Notesale: Turn your study into money

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Summary financial - Samenvatting Principles of Corporate
Finance
Financial Engineering (Technische Universiteit Delft)

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You believe that short-term rates will be higher in the future
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A dollar today is more worth than a dollar tomorrow

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NPV depends solely on the forecasted cash flows and the opportunity cost of capital
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Only cash flow is relevant
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Be consistent in your treatment of inflation
Net cash flow = cash flow from capital investment and disposal
+ cash flow from changes in working capital
+ operating cash flow
Operating cash flow is simply the dollars coming in less the dollars going out
Always separate investment and financing decisions
Depreciation of assets can provide a tax shield
Projects might be even more valuable when undertaken in the future
Equivalent annual cash flow is the annual cash flow sufficient to recover a certain capital
investment, including the cost of capital for that investment
Rule for choosing between plant and equipment with different economic lives: select the asset with
the lowest fair rental charge, that is, the lowest equivalent annual cost

Chapter 7: Introduction to risk and return
Treasury bills are the safest investment there is, there is almost no risk of default; however, there is
still some uncertainty about inflation
Risk premium is the difference between the rate of return of the asset and the rate of return on
treasury bills
Many financial economists rely on historical evidence to calculate the risk premium, which is about
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Portfolio variance = X12 σ12 + X22 σ22 + 2(X1X2ρ12σ1σ2)
The risk of a well-diversified portfolio depends on the market risk of the securities inside the portfolio
The sensitivity to market movements is called beta (β)
Two crucial points about security risk and portfolio risk:
- Market risk accounts for most of the risk of a well-diversified portfolio
- The beta of an individual security measures its sensitivity to market movements
Beta is calculated as the ratio between the covariance of the stock returns and the market returns
and the variance of the returns
Investors can diversify on their own so they will not pay extra for firms that diversify

Chapter 8: Portfolio theory and the capital asset pricing model
Efficient portfolio are the portfolios which offers the highest expected return for any level of risk
The Best efficient portfolio is the one with the highest ratio of risk premium to standard deviation,
this ratio is called the sharpe ratio:
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =

𝑟 − 𝑟𝑓
𝑅𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚
=
𝜎
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

The difference between the return on the market and the interest rate is called the market risk
premium
An answer to the expected risk premium when beta is not 0 or 1 can be found in the Capital Asset
Pricing Model (CAPM)
The expected risk premium is linear with the beta:
Expected risk premium = beta x expected risk premium on market ( 𝑟 − 𝑟𝑓 = 𝛽(𝑟𝑚 − 𝑟𝑓 ))
There are some reasons why CAPM may not be the whole story, but in general it holds
Chapter 9: Risk and the cost of capital
The Company cost of capital is defined as the expected return on a portfolio of all the company’s
existing securities; the opportunity cost of capital for investment in the firm’s assets
The Weighted-Average Cost of Capital (WACC) is the blended measure of the company’s cost of
capital (assets and debts)
Interest on debt is a tax-deductible expense for corporations
Calculating after-tax WACC = (1-tax) x interest over debt x (D/V) + equity cost of capital x (D/V)
When estimating the long-term discount rate the rate for long-term bonds has to be deducted by the
risk premium for those bonds
Asset beta is the direct measure of calculating project risk
Cyclical firms which depend highly on the state of the business cycle have higher betas
A production facility with high fixed costs relative to variable costs has high operating leverage, and
therefore high betas
𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒) − 𝑃𝑉(𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑐𝑜𝑠𝑡)
𝑃𝑉(𝑎𝑠𝑠𝑒𝑡)
The Certainty Equivalent is the amount you get if you take away the uncertainty, the value
equivalent of a safe cash flow
𝛽𝑎𝑠𝑠𝑒𝑡𝑠 = 𝛽𝑟𝑒𝑣𝑒𝑛𝑢𝑒 ∗

Chapter 10: Project Analysis

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Debt x return on debt) + (proport
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The firm’s capital structure determines whether operating income is paid out as interest or equity
income; interest is taxed only at the personal level, equity income is taxed at both corporate and
personal level; however TpE can be less than Tp
Value of firm = value if all-equity financed – PV(tax shield) – PV(costs of financial distress)
In case of bankruptcy creditors get payed first before stockholders
There are high costs involved in bankruptcy, legal costs (direct) and indirect costs
In case of financial distress games can be played that benefit the stockholder or the bondholder, but
are not in the general interest
Costs of distress vary with type of asset
The trade-off theory states that the firm’s debt-equity decision is a trade-off between tax shields and
the costs of financial distress
If external finance is required, firms issue the safest security first; that is, they start with debt, then
possibly hybrid securities such as convertible bonds, then equity as a last resort

Chapter 19: Financing and valuation
𝐷

𝐸

After tax WACC = 𝑟𝐷 (1 − 𝑇𝑐 ) 𝑉 + 𝑟𝑣 𝑉
Valuing a company uses the same method as valuing a project
If the debt ratio of a project differ from that of the business, the WACC has to be calculated
differently:
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Estimate the cost of debt at the new debt ratio, and calculate the new cost of equity
rE = r + (r-rD)D/E
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Options are values using equivalent stock with the same payouts; the equivalent stock is called the
replicating portfolio
The number of shares needed to replicate one call is called the hedge ratio or option delta
Option delta = spread of possible option prices / spread of possible stock prices
The value of an option can also be calculated via a risk-neutral evaluation; calculate the expected
future value of the option and discount it at the risk-free interest rate
Black-Scholes formula: value of call option = (delta x share price) – bank loan
(N(d1) x P ) – (N(d2) x PV(EX))
𝑑1 =

log (P/PV(EX))
σ√t

𝑑2 = 𝑑1 − 𝜎√t

+

𝜎 √t
2

P= Price of stock now
EX = exercise price
σ = standard deviation of continuously compounded annual returns
t = years to maturity

Chapter 22: Real options
4 kinds of real options defined in chapter 10:
The option to expand if the investment succeeds
The option to wait and learn before investing
The option to shrink or abandon
The option to vary the mix of output or the firm’s production methods
A chance to invest in a project in a couple of years can be seen as a put option (real option); it can be calculated
using the black-scholes formula
A positive NPV is not a sufficient reason for investments; the option to wait a year could be worth more
The option to abandon a project is equivalent to a put option

Chapter 23: Credit risk and the value of corporate debt
The difference between government and corporate bonds is that the government always pays his debt,
companies not always
Buying a credit default swap (CDS) is an insurance for corporate bonds; if you buy a CDS, you commit to pay a
regular insurance premium (or spread), in return, if the company subsequently defaults on its debt, the seller of
the swap pays you the difference between the face value of the debt and its market value
The difference between a corporate bond and a comparable treasury bond is that the company has the option
to default, the government supposedly doesn’t
When a company borrows, it in fact acquires an option to default; if the asset value turn out less than the debt,
the company will choose to default on the debt and the bondholders will get to keep the assets
Bond value
= asset value – value of call
= present value of promised payment to bondholders – value of put
Valuing corporate bonds should be a two-step process:
Bond value
= bond value assuming no chance of default – value of put option on assets
But also owning a corporate bond is equivalent to owning the firm’s assets but giving a call option on these
assets to the firm’s stockholders:
Bond value
= asset value – value of call option on assets
In a company with unlimited liability, the equity-holder bears all the risk; in a company with limited liability, the
debtholders bear part of the risk
Bonds rated below Baa are called junk bonds
Key numbers such as the firm’s debt ratio, the ratio of earnings to interest, and the return on assets determine
the rating

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