Summary
Samenvatting - Corporate Finance
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Complete summary of all Corporate Finance lectures. The course is part of the EBE study at VU Amsterdam.
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Lecture 1: Introduction lectureRepetition 1: Time value of money
€1 is worth more today than €1 next year
- Opportunity cost > €1 could have been used for consumption or investment
- Inflation > Purchasing power of €1 generally lower due to increasing price levels
In order to build valuation models, we need a tool that makes cash flows at different points in
time comparable.
a simple DCF model
Let δ𝑖 be a factor that makes an expected period i cash flow comparable to a cash flow
today. Then we can define the present value of stream of cash flows as:
𝐶𝐹1 𝐶𝐹2 𝐶𝐹3
𝑃𝑉 = δ1
+ δ2
+ δ3
+...
Assuming a constant discount factor 1/(1 + 𝑟) per period of time, we can rewrite instead:
𝐶𝐹1 𝐶𝐹2 𝐶𝐹3
𝑃𝑉 = 1+𝑟
+ 2 + 3 +...
(1+𝑟) (1+𝑟)
Remember: The simplification is for illustration purposes. As it gives us shorter formulas, we
rely on it for most parts of the course.
Net present value (NPV)
Our main decision criteria to evaluate investment projects (or value projects and entire firms)
𝑁𝑃𝑉 = 𝑃𝑉 (𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠) − 𝑃𝑉 (𝑐𝑜𝑠𝑡𝑠)
NPV Rule
➢Take all projects with NPV>0
➢Reject all projects with NPV<0
➢If projects are mutually exclusive, choose the one with the highest NPV.
Arbitrage and the Law of one price
Arbitrage: buying and selling equivalent goods in different markets to exploit a price
difference.
Arbitrage opportunity: make a profit without taking any risk or making any investment: like
money lying in the street; once spotted, it will quickly disappear.
If the prices in two markets differ, you can make a profit immediately by buying cheap and
selling expensive. – In doing so, they will equalize the prices. – Prices will not differ for long.
The Law of One Price: If equivalent investment opportunities trade simultaneously in
different competitive markets, then they must trade for the same price in all markets.
Discounting: useful present-value formulas
𝐶𝐹
➢ Perpetuity of cash flows CF: 𝑃𝑉 = 𝑟
𝐶𝐹
➢ Perpetuity of cash flows CF growing at the rate g: 𝑃𝑉 = 𝑟−𝑔
1 1
➢ Annuity that pays cash flow CF for T consecutive years: 𝑃𝑉 = 𝐶𝐹 ∙ ( 𝑟 − 𝑇 )
𝑟 · (1+𝑟)
,Repetition 2: discount rates and risk
What is a sensible discount rate?
→ 𝑟 = 𝑟𝑓 + 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑓𝑜𝑟 𝑟𝑖𝑠𝑘
Capital asset pricing model (CAPM)
Investors hold well-diversified portfolios
⇒ Idiosyncratic (firm-specific) risk are wiped out
⇒ Only systematic (economy-wide) risk is priced
𝑟𝑖 = 𝑟𝑓 + β𝑖 · (𝑟𝑀 − 𝑟𝑓)
Here the weighted average cost of capital (WACC) is calculated
𝑐𝑜𝑣(𝑟𝑖,𝑟𝑀)
Systematic risk: β𝑖 = 𝑉𝑎𝑟(𝑟𝑀)
Market risk premium: (𝑟𝑀 − 𝑟𝑓)
Risk-free rate
Conceptually, a risk-free interest rate is important.
➢ To discount a cash flow, we want to use the risk-free rate that matures on the date when
cash flow accrues.
➢ Lacking a better alternative, we generally use interest rates of long-term government debt
➢ On the short-term end of the yield curve there is often variation, less so on the long-term
end
Lecture 2: Modigliani-Miller
1.1 The four types of firms
We begin our study of corporate finance by introducing the four major types of firms: sole
proprietorships, partnerships, limited liability companies, and corporations. We
explain each organizational form in turn, but our primary focus is on the most important form
> the corporation.
1. Sole proprietorship: in this form there is a single owner. It has unlimited liability and
limited life. Examples are cafes or restaurants
2. Partnership: partnership firms can be divided into:
- General partner (GP): unlimited liability, run firm day-to-day basis
- Limited partner (LP): limited liability, no management role
Examples are law firms, consultancies, hedge funds
3. Limited liability company (LLC): all owners limited liability, but they run the
business. Examples are Virgin Atlantic
4. Corporation: separation of ownership (shareholders) and control (manager).
Shareholders have limited liability and receive dividend.
The major types of financial securities by corporations are: Debt, common equity, convertible
debt, preferred stocks, and warrants (options). Our focus is on debt and common equity.
Capital structure: is the relative proportions of debt and equity that a firm has outstanding.
Our main focus is the target leverage (D/E ratio) a firm should aim to maintain.
Most relevant Differences between Debt and Equity
➢ Debt claims: a higher seniority, i.e. interest payments paid out prior to dividends
➢ Equity holders (owners): voting rights & ultimate residual claimants
,➢ Equity holders: limited liability
Financing a firm with equity
→ example: Considering an investment opportunity.
Initial investment $800 this year: generates cash flows of either $1400 or $900 next year,
depending on whether the economy is strong or weak. Both scenarios are equally likely.
Because the project cash flows depends on the overall economy, they contain market risk.
As a result, investors demand a risk premium. Suppose you demand a 10% risk premium
over the current risk−free interest rate of 5% to invest in it.
> What is the NPV of this investment opportunity?
1 1
The expected cash flow is: 2
($1400) + 2
($900) = $1150
The cost of capital for this project is 15% (10% + 5%??). Therefore NPV of the project is:
$1150
𝑁𝑃𝑉 = − $800 + 1.15
= − $800 + $1000 = $200
Cost of capital is determined by: Risk-free interest rate + risk premium
All equity financing
Equity in a firm with no debt is called unlevered equity. If you finance this project using only
equity, how much would investors be willing to pay for the project?
$1150
PV (equity cash flows) = 1.15
= $1000
If you can raise $1000 by selling equity in the firm, after paying the investment cost of $800,
you can keep the remaining $200, the NPV of the project, as a profit, because there is no
debt, the cash flows (CFs) of the unlevered equity = CFs of the project.
If the stockholder’s returns for both a strong and a weak economy are given we can
calculate the expected return.
Shareholder’s returns are either 40% or -10%
1 1
This gives: Expected return: 2
40% + 2
− 10% = 15%
Because the cost of capital of the project is 15%, shareholders are earning an appropriate
return for the risk they are taking.
The expected return can be calculated with the following formula when the future returns are
not given as percentages, but as the future expected value of the assets:
𝑐ℎ𝑎𝑛𝑐𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑠𝑡𝑟𝑜𝑛𝑔 𝑒𝑐𝑜𝑛𝑜𝑚𝑦 ·𝑓𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑎𝑠𝑠𝑒𝑡𝑠 𝑠𝑡𝑟𝑜𝑛𝑔 𝑒𝑐𝑜𝑛𝑜𝑚𝑦 + '''' 𝑤𝑒𝑎𝑘 𝑒𝑐𝑜𝑛𝑜𝑚𝑦 · '''' 𝑤𝑒𝑎𝑘 𝑒𝑐𝑜𝑛𝑜𝑚𝑦
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑠𝑠𝑒𝑡𝑠
−1
Financing a firm with debt and equity
Suppose you decide to borrow $500 initially, in addition to selling equity (called Levered
Equity). Because the project’s CFs will always be enough to repay the debt, the debt is risk
free, and you can borrow at the risk−free interest rate of 5%. You will owe the debt holders
$500 × 1.05 = $525 in one year.
Given the $525 debt obligation, shareholders will receive only
i. $875 (= $1400 − $525) if strong economy
ii. $375 (=$900 − $525) if weak economy.
The modigliani and Miller theorem
, Modigliani and Miller argued that with perfect capital markets, the total value of a firm should
NOT depend on its capital structure. They reasoned that the firm’s total cash flows still equal
the cash flows of the project and, therefore, have the same present value.
Because the CFs of the debt and equity sum to the CFs of the project, by the Law of One
Price the combined values of debt and equity must be $1000.
Therefore, if the value of the debt is $500, the value of the levered equity must be $500.
E = $1000 − $500 = $500.
Bc the CFs of levered equity < CFs of unlevered equity, levered equity will sell for a lower
price ($500 v.s. $1000).
– Nevertheless, can still raise $1000 by issuing both debt and levered equity.
– Consequently, would be indifferent between these two choices for the firm’s capital
structure.
The effect of leverage on risk and return
However, leverage increases the risk of the equity of a firm. Therefore, it is inappropriate to
discount the CFs of levered equity at the same discount rate of 15% used for unlevered
equity. Investors of levered equity will require a higher expected return to compensate for the
increased risk. This increased risk is called Systematic risk. It is used to compensate for
the higher risk (more volatile returns), levered equity holders have.
The relationship between risk and return can be evaluated by computing the sensitivity of
each security’s return to the systematic risk of the economy.
Bc debt’s return bears no systematic risk, its risk premium is 0. Here, the levered equity has
twice the systematic risk of the unlevered equity, thus has twice the risk premium.
So, the return sensitivity is calculated with: ∆𝑅 = 𝑅(𝑠𝑡𝑟𝑜𝑛𝑔) − 𝑅(𝑤𝑒𝑎𝑘)
In summary:
- If the firm is 100% equity financed, equity holders will require a 15% expected return.
- If the firm is financed 50% with debt and 50% with equity, debt holders’ return is 5%,
while levered equity holders require an expected return of 25% (due to higher
systematic risk).
❖ Leverage increases the risk of equity even when there is NO default risk.
➢while debt is cheaper, it raises the cost of capital for equity. Firm’s average cost of capital
with leverage is the same as for the unlevered firm →
(500/1000)*5% + (500/1000)*25% = 15%.
Modigliani and Miller (MM) showed that the results hold under a set of conditions known as
perfect capital markets:
1. Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cash flows.
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