows 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
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 riskfree 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.
To eliminate any arbitrage opportunity, the highest bid-price (biedprijs van makelaar voor
jouw aandeel) should be 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.
4.1 The timeline
Always draw a timeline with a stream of cash flows!
4.2 The three rules of time travel
Rule 1:
It is only possible 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)n n=number of years.
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4.3 Valuing a stream of cash flows
General formula for a cash flow stream:
Present value of a cash flow stream is the summation of the discounted values:
∑ C n /(1+r)n
4.4 Calculating the Net Present Value
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.
NPV = PV (benefits) – PV (Costs)
The NPV of an investment opportunity is also the present value of the stream of cash flows.
4.5 perpetuities, annuities and other special cases
Perpetuity = A stream of equal cash flows (bv1000,1000,1000) that occur at regular
intervals(elk jaar, 2 maanden, etc) and last forever.
Voldoet een stroom van cashflows niet aan al deze eisen, dan moet je elke stroom een voor
een disconteren/compounden!
The present value formula for the perpetuity already discounts the cash flows to one
period prior to the first cash flow!!
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
4.7 Solving for variables other than Present Value or Future Value
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.
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
5.1 Interest Rate Quotes and Adjustments
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.
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. This is
necessary to apply the perpetuity or annuity formulas.
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)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 of
compounding.
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.
5.2 Application: Discount Rates and Loans
Amortizing loans: each month you pay interest on the loans plus some part of the loan
balance.
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.
5.3 The Determinants of Interest Rates
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 r : The rate of growth of your purchasing power, after adjusting for
inflation.
= Growth of money/growth of prices
Growth in purchasing power = 1 + r r = (1+r)/(1+i)
where r is the nominal interest rate, I is the rate of inflation
Real Interest Rate =
r r = (r–i)/(1+i) =ongeveer r-i
The real interest rate should 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 this book we will always forecast actual cash flows including any growth due to
inflation, and discount using nominal interest rates.
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.
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 interest
rate, 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 comes
out of a recession and interest rates are expected to rise.
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5.4 Risk and Taxes
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.
where t=tax rate.
= r (1 – t)
In some cases, the interest on loans is tax deductible. In that case, the cost of paying interest
on 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).
5.5 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
6.1 NPV and Stand-Alone Projects
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.
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.
6.2 The Internal Rate of Return 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.
Pitfall #1: Delayed investments
The IRR rule is only guaranteed to work for a stand-alone project if ALL of the project’s
negative cash flows precede its positive cash flows.
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.
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.
6.3 The Payback Rule
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.
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?).
6.4 Choose between projects
NPV Rule: Pick the project(s) with the highest NPV.
IRR rule: 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 tells us the discount rate at which it become
profitable to switch from one project to 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 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.
6.5 Project selection with resource constraints
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.
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 to
undertake. “bang for the buck”
= NPV / Resource Consumed
Starting with the project with the highest index, we move down the ranking, taking all
projects until the resource is consumed.
Two conditions must be satisfied:
1. The set of projects taken following the profitability index ranking 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)
7.1 Forecasting Earnings
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.
First-> Incremental earnings forecast
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.
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 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-t c )
=(Revenues – Costs – Depreciation) x (1 – t c )
Revenues = sales and other gains, costs = c.o.g.s etc.
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Indirect Effects on Incremental Earnings
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 Costs
The 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.
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 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 – t c )
+ Depreciation +CapEx - ΔNWC
Free Cash Flow = (Revenues – Cost) x (1 – t c ) – CapEx – ΔNWC + t c x Depreciation
Depreciation tax shield = t c 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.
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).
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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 - (t c x Gain on Sale)
when an asset is fully depreciated when it’s sold, the entire Sale Price is taxable.
-Sometimes the firm explicitly forecasts free cash flow over a shorter horizon than the full
horizon 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 theterminal or continuation value = represents the market value of the free cash flow from the
project at all future dates.
-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 of
errors 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, the
face 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 called
pure 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 to
maturity!!
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. R f n = YTM n
Spot interest rates = default-free, zero-coupon yield
P = FV/(1+YTM n )n
n = periods, FV = face value
1/n
YTM n = (FV/P) -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.
Zero-coupon bond ->
Coupon bonds = pay investors their face value at maturity, but in addition, these bonds
make 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
Then the bond
trades This occurs when -
Greater than FV
‘at a premium’ or
‘above par’
Coupon rate > YTM
Equal to FV
‘at par’
Coupon Rate = YTM
Less than FV
‘at a discount’ or
‘below par’
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 price
differences.
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.
PV = PV (Bond Cash Flows)
CPN
CPN
CPN + FV
=
+
+  +
2
1 + YTM 1
(1 + YTM 2 )
(1 + YTM n ) n
P =
100
100
100 + 1000
+
+
=
2
1.035
1.04
1.0453
$1153
The information in the zero-coupon yield curve is sufficient to price all other risk-free bonds.
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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 ->
100
100
100 + 1000
P =
+
+
= 1153
$
2
1.0444
1.0444
1.04443
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 zerocoupon 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 with
high 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.
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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 to
investors (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 = the
difference 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 some
expectations 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 r E = 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 P 0 , 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 + Cash
The 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 r wacc !!
Firm no debt -> r wacc = r E
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.
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Present Value of…….
Dividend Payments
Total Payouts (dividends and repurchases.)
Free Cash Flow (cash available to pay all
security holders)
Determines the…….
Stock Price
Equity Value
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 amount
of 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 cash
flows, 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 flows
have 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] = P R x R
(probability x return)
2
Variance Var (R) = P R x (R – E[R])
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 =r E
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 R annual = (1 + R Q1 )(1 + R Q2 )(1 + R Q3 )(1 + R Q4 )
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 )) ∑ (R t – Rbar)2
Standard Deviation = Volatility = Square root (variance)
We can use a security’s historical average return to estimate its actual expected return
Two 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 / �𝑁𝑢𝑚𝑏𝑒𝑟 − 𝑜𝑓 − 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠
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 Average
Return 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 large
portfolio’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/�𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠
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 large
portfolio.
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[R mkt ] – r f
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 of
other stocks in the portfolio.
= r f + B x (E[R mkt ] - r f
Security’s Cost of Capital
= E [R]
= 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 main
method 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 R p = ∑x i R i
R i = historical Returns individual investments
Expected return of a portfolio E[R p ] = ∑x i E[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.
-By combining stocks into a portfolio, we reduce risk through diversification. Because the
prices 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.
Covariance(R i , R j ) =
Covariance(R i , 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 (R 1 , R 2 ) = Corr (R 1 , R 2 ) x SD(R 1 ) x SD(R 2 )
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 30
stocks. Even for very
large portfolio, we
cannot eliminate all of
risk.
The variance of the portfolio is at least (maximum diversification)
�(𝒂𝒗𝒂𝒓𝒂𝒈𝒆 𝒄𝒐𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆)
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 portfolio is less than the weighted average volatility (if the corr’s <1). We
can eliminate some volatility by diversifying!
The Effect of correlation.
+1 perfectly positively
correlated -> no
diversification possible.
<1 -> diversification
possible.
-1 perfectly negatively
correlated -> it becomes
possible to hold a portfolio
that bears absolutely no
risk.
11.4 Risk versus return: Choosing an Efficient Portfolio
Inefficient portfolio = whenever it is possible to find another portfolio that is better in terms
of both expected return and volatility.
Efficient Portfolio = There is no other portfolio of stocks that offers a higher expected return
with lower volatility. We cannot easily rank the efficient ones. Investors will choose among
them based on their own preferences for return versus risk.
Long position = a positive investment in a security (<0%)
Short position = a negative amount in a stock. (possibly more than 100%)
In a short sale you sell a stock that you do not own and then buy that stock back in
the future.
Short selling is profitable if you expect a stock’s price to decline in the future!
Short selling can greatly increase the risk of the portfolio!
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Efficient frontier = the line
with the efficient portfolio’s
When the set of investment
opportunities increases , the
efficient frontier improves
(due to diversification) (less
risk for the same expected
return).
Even when added stocks
appear to offer inferior riskreturn combinations on their
own, they allow for additional
diversification, the efficient
frontier improves with their inclusion. We should keep adding stocks until all investment
opportunities are represented.
11.5 Risk-Free Saving and Borrowing (investing in portfolio’s)
Another way besides diversification to reduce risk -> keep some of our money in a safe, norisk investment. (it is likely this will reduce also the expected return).
Aggressive investors are able to borrow money to invest even more in stock market
Investing fraction x in market portfolio and (1-x) in risk-free (Treasury bills)
Expected return ->
Because the risk-free rate r f is fixed and does not move with (or against) our portfolio, its
volatility and covariance with the portfolio are both zero!
Thus, the volatility of
portfolio including risk-free
saving ->
As we increase the fraction x
invested in P, we increase both our risk and our risk premium proportionally.
Buying stocks on margin = Borrowing money to invest in stocks
To earn the highest possible expected return for any level of volatility we must find the
portfolio that generates the steepest possible line when combined with the risk-free
investment. The slope of the line through a given portfolio P is often referred to as the
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Sharpe Ratio =
Measures the ratio of reward-to volatility provided by a portfolio. The optimal portfolio to
combine with the risk-free asset will be the one with the highest Sharpe ratio, where the line
with the risk-free investment just touches, and so is tangent to, the efficient frontier of risky
investments.
Tangent Portfolio = the portfolio that generates this tangent line.
Tangent portfolio has the highest Sharpe ratio.
The tangent portfolio is efficient and, once we include the risk-free investment, all efficient
portfolios are combinations of the risk-free investment and the tangent portfolio.
Therefore, the optimal portfolio
of risky investments no longer
depends on how conservative
or aggressive the investor is
every investor should invest in
the tangent portfolio
independent of his or her taste
for risk. The investor’s
preferences will determine
only how much to invest in the
tangent portfolio versus the
risk-free investment
The Efficient Portfolio is the
tangent portfolio (just one)
11.6 The Efficient Portfolio and Required Returns
Portfolio improvement
Take an arbitrary portfolio P, and let’s consider whether we could raise its Sharpe ratio by
selling some of our risk-free assets (or borrowing money) and investing the proceeds in an
investment i. Two consequences ->
1. Our expected return will increase by I’s excess return E[R i ] – r f
2. We will add the risk that I has in common with our portfolio.
Adding I to the portfolio P will improve our Sharpe ratio if ->
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The Beta of investment I with Portfolio P
Measures the sensitivity of the
investment I to the fluctuations of
the portfolio P.
Increasing the amount invested in I will increase the Sharpe ratio of portfolio P if its
expected return E[R i ] exceeds its required return given portfolio P, defined as ->
A portfolio is efficient if and only if the expected return of every available security equals its
required return.
We can determine the appropriate risk premium for an investment from its beta with the
efficient portfolio. The efficient or tangent portfolio, which has the highest possible Sharpe
ratio of any portfolio in the market, provides the benchmark that identifies the systematic
risk present in the economy.
11.7 The Capital Asset Pricing Model
Capital Asset Pricing Model (CAPM) = This model allows us to identify the efficient portfolio
of risky assets without having any knowledge of the expected return of each security.
Instead, the CAPM uses the optimal choices investors make to identify the efficient portfolio
as the market portfolio, the portfolio of all stocks and securities in the market.
CAPM assumptions ->
1. Investors can buy and sell all securities at competitive market prices (without incurring
taxes or transactions costs) and can borrow and lend at the risk-free interest rate.
2. Investors hold only efficient portfolios of traded securities
Homogeneous expectations = all investors have the same estimates concerning future
investments and returns
3. Investors have homogeneous expectations regarding the volatilities, correlations and
expected returns of securities.
Given homogeneous expectations, all investors will demand the SAME efficient portfolio of
risky securities.
The combined portfolio of risky securities of all investors must equal the efficient portfolio.
The demand for market portfolio must equal the supply of the market portfolio.
When the CAPM assumptions hold, an optimal portfolio is a combination of the risk-free
investment and the market portfolio.
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Capital Market Line (CML) =
When the tangent line goes
through the market
portfolio, it is called the
capital market line.
The expected return and
volatility of a capital market
line portfolio
are
x = proportion in mrkt portf.
11.8 Determining the Risk premium
Given an efficient market portfolio, the expected return of an investment is ->
There is a linear relationship between a stock’s beta and its expected return ->
Security Market Line = is graphed as the line through the risk-free investment and
the market.
According to the CAPM, if the expected return and beta for individual securities are plotted,
they should all fall along the SML.
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The distance of each stock to the right of the capital market line is due to its diversifiable
risk. The relationship between risk and return for individual securities becomes evident
only when we measure market risk rather than total risk.
According to the CAPM, the market portfolio is efficient, so all stocks and portfolios
should lie on the SML.
Beta of a portfolio (with market portfolio) = the beta of a portfolio is the weighted average
beta of the securities in the portfolio
Summary CAPM ->
assumptions -> markets are competitive, investors choose efficient portfolios
and investors have homogeneous expectations.
Conclusions -> -The market portfolio is the efficient portfolio.
-The risk premium for any investment is proportional to its beta with
the market.
Accuracy -> not completely accurate, because it doesn’t fully describe investor’s
behaviour
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Chapter 12: Estimating the Cost of Capital
12.1 The Equity Cost of Capital
Recall that the cost of capital is the best expected return available in the market on
investments with similar risk!
The Capital Asset Pricing Model (CAPM) provides a practical way to identify an investment
with similar risk. Under the CAPM, the market portfolio is a well-diversified , efficient
portfolio representing the non-diversifiable risk in the economy. Therefore, investments
have similar risk if they have the same sensitivity to market risk, as measured by their beta
with the market portfolio. (also according Law of One Price).
So, the cost of capital of any investment opportunity equals the expected return of available
investments with the same beta. This estimate is provided by the Security Market Line
equation of the CAPM, which states that, given the beta B, of the investment opportunity, its
(Equity) cost of capital is ->
= E[R i ] = r E
As our first application of the CAPM, consider an investment in the firm’s stock. As we
demonstrated in Chapter 9, to value a share of stock, we need to calculate the equity cost of
capital.
Two key inputs ->
-Construct the market portfolio and determine its expected excess return over
the risk-free interest rate (12.2)
-Estimate the stock’s beta (12.3)
12.2 The Market portfolio – equity cost of capital
The investment in each security I is proportional to its market capitalization MV= ( N x P).
We then calculate the portfolio weights of each security as follows->
x i = Mv / total Mv of portfolio
Value-weighted portfolio = A portfolio like the market portfolio, in which each security is
held in proportion to its market capitzalization.
Equal-ownership portfolio = An value-weighted portfolio. We hold an equal fraction of the
total number of shares outstanding of each security in the portfolio, even when market
prices change.
Passive portfolio = a portfolio with very little trading, like a value-weighted portfolio.
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Market indexes -> report the value of a particular portfolio of securities
-S&P500, Wilshire 5000,
-Down Jones Industrial Average (=price-weighted portfolio)
Price-weighted portfolio = holds an equal number of shares of stock, independent of their
size (dependent of price).
Market proxy =a portfolio whose return they believe closely tracks the true market
portfolio.
Key ingredient to the CAPM is the market risk premium.
Before we can estimate it, we must first discuss the choice of the risk-free interest
rate use the CAPM.
risk-free interest rate ->
1. using the yields on U.S. Treasury securities
While U.S. Treasuries are free from default risk, they are subject to interest
rate risk unless we select a maturity equal to our investment horizon!
2. Use the historical average excess return of the market over the r f rate.
-This use faces standard errors
-they are backward looking, not sure they are representative
3. Given an assessment of future cash flows
-This model is highly inaccurate for an individual firm, but more reasonable
when considering the overall market
12.3 Beta Estimation - equity cost of capital
The next step in implementing the CAPM is to determine the security’s beta.
Ideally, we would like to know a stock’s beta in the future, that is, how sensitive will its
future returns be to market risk. In practice, we estimate beta based on the stock’s historical
sensitivity. This approach makes sense if
a stock’s beta remains relatively stable
over time, which appears to be the case
for most firms.
Beta corresponds to the slope of the
best-fitting line in the plot of the
security’s excess returns versus the
market excess return.
Note though, that in any individual
month, the security’s return will be
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higher or lower than the best-fitting line. Such deviations from the best fitting line result
from risk that is not related to the market as a whole. These deviations are zero on average
in the graph, as the points above the line balance out of the points below in the line. They
represent firm-specific risk that is diversifiable and that averages out in a large portfolio.
Linear regression = the statistical technique that identifies the best-fitting line through a set
of points.
Last term, epsilon = the error (or residual)
term = it represents the deviation from the
best fitting line and is zero on average (or else it could improve the fit). This error term
corresponds to the diversifiable risk of the stock, which is the risk that is unrelated to the
market.
The expected return of a security =
The constant alpha = measures the historical performance of the security relative to the
expected return predicted by the security market line – it is the distance the stock’s average
return is above or below the SML.
According to the CAPM, alpha should not be significantly different from zero!!
Using Excel’s regression data analysis tool, we can calculate the estimated beta. Assuming
the security’s sensitivity to market risk will remain stable over time, we would expect its beta
to be in this range in the near future. With this estimate in hand, we are ready to estimate
its equity cost of capital.
Alphas like expected returns, are difficult to estimate with much accuracy without a very
long data series. Moreover, the alphas for individual stocks have very little persistence.
Thus, although its return has exceeded its required return in the past, it may not necessarily
continue to do so.
12.4 The Debt cost of Capital
Debt cost of capital= the cost of capital that a firm must pay on its debt
The debt cost of capital will be helpful when estimating the cost of capital of a project.
Recall from Chapter 8 that the yield to maturity of a bond is the IRR an investor will earn
from holding the bond to maturity and receiving its promised payments.
If there is little risk the firm will default, we can use the bond’s yield to maturity as an
estimate of investors’ expected return. If there is a significant risk that the firm will default
on its obligation, however, the yield to maturity of the firm’s debt, which is its promised
return, will overstate investors’ expected return.
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The Expected return of a bond ->
Y = YTM, p = probability of default, L = expected loss per dollar.
The importance of these adjustments will naturally depend on the riskiness of the bond,
with lower-rated (and higher-yielding) bonds having a greater risk of default.
Debt Betas -> Alternatively, we can estimate the debt cost of capital using the CAPM.
In principle it would be possible to estimate debt betas using their historical return in the
same way that we estimated equity betas.
However, because bank loans and many corporate bonds are traded infrequently if at all, as
a practical matter we can rarely obtain reliable data for the returns of individual debt
securities. Thus, we need another means of estimating debt betas.
Debt betas tend to be low, though they can be significantly higher for risky debt with a low
credit rating and a long maturity.
Note that both of the methods discussed in this section are approximations!
12.5 a project’s Cost of Capital
In Chapter 7, we explained how to decide whether or not to undertake a project. The
project’s cost of capital is required to make this decision. As we did in Chapter 7, we will
assume the project will be evaluated on its own, separate from any financing decisions.
Thus, we will assume that the project will be purely equity financed.
In the cased of a firm’s equity or debt, we estimate the cost of capital based on the historical
risk of these securities. Because a new project is not itself a publicly traded security, this
approach is not possible. Instead, the most common method for estimating a project’s beta
is to identify comparable firms in the same line of business as the project we are
considering undertaking. If we can estimate the cost of capital of the assets of comparable
firms, we can use that estimate as a proxy for the project’s cost of capital.
All-Equity Comparables = if the firm’s average investment has similar market risk to our
project, then we can use the comparable firm’s equity beta and cost of capital as estimates
for beta and the cost of capital of the project.
Levered firms as comparables = if the comparable firm has debt, the cash flows generated
by the firm’s assets are used to pay both debt and equity holders. Because of the firm’s
leverage, the equity will often be much riskier.
Because the firm’s cash flows will either be used to pay debt or equity holders, by holding
both securities we are entitled to all of the cash flows generated by the firm’s assets. The
return of the firm’s assets it therefore the same as the return of a portfolio of the firm’s debt
and equity combined. The beta of the firm’s assets will match the beta of this portfolio.
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Asset cost of capital or unlevered cost of capital = the expected return required by the
firm’s investors to hold the firm’s underlying assets
E and D = the total market value of equity and debt. r E = equity cost of capital, r D = debt cost
of capital.
When debt is highly rated, we can approximate its debt cost of capital using the debt yield.
Assuming so, we could also assume a debt beta of zero.
Large cash balances -> cash represents a risk-free asset on the firm’s balance sheet, and
reduces the average risk of the firm’s assets. Often, we are interested in the risk of the firm’s
underlying business operations, separate from its cash holdings. That is, we are interested in
the risk of the firm’s enterprise value, which we defined as V + debt – excess cash.
net debt = debt – excess cash and short term investments
The intuition for using net debt is that if the firm holds 1 dollar in cash and 1 dollar in riskfree debt, then the interest earned on the cash will equal the interest paid on the debt. The
cash flows from each source cancel each other, just as if the firm held no cash and no debt.
If the firm has more cash than debt, its net debt will be negative. In this case, its unlevered
beta and cost of capital will exceed its equity beta and cost of capital, as the risk of the firm’s
equity is mitigated by its cash holdings.
D changes in net debt, so could be negative.
The equity is then less risky than the assets.
Now that we can adjust for the leverage of different firms to determine their asset betas, it
is possible to combine estimates of asset betas for multiple firms in the same industry or
line of business. Doing so is extremely useful, as it will enable us to reduce our estimation
error and improve the accuracy of the estimated beta for our project.
D/V = fraction of debt financing (1 – D/V = fraction of equity financing).
Note that businesses that are less sensitive to market and economic conditions, such as
utilities and household product firms, tend to have lower asset betas than ore cyclical
industries, such as luxury goods and high technology.
12.6 Project Risk Characteristics and Financing
Firm asset betas reflect the market risk of the average project in a firm. But individual
projects may be more or less sensitive to market risk. A financial manager evaluating a new
investment should try to assess how this project might compare with the average project.
Financial managers should evaluate projects based on asset betas of firms that
concentrate in a similar line of business. Multi-divisional firms should evaluate projects
based on asset betas of firms in a similar line of business.
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Another factor that can affect the market risk of a project is its degree of operating
leverage, which is the relative proportion of fixed versus variable costs.
Holding fixed the cyclicality of the project’s revenues, a higher proportion of fixed costs will
increase the sensitivity of the project’s cash flows to market risk and raise the project’s beta.
We should assign projects with an above-average proportion of fixed costs, and thus greaterthan-average operating leverage, a higher cost of capital.
Variable costs-> determining cost of capital using CAPM, the value of a project =
revenues – cost / cost of capital
Fixed costs -> determining cost of capital using CAPM for the revenues. Discount the costs at
the risk-free rate. Revenues – costs = value of project.
Beta of new project -> using Asset Beta formula, D(negative) = costs / r f interest r.
In section 12.5 we presumed the project we are evaluating is all-equity financed. How might
the project’s cost of capital change if the firm does use leverage to finance the project?
Perfect capital markets -> by which we mean no taxes, transactions costs or other frictions,
the choice of financing does not affect the cost of capital or NPV of a project. Rather, a
project’s cost of capital and NPV are solely determined by its free cash flows. In this setting
then, our assumption regarding the project’s financing is innocuous. Its cost of capital would
be the same whether and to what extent, it is financed in part with debt. The intuition for
this result, is that in a competitive and perfect market, all financing transactions are zeroNPV transactions that do not affect value.
A big imperfection -> taxes. When markets frictions do exist, the firm’s decision regarding
how to finance the project may have consequences that affect the project’s value.
Corporate tax code, which allows the firm to deduct interest payments on debt from its
taxable income. If the firm pays interest rate r on its debt, then once the tax deduction is
accounted for, the net cost to the firm is given by ->
Effective after-tax interest rate = r(1 – t c )
When the firm finances its own project using debt, it will benefit from interest tax deduction.
One way of including this benefit when calculating the NPV is by using the firm’s effective
after-tax cost of capital, which we call the
weighted-average cost of capital or wacc.
pretax WACC = The unlevered cost of capital. Key distinctions between them ->
Unl. 1. It can be used to evaluate an all-equity financed project with the same risk.
WACC 2. The WACC can be used to evaluate a project with same risk and financing
CAPM is not perfect, but generates small errors. It makes the cost of capital objective
instead of subjective to the managers thoughts. The CAPM gets managers to think about risk
in the correct way (they don’t worry about the diversifiable risk).
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