FINANCE
Chapter 1
The Four Types of Firms
• Sole Proprietorship,
Owned only by 1 person and has few employees, is very easy to create but has an unlimited
personal liability. Is the first firm’s type in the US, although they generate just 4% of the revenues.
• Partnership
Similar but there are many owners. All the partners liable for all the debts, one partner can repay
all the debts.
Special case is the limited Partnership in which there are 2 distinctive types of partners.
We must distinguish general and limited partners:
General partners have unlimited liability. Can have Managing possibilities.
Limited partners have limited liability until their initial investment, but cannot manage.
• Limited Liability Company:
PS All the owners have limited liability but can manage the business. Is like SRL
• Corporation
A legal entity separated from its owners. The board of directors has the actual control on the
management. But the shareholders have the real owners of the firm and have limited liability for
the amount of their stocks.
TAX SYSTEM
The corporations have a double tax system:
The first one on the company profit, the second one on the shareholders by dividend.
S corporations don’t pay corporate taxes,
1.2 Corporate Ownership Versus Control
The ownership is handed by the shareholders, instead the control organ is the board of directors
(elected by the shareholders).
Chief Executive Officer, take the decisions, nominated by the board.
Chief Financial Officer, manage all the financial aspects:
Right investments
Financing decisions
Manage Cash
Shareholders just expect that firms take care about their interest, improving the market value of
the stock, but companies, especially nowadays, must take care about the environmental and social
policies.
Agency problems, when managers act in their own interest instead of shareholders. One way to
reduce it is to tie management’s compensation with firm performance.
Hostile takeover, happens when the stock price is very low, so a shareholder or a group, can buy
enough stocks to control the company management.
• Primary Markets
When a corporation itself issues new shares of stock and sells them to investors, they do so on the
primary market.
• Secondary Markets
After the initial transaction in the primary market, the shares continue to trade in a secondary
market between investors.
Fintech refers to the relation between financial innovation (new financial products) and technical
innovation
Blockchain
- A technology that allows a transaction to be recorded in a publicly verifiable way without the
need for a trusted third party to certify the authenticity of the transaction
• Cryptocurrency
- A currency whose creation and ownership is determined via a public blockchain
Ratio
What are the main statement?
What kind of RATIO exists, their calculation and correlation
Chapter 2 Financial Information
Each listed company must send periodic financial information to stock exchange and make the
annual report shareholders. Accounting rules are IFRS. Corporations must hire audit company to
check their accounts.
1. Balance Sheet, lists the firm’s assets (what a company owns) and liabilities, (what a
company owes) providing a snapshot of the firm’s financial position at a given point in
time.
a. Assets= Liability + Stockholders Equity
b. Market Value of Equity (Market Capitalization)= Share Price × Number of Shares >0
≠ BV(Book Value of equity)
c. Market-to-book (MB) ratio=MV/BV -> Most of the companies >1
2. Income Statement, calculates income generated by the company’s assets
and liabilities between two dates
3. Statement of Cash flows, reflects the amount of cash that a company has or have spent. Is
divided in 3 sections
a. Operating Activity, adjusts net income by all non-cash items related to operating
activities and changes in net working capital
- Depreciation − add the amount of depreciation
- Accounts Receivable − deduct the increases
- Accounts Payable − add the increases
- Inventories − deduct the increases
b. Investment Activity, Capital Expenditures
c. Financing Activity, dividends, borrowing
4. Others, Statement of Stockholders Equity
Chapter 3 Investment Decisions
In theory, there are four recurring themes to help financial managers to make financial decisions:
1. Corporate finance is all about maximizing value.
2. The opportunity cost of capital sets the standard for investment decisions.
3. A safe dollar/euro is worth more than a risky dollar/euro.
4. Smart investment decisions create more value than smart financing decisions.
To make a valid comparison, finance tools will help to express all costs and benefits in common
terms. One of the most important models is named the Valuation Principle. This principle is
related to the concept of net present value (NPV), which is essential to the NPV decision rule.
In order to determine market values of assets/financial products two related concepts deserve
also special attention: the Law of One Price and Arbitrage.
We cannot simply add up benefits and costs over time because of time value of money (money
earns interest)
Future value of cash0: Cash1=Cash0×(1+r) (compounding)
Present value of cash 1: Cash0=Cash1/(1+r) (Discounting)
High risk investment has high interest rate
The Net Present Value (NPV)= Present Value (Benefit)- PV (Costs)
Only accept project with a positive NPV
Investing in a 0, doesn’t make difference, but could leave the company to other benefit aspects.
IT’s up to the company. The company would choose this option just if they have only one
investment option.
Arbitrage and the law of one price
Arbitrage: buying & selling equivalent goods in different markets to take advantage of a price
difference. An arbitrage opportunity happens when there is the possibility to make a profit
without any risk.
Law of One Price: if equivalent investment opportunities trade simultaneously in different
competitive markets, then they must trade for the same price in both markets. This is the NO
Arbitrage rule, this how should be.
Safe and risk dollar. The safe dollar is more safe, but doesn’t offer a lot of profit.
No arbitrage when NPV = -P+PV(all cash flows)=0, therefore must be compare Price= PV (all cash
flows)
If P< PV everybody wants that investment because offer a bigger cash flow than the payee price.
If P> PV asset is overvalued, nobody wants it
The Three Rules of Time Travel:
1. Only values at the same point can be compared.
2. To move a cash flow forward must be compound. C* (1+r)n.
3. To move a cash flow backward must be discount. C/(1+r)n.
Annuities
A constant cash flow C that occurs at regular intervals for a finite number of N periods
Formula to calculate the Present Value of Annuity:
C/r [1- 1/(1+r)N]
Formula to calculate the Future Value of Annuity:
C/r [1- 1/(1+r)N * (1+r)N]  C/r [(1+ r)N -1
Perpetuities
When a constant cash flow will occur at regular intervals forever: PV= C/r
Growing Annuity, perpetuity
The present value of a growing annuity with the initial cash flow C, growth rate g, and interest rate
r is defined as:
Perpetuity= C/r-g
C/r-g [1- (1+g/1+r)N ]
If everything it’s not annual, you just must adapt to the right scale.
Chapter 6 Bonds and Bonds Valuation
bond is a security sold by governments and corporations to raise money from investors today, in
exchange for promised future payments.
Are issued by corp or governments in the primary market, but then traded in the secondary
market.
The terms of the bond are described in bond certificate.
The payment is made until a final repayment date, called the maturity date of the bond.
The term is the time until the final repayment.
Bonds typically make two types of payments to their holders.
The promised interest payments are called coupons and are paid periodically (every 6 months)
The face value instead, is the amount of money borrowed with the bond, is typically paid at the
maturity date.
To calculate the amount of the coupon we use CPN = Coupon rate * Face Value / the number of
payments per year
Zero Coupon Bond
Is the simplest type of bond and doesn’t make coupon payment. So the only payment is on the
maturity date and correspond to the face value of the bond, considering that money in a year have
a less value today, people would pay a lower amount then the face value, and earn from that
difference.
Therefore, investors are compensated for the time value of their money
The yield to maturity of a bond is the discount rate that set present value equal to the price
market.
For example, the face value of the bond is 100k, the purchased price is lower, the YTM is the
discount rate that set the ratio.
Yield to Maturity of an n-Year Zero-Coupon Bond is the per-period rate of return for holding the
bond from today until maturity on date n.
We’re calling the risk-free interest rate as a Yield rate to maturity rn = YTMn
Coupon Bonds
This type of bonds pays the face value at the maturity date but also some regular payment based
on a fix coupon rate
Coupon rate (% of FV): Determines the amount of each coupon payment
• Coupon payment: Face Value * coupon Rate/ Number of payments
Coupon bonds may trade:
1. at a discount, a price is less than their face value (happens when the YTM > coupon rate)
2. at a premium, a price greater than their face value (happens when the YTM < coupon rate)
3. or at par a price equal to their face value (happens when the YTM = coupon rate)
Once P=FV the YTM= coupon rate.  the formula will be YTM= C/FV
If a coupon bond’s yield to maturity exceeds its coupon rate, the present value of its cash flows at
the yield to maturity will be less than its face value, and the bond will trade at a discount.
The coupon bond tends to be traded at par or close to, the zero-coupon are traded at discount.
To understand the price of each bond type we have to use this formula:
If a bond’s yield to maturity has not changed, then the IRR (return) of an investment in the bond
equals its yield to maturity even if you sell the bond early.
Bigger is the discount rate more the price will decrease, considering a constant YTM
What Happens if the YTM change?
We focus on two potential determinants of interest rate risk
1. bond maturity N
a. Considering 2 bonds with the same terms, but different N if YTM increases of 1%
the price of the bond with the bigger N will decrease more than the other with a
lower N
b. Long term bonds suffer more from yield rises than shorter term bonds
2. Level of the coupons CPN
a. Considering 2 bonds with the same N but different coupon rates if YTM increases of
1% the price of the bond with the smaller coupon will decrease more than the
other with a bigger coupon
b. Small coupon bonds suffer more from yield rises than large coupon bonds (keeping
all else equal)
Investments on bond before the maturity depends on the rate expectations of the investors.
SO if I have an expectations of rate al ribasso I think that Price in the future will increase so I would
take a bond with an high duration.
The opposite is also correct
Corporate Bonds
Investors comparing two equal bonds, would spend less money on the more risky
Considering bonds with default possibility:
Certain sure default of 90% of the FV
I would calculate the Price discounting with a YTM but considering 90% of FV 1000 (900)
P = FV/ 1+YTM
ER= FV with default/ Price
1. Measures of credit risk
Ratings (Moody’s, Standard&Poors): qualitative assessments
2. Default Spread (credit spread) : difference between the yield on corporate bonds (risky)
and (US) Treasury yields (riskfree) of same maturity
a. often anticyclical (= it widens during economic recessions and/or crises)
YTM increase when the time pass, but low ratings bonds’ YTM will increase more than the others,
the most stable are the government bonds.
Sovereign Bonds
U.S. Treasury securities are generally considered to be default free.
- But: not all sovereign bonds are default-free,
Greece defaulted on its outstanding debt in 2012
Interest rate quotes
Effective Annual Rate (EAR) is the effective amount of interest earned in 1 year (considering the
compound effect). Is necessary adjust the discount rate of different period, 5% annual is not the
same of 2.5% in 6 months.
Equivalent n-Period discount rate (1+r)n -1. If you have EAR of 9% and you want to know the
amount of each 5 months (power of 1/5)
To determine the amount to save each quarter to reach the goal of $25,000 in five years, we must
determine the quarterly payment, C:
The annual percentage rate (APR) indicates the amount of simple interest earned in one year
without the effect of compounding.
The APR itself cannot be used as a discount rate. Is a way to quote the actual interest earned each
compounding period.
I can convert an APR to EAR
K = the compounding period, could be 12 months or 100 days
Macroeconomics perspective, r = re +  (inflation)
An increase of the inflation (expected inflation) will increase r, so the Price decrease and the
demand of the bond increase.
Is bad for bond holders (creditors) because Price is going down, so will receive less money
Is good for issuers (debtors) because the real debt decrease due by inflation.
An economic expansion make people ask for bonds, therefore make companies bid for bonds.
Increase of offer and demand
For risk free zero coupon bond, the law of one price establish that the future value is identical to:
Long term interest rate R is approximately the average of the current and expected short term
interest rates.
If R-r1>0 you expect a rise of the rate in the future
If R-r1<0 you expect a fall of the rate in the future
NPV is not the only method to valuate investments.
Why do we also use other methods?
1) NPV may be too complex/too costly/ too uncertain to estimate future cash flows/discount rate
(e.g. nonlisted companies)
2) Alternatives provide robustness check for NPV provided these other methods apply
Internal Rate of Return (IRR)
Discount rate for which NPV=0
It’s difficult to calculate IRR, we can do it on Excel, otherwise we can calculate it only if has 2 cash
flows: Price and Face Value (Zero coupon Bond)
Investment Rule: take any investment that has IRR> CC (capital cost)
We can calculate only 1 investment with this rate rule.
The Payback Rule
• Payback period: amount of time it takes to recover or pay back the initial investment.
If it is less than a benchmark period (pre-specified length of time), you accept the project.
Incremental IRR Investment Rule
Apply the IRR rule to the difference between the cash flows of two mutually exclusive alternatives.
So we can see the NPV of each strategy and choose the best. The common point where the IRR the
same, is the turning point of the decision.
The incremental IRR may not exist (no crossing)
Multiple incremental IRR could exist.
Profitability Index
• The profitability index can be used to identify the optimal combination of projects to undertake
Valuing Stocks
There are two potential sources of cash flows from owning a stock.
First, the firm might pay out cash to its shareholders in the form of a dividend.
Second, the investor might generate cash by choosing to sell the shares at some future date.
So the Price today reflects the possibility of receiving dividends and increasing price, everything is
discounted to the expected rate.
P0 = (Div1 + P1) / 1+r
The dividend yield is the percentage return the investor expects to earn from the dividend paid by
the stock
Capital gain rate is how much the Price gained in percentage.
All this is equal to the total return, how much the investment is going to pay after one year.
The total return of the stock should equal (to the equity cost of capital) the expected return of
other investments available in the market with equivalent risk.
Constant Dividend Growth
Every investor hope that dividends grow up during the years.
We can consider the dividend growth as a Perpetuity so
The firms can increase their dividends in 3 ways:
1. It can increase its earnings (net income).
2. It can increase its dividend payout rate.
3. It can decrease its shares outstanding.
Companies have to face a trade off, give dividends or invest their earnings, they should do it and
increase their value just if NPV of the new investments is higher than equity cost of capital rE.
Young firms often have very high initial earnings growth. During this period, these firms often
retain 100% of their earnings to exploit profitable investment opportunities
As they mature, their growth slows and at some point, their earnings exceed their investment
needs, and they begin to pay dividends.
Dividend discount model
Limitations of this model:
The growth rate of firms is not constant and is not easy to forecast, small changes can have a huge
impact,
The paying rate is how much dividend you keep on the firm.
Two alternative approaches to valuing the firm’s shares respect the dividend-discount model.
1. Total payout model, which allows us to ignore the firm’s choice between dividends and
share repurchases.
Some firms started shares repurchases: firms buy their own shares but they have less money to
give as dividends, and this will increase the amount of earnings and dividends per share basis.
The total payout model is based on discount the total payouts that the firm makes to
shareholders, (which is the total amount spent on both dividends and share repurchases). Divided
by the total amount of shares, to calculate a share price.
2. Discounted free cash flow model, which focuses on the cash flows to all of the firm’s
investors, is discounted with the weighted average cost of capital rwacc (because we are
not considering only the dividends as the previous model, but we’re also considering debt
and cash). So it’s basically the discount of free cash flow with the rwacc.
a. Is focused on the enterprise value= Market Value of Equity + Debt – Cash. So it’s b
How we calculate the Free cash Flow:
Free Cash Flow = EBIT * (1 - t) + Depreciation - Capital Expenditures - Increases in Net Working
Capital
Valuation with Comparable Firms
1) The Price-Earnings Ratio (P/E)
a. P0 of apple= EPS (apple) * P/E (average of the competitors)
2) Enterprise Value Multiples
Common measures of return
 Average return= sum of return/ number of return
 Variance and standard deviation
 Expected return  amount invested (x1) * return
X1 = Value of investment/total value of portfolio
We can put all of this in an interval of confidence  Estimate average return  2Std. Error
Standard deviation can change (volatility of the stock) based on firm specific news (Unsystematic)
or on market-wide news common to all companies (Systematic).
SD is the return of a stock
Systematic or systemic is a common risk that hit each company in the market
Unsystematic is a specific risk of a company
Risk diversification: unsystematic risk disappears in large portfolios because it is by definition
uncorrelated across firms. In portfolio I have different type of stocks so the risks of each stock is
reduced by the potential gain of the others.
Systematic risk stays because firm stocks co-move due to market-wide news
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For individual stocks SD measures total risk
For (large) portfolios, SD only reflects systematic risk
Model of the risk-return trade off for portfolios: Modern Portfolio Theory (MPT)
We assume that investor likes return but dislikes risks for that creates portfolios, to delate
unsystematic risk.
Portfolio Return  %invested in R + %invested in R2
X1 = Value of investment/total value of portfolio
We can also calculate the Expected Value, Variance and Covariance.
Variance of a portfolio: Var(RP) = x21 Var(R1) + x22 Var(R2) + 2x1x2 Cov(R1,R2)
Var(RP) = x21 Var(R1) + x22 Var(R2) + 2x1x2 Corr(R1,R2)* SD1*SD2
Covariance could be positive or negative depends on the direction of the stocks, if one increase
(positive) and the other decrease (negative) the covariance will be negative.
Correlation instead can have value in a range between [-1 ; +1]
Correlation is Cov (R1,R2)/SDR1 * SDR2
If correlation is +1 the stocks tend to move in the same direction, this means that have common
risk.
If correlation is – 1 the return goes in opposite direction
If correlation is 0 the stocks don’t have any things in common this mean that have different
returns.
Capital Market Line
Shows the ratio between the Expected Return of a portfolio and its volatility (that is Standard
Deviation)
SD is the total risk (systematic and unsystematic combined)
Adding more stocks to a portfolio reduces the remaining unsystematic risk
Curve represents the best combination to maximize the risk, and his only portfolio the individual
stock are behind the curve
The 45 degree line is the max expected return that someone could have.
Y= mx + q
q= is the risk free rate
m= SD
x= is the risk
y= expected return
In a low risk AREA at the left of the curve you have to lend money
In a high risk AREA at the right of the curve you can have that risk only if you borrow money
Sharpe ratio = Expected Return – risk free rate/ Std Deviation
You can calculate this for a portfolio
SD is important to know for the exam: IS THE TOTAL RISK OF THE PORTFOLIO
Var(RP) = x21 Var(R1) + x22 Var(R2) + 2x1x2 Corr(R1,R2)* SD1*SD2  rad Var(RP)
Equally weighted portfolio, a portfolio in which the same amount is invested in each stock. Where
n is the amount of stocks.
Instead the volatility for a portfolio with different amount invested in each stock
The Capital Asset Pricing Model (CAPM)
CAPM Assumptions
• Investors can buy and sell all securities at competitive market prices (without incurring taxes or
transaction costs) and can borrow and lend at the (same) risk-free interest rate.
• Investors hold only efficient portfolios of traded securities (portfolios that yield the maximum
expected return for a given level of volatility)
• Investors have homogeneous expectations (= same information) regarding the volatilities,
correlations, and expected returns of securities.
Notice these are basically the same assumptions as for the MPT.
Firs of all we have to introduce beta, measures the sensitivity of the investment i to the
fluctuations of the portfolio P. That is, for each 1% change in the portfolio’s return, investment i ’s
return is expected to change by beta percent due to risks that i has in common with P.
Also, Beta is equal to Cov/Var
The required return is the expected return that is necessary to compensate for the
risk investment i will contribute to the portfolio.
So, a portfolio is efficient if and only if the expected return of every available security equals its
required return. E (R) = ri
In other words: the security’s risk premium is proportional to the market risk premium.
Basically Beta describes how sensitive are the revenues compared to the general economic
conditions. In Beta Zero stocks E(Ri)= rf.
In other words, stocks that are more sensitive to systematic risk have higher risks.
If you have a stock with beta= 1.5 and another one of -1.5 you can eliminate the market risk
adding these stocks in the same portfolio. Considering that the B of this portfolio is 0 in the
equation above, the expected value of the portfolio is the same of the risk-free rate, E(Ri)= rf.
AT THE EXAM they can give you the premium rate that is basically the return of the market minus
the risk free rate.
Security Market Line
There is a linear relationship between a security’s beta and its expected return.
The equation above is a straight line in a graph comparing Beta and the expected return of the
portfolio (or the stock) when x=0 so Beta=0 expected return is rf that is the point where the line
cross the y axe. The stocks that are above the line are undervalued (offer with the same Beta an
higher return)
The stocks that are under the line are overvalued (offer with the same Beta a lower return)
The beta of a portfolio is the weighted average beta of the securities in the portfolio. If two stocks
lie on the security line a combination of both is also on the line.
The risk adjusted discount rate: assuming that companies finance themself just with equity.
Same formula of the one above, of the Expected Return.
Market Portfolio
A value-weighted portfolio is an equal-ownership portfolio; every investor has equal fraction of
the total number of shares outstanding of each security in the portfolio. For example in S&P500
every investor has the same amount of stock of each company considered in the portfolio
weighted with the single value. Same value for each different stock
A price-weighted portfolio is the equal nr of shares for each stock in portfolio. Same amount each
stock. Doesn’t care about the size
Passive Portfolio: a portfolio that is not rebalanced in response to price changes
The Market Risk Premium E[RMkt] − rf
To Estimate the risk premium (E[RMkt] − rf) using the historical average excess return of the
market over the risk-free interest rate.
The problem using old data is that SD is very high, so doesn’t represent current expectations.
We can also try to estimate beta using a linear regression
εi is the error term and represents the deviation from the best-fitting line and is zero, on average.
αi represents a risk-adjusted performance measure for the historical return.
Trying to understand the linear regression:
if alpha is positive the stock performed better than the expectations of the CAPM and is above the
SML
if alpha is negative the stock performed less than the expectations of the CAPM and is belove the
SML
Cost of Debt Capital
Is the expected return on investments of comparable risk.
If risk free, cost of debt= YTM
If the risk is high YTM is higher than cost of debt
To determine the cost of debt I need rating classes and debt beta, also L= is the amount of the
Loss and p= is the probability of the loss.
We can also estimate the cost of debt using the CAPM
Using the classic formula we can calculate the cost of capital
The weighted average cost of capital
Assuming a corporation funded with equity and debt, we can calculate the r wacc
where E represents the market value of equity,
D represents the market value of debt,
rE represents the cost of equity (measured by CAPM), is the return that investors expect investing
on the company; for the company is a cost because is what have to return
rD represents the cost of debt (measured by the average yield to maturity of outstanding debt), is
the YTM  is also the probability of loss* L
and τC represents the corporate tax rate.
Cost of Capital =
Options
It gives owner right (not the obligation) to purchase or sell an ‘underlying’ asset at a fixed price
somewhere in the future.
Call: give to the owner the opportunity to buy the asset. You set the price to the value at that
moment, so you expect that the price rises so you can buy at a lower price an asset that values
more. Fixed price at 100 and now the asset is a 105. If the price goes down, I will not call
Put: give to the owner the opportunity to sell the asset. You expect that the price goes down so
you can sell at an higher price an asset that values less. Put options are basically an insurance to
hedge other risk in a portfolio.
Expiration Date: last date on which an option holder has the right to exercise the option
• American Option: allows holder to exercise the option on any date up to, and including, the
expiration date
• European Option: allows holder to exercise the option only on the expiration date
The names of the options don’t mean that are just in these countries.
Combination of both happens when the stock is very volatile, and they don’t know in which way
will go.
Straddle, do both call and options fixing the same price
Strangle, when the strike price on the call exceeds the strike price on the put
• Example with strike prices of 30 (put) and 40 (call)
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A straddle strategy makes money when the stock and strike prices are far apart
wheras a butterfly spread makes money when the stock and strike prices are close. (Less
volatile)
For AO Price increases if Time to maturity increases
American options (AO) become more expensive for longer maturity dates (keep all else equal)
Options Price increases with volatility, (or Sd) an higher SD means a wider curve, so people expect
more return
A call option cannot be worth more than the stock
itself.
A put option cannot be worth more than its strike
price.
Put Call Parity
C= P+ S-PV(K) – PV(Div)
Sustainable Finance and Investment
Not always the 3 CAPM assumptions is true because people would choose the environment before
the others. Investors may have different preferences. Some derive utility from holding stocks that
have positive sustainability characteristics.
Main motive to buy sustainable stocks is not the return, but social preferences and social returns.
People are willing to invest in sustainability, most of it think that they should invest more.
It is often claimed that sustainability reduces a company’s cost of capital
Investors think that sustainable companies are less risky, for that the cost of capital is lower than
for the others.
Airline B has trouble raising financing because risk reduces its cash flows, not because risk
increases its cost of capital
• It is not a foregone conclusion that sustainability affects systemic risk
People care about sustainability so they will ask more return to unsustainable firms because they
have higher risk.
4 basic ways to invest:
1. Exclusion of certain companies (I don’t want to invest my money in tobacco)
o ABP, is a public fund that stopped to invest in fossil fuels
o No financial based
2. “Inclusion” you can include in your Cf analyses some sustainable aspects positive/negative
that can modify your cash flow (higher or lower)
o The example of the house in Florida that could lose its value, because it’s too close
to the sea, someone put into the analyses the level of the sea
3. “Engagement” with companies, is basically the Active Ownership so an owner can speak
with the board or impact with his actions the company’s decisions.
o Aka stewardship or shareholder engagement.
4. Impact Investing, is based on the production of an impact.