Advanced Finance

• Introduction
• Agency Problems and Corporate Governance
• Stakeholder Capitalism and Responsible Business
• Credit Risk and the Value of Corporate Debt
• The Many Different Kinds of Debt
• Leasing
• Managing Risk, Options
• International Financial Management
• Financial Analysis
• Financial Planning, Working Capital Management
• Treasury at Holcim / Amrize Case
• Mergers
• Corporate Restructuring
• Financial Crises and Regulatory

Introduction

First Principles: maximize the value of the business:

1. The investment Decision
   • the hurdle rate should reflect the skiness of the investment
   • the return should reflect the magnitude and the timing of the cash-flows
2. The Financing Decision
   • the optimal mix of debt and equity that maximize firm's value
   • the right kind of debt matches the tenor of the firm's assets
3. The Dividend Decision: if the firm cannot find a investment that meets its minimum acceptance rate, return the cash to the owners
   • How much cash you can return depend on the current and potential opportunities
   • How you choose to return the cash to the owners will depend wheter they prefer dividends or buybakcs

Corporate Finance is not a perfect science!
It applies mathematical models and statistics but interprets and tests them in a real-world economic and behavioral contexts.

Recall that the finance goals of the corporatio are, from the stockholders' point of view:

• maximize current wealth
• transform wealth into most desirable time pattern of consumption
• manage risk characteristics of the choosen consumption plan

But... how do cash flow between financial markets and the firm's operations?

Recall that, in presence of such cash-flows, the Net Present Value (NPV) is defined as:

• NPV depdens only on the forecasted cash flows and the opportunity cost of capital $r$
• $\text{NPV}(A+B)=\text{NPV}(A)+\text{NPV}(B)$

1. Agency Problems and Corporate Governance

The agency problem is defined as a conflict of interest inherent in any relationship when one party is expected to act in another's best interests.

In particular, the principal-agent problem is a conflict of interest that occurs when an agent (manager) authorized to act on behalf of a principal (owner) pursues their own self-interests rather than maximizing the principal's goals

Agency costs reduce firm value due to agency problems:

• value lost because managers do not maximize the value of the firm
• costs of monitoring managers and intervening when problems arise.

Principals agency problems come from:

• not put in sufficient efforts
• use cash on perks and private benefits
• over-invest in search of power and prestige
• be reluctant to take risks or take too many risks
• focus on short-term results at the expense of long-term value

In the corporate world, Boards of Directors exist to solve this problem.
In particular, in the US and the UK, boards are composed as follows:

• One single board with outside non-executive directors and inside executive directors (CEO, CFO) to provide the board with necessary expertise and information about the firm.
• The majority of the directors has to be indipendent according to NYSE and NASDAQ (in practise, around 85% are independent) to ensure that the people monitoring the managers aren't also friends with them or financially dependent on them.
• It should not be too big to generate a free-rider problem and not too small to be unable to handle the complexities.
• Directors should not sere too many boards.
• Annual elections for a share of the board, some directors are not changed yearly.

On the other hand, shareholders can also play a strong role in monitoring the firm with three main tools:

• Voting
  • Binding versus Advisory votations
  • Proxy fight (aggressive move where an activist shareholder tries to replace the current board by persuading other shareholders to use their "proxy" votes and vote on behalf of another.)
  • Dual-Class Equity when some shares (usually held by founders) have more voting power (example: 10x, 100x) of "normal" shares.
• Engagement
• Governance through exit from the company

Auditors monitor the firm ensuring consistency with generally accepted accounting principles (GAAP):

• in case of no problems: document certifying that the financial statements fairly represent the company's financial conditions
• in case of problems:
  1. Qualified option: accounts have not fully acted according to GAAP
  2. Adverse option: accounts violate many GAAP rules.

Moreover, lenders usually track company's asset. Takeover involves funding the acquisition of a target company, typically through cash, debt, equity issuance, or a mix of these methods when assets are not being used efficiently.

2. Stakeholder Capitalism and Responsible Business

Stakeholders are individuals, groups, or organizations with a vested interest in, or who are affected by, the actions, decisions, and success of a project, company, or organization

• employees
• customers
• suppliers
• local and regional communities
• the enviroment
• the government

Milton Friedman in 1970 with its article The Social Responsibility of Business is to increase its profits rejected stakeholder capitalism and argued that a company’s only responsibility is to its the shareholders:

Friedman's argument is based on three points:

• maximizing shareholder value requires to invest in stakeholders and take them seriously
• government policies ensure companies will engage in socially responsible behavior
• maximizing shareholder value gives shareholder maximum freedom to support the social objectives they care about.

With that, Friedman also pointed out that it is in the companies' self interest to invest in their local community and proposed that all future cash flows should be included into the NPV calculation, including those arising through stakeholders.

According to this view, since prosperity depends on profits and externalities and externalities are usually addressed by laws and government, the market cannot police itself regarding social harm; that is the job of the state.
In other words, the government sets the "rules of the game.", then the company plays to win (maximize profit) within those rules.

From the individual investor's perspective, each person has his own values and social goals, so the management should just give the shareholder the maximum amount of money and leave him with maximum flexibility on how to spend it.

This is called Enlightened Shareholder Value (ESV) Theory that, from a practical point of view, has two main advantages:

• it provides a clear criterion for making investment decisions (positive NPV)
• it proivides a clear criterion for judjing performances (stock price).

Violations of Friedman's assumptions may justify stakeholder capitalism:

• Assumption 1: well functioning governments:
  • government may be influenced by lobbying
  • elections are not very frequent
  • regulation cannot regulate qualitative issues effectly (negative externalities are not priced!)
• Assumption 2: companies have no comparative advantage in serving society
  • companies have comparative advantages in activities they control
  • companies have comparative advantages in expertise
• Assumption 3: investing in stakeholders is instrumental and functiona to increase profits
  • it's impossible to calculate the return of investing in stakeholders

In reality, investing in stakeholders splits the pie in short-term but grows it in the long-term in ways that could not be predicted (uncertainty, NPV calculation,..) and, at the end, both shareholders and stakeholders are better off than before

The potential advantage of stakeholder capitalism is that allows managers to pursue stakeholder interest even if doing so can't be justified by an NPV calculation.
However, this causes:

• no clear rule to replace NPV
• accountability to everyone means accountability to no one.

Moreover, there's arbitrariness at least regarding two dimensions:

• weighting: how much shareholders vs stakeholders value
• comparability: how to measure shareholder value (USD) vs staekeholder value _(salary, happines, enviroment etc...)

Responsible business lies at the middle between shareholder and stakeholder capitalism.

• It creates value for shareholders by creating value for society ç(with an explicit duty to shareholders)_
• While Corporate Social Responsibility relates to non-core activites (donations, philantropy), responsibl business is about the core activites of a firm.
• Guiding Principle: create vaue for society and at least don't reduce shareholder value significantly.
  • Principle of Multiplication: does an investment in a stakehlder generate a greater benefit?
  • Principle of Comparative Advantage: can the company deliver more value through an activity than others?
  • Principle of Materiality: are the stakeholders an objective of the company's business?

Generally speaking, some firms tie CEO and management's pay to ESG targets, so the company is more aligned and motivated to hit them. In 2023, 76% of S&P500 firms linked executive pay to at least one ESG target.
However, the CEO may focus only on the metric and miss the point. Secondly, it's an extrinsic, not intrinsic, motivation: CEOs focus on ESG target because they earn a bounus, rathen than care really about the enviroment.

To ensure that companies are being run responsibly, ESG rating agencies provide an overall assessment of a company's ESG performance, similar to how credit agencies apply a reding on creditworthiness, however:

• ESG ratings are inconsistent. The correlation between ratings of two different agencies are, on average, 0.28-0.71; compare do 0.9 for credit ratings.
• 38% is casued by the use of different attributes
• 56% is due to measurement
• 6% is due to weigh: different providers place different importance on individual indexes/components of the rating.

3. Credit Risk and the Value of Corporate Debt

The price of a bond s the present value of all cash flows generated by the bond (coupons and face value at maturity $T$) discounted at the required rate of return $r$.

Note that the price of long-term bonds is more sensitive to changes in the interest rate than the price of short-term bonds.

However, it is very important to distinguish between promised and expected yields.

Suppose Giacomo GmbH offers a 5% 1-year note, emitted at par ($1000CHF$), with a risk-free rate $5$.
Consider also that, unfortunately, Giacomo has a $20$ chance of default and only pay $500CHF$.

The Present Value of the Note is then:

However, considering the risk of default, we can calcualate the expected payoff of the note as:

We thenm discount the expected payoff to obtain the present value of the bond:

If we consider the face value promised by Giacomo (hence excluding the possibility of default), we obtain the Promised Yield:

Note that, even if the promised yield is so high, the expected yield is always 5%:

$AAA$ bonds by Moody's are the highest-grade bonds and are issued only by a few blue-chips companies.
Historically, the promised yield on these bonds has been about $1$ higher than the yield on 10-Year Treasuries.
On the other hand, $BAA$ bonds are rated three so called notches lower, and the yield is historically $2$ higher.

The total return on a bond investment over a specific period, accounting for both the coupons received and the change in the bond's market price.

YTM is the internal rate of return (IRR) earned by an investor who buys the bond today at the market price and holds it until maturity, assuming that all coupons are reinvested at the same rate.

Duration is the weighted average of the times to each of the cash payments. It is the primary tool for estimating a bond's sensitivity to interest rate changes.

Often we use Modified Duration to calculate the actual percentage change in price for a 1% change in yield ($y$):

Duration is a linear approximation of the interest rate and the price, convexity takes into account the second order relation, especially important for bigger interest rate changes.

Intuition: A bond with higher convexity drops less when rates rise and gains more when rates fall compared to a bond with lower convexity.

It is possible to insure corporate bionds with financial instrument called Credit Default Swap (CDS) (Warren Buffet call them "financial weapons of mass destructoin")

CDS are financial derivatives acting as an insurance against the risk of a borrower defaulting on debt (bonds). The buyer makes regular premium payments to a seller, who agrees to compensate them if a specific credit event, like bankruptcy or insolvency, occurs.

CDS are traded over-the-counter (OTC) and their premiums are quoted in basis points, reflecting the market’s view on the risk of default.

Note that a buyer doesn't have to own also the underlying (the debt, bonds), he can just buy a CDS simply betting that the borrower’s credit health will decline or that they will default (speculation). In this case, they are called "naked" Credit Default Swaps.

Regarding naked CDS, especially after 2008-crisis, CDS are heavily regulated. For example, in the EU, buying naked CDS on government bonds is NOT allowed to avoid speculation attacks on countries.

Example during the Credit Suisse Crisis, CDS of that banks went incredibily high.

The main difference between corporate and treasury bonds is that the company has the option to default, whereas the government supposedly doesn't.

Consider the following example:

Giacomo's GmbH borrowed $50CHF$ per share but then the firm faced hard itmes and market value of its assets fell to $30CHF$.
Giacomo's Bond and stock prices fell respectively to $27CHF$ and $3CHF$.

If Giacomo's debt were due and payable now, the frm could not pay the $50CHF$ originally borrowed, it would default leaving bondholders with assets worth USD 30 and shareholders with nothing.

However... the reason the stock ahs a market value of $3 CHF£ is that the debt is NOT due immediately, but oneyear fromm now.

But, Giacoo is not compeòlled to repay the debt at maturity, why?

• If the value of assets $<50CHF$: the value of the assets is less that it owens to the bondholders. THerefore, it will exercise its option to defulat on the debt and the debtholders will receive the assets.

So, Giacomo's GmbH issued a safe bond, but at the same time acquired an option to sell the firm’s assets to the bondholders for the amount of the debt. The exercise price is $50CHF$ for this bond, e.g., the face value of the bond

• If the value of assets $>50CHF$: Giacomo will not exercise the option to default.

In general terms, we can say:

Intuition: the Default Put represents the value of the "limited liability" granted to the company's owners.

For example, if we assume returns on firm's assets $60$, risk free-rate $10$ and a current value of assets $30CHF$, exercise price of default option $50CHF$, we get:

From the Black Scholes model, we get that the value of the default put is $18.6CHF$ and:

In, general, we can incurr in the following scenarios:

Ratings are given by ratings agencies (S&P, Moody's, Fitch, AM Best etc etc...).
The highest quality bonds are rated triple-A ($AAA$).

• Investment-grade bonds are the equivalent of $BAA$ or higher
• Below that, they are called junk bonds (or NON-investment-grade).

_Based on the financial ratios, this is an overview of the median rations for U.S. nonfinancial firms.

Instead of comparing different ratio, a common way of evaluating the possibility of default is merging them in a single index: The Altman's Z Score, computed as:

where:

• $x_1:$ working capital / total assets
• $x_2:$ retained earnigs / total assets
• $x_3:$ EBIT / total assets
• $x_4:$ market value of equity / total liabilities
• $x_5:$ sales / total assets

Common interpretations:

• $Z>2.99$: safe zone
• $1.81<Z<2.99$: grey zone
• $Z<1.81$: red zone

4. The Many Different Kinds of Debt

Before we start, some bond terminology:

• indenture/trust deed: between the c9ompany and a trustee that represents the bond-holders. The trustee must see that the terms of the identure are respected and look after the bond-holders in case of default. (usually a big commercial bank that monitors and acts in case of default)
• registerd bond: the company keep records of the owners, interest and principal are paid directly to the bondholders (the big majority of bonds traded today)
• bearer bond: the company doesn't keep records of the owners, that have to physically cut off a coupon and present it to a bank to receive the interest payment
• accrued interest: amount of accumulated interest since the last coupon payment
• coupon: annual/semi-annual interest paid on a bond
• depentures (=bonds): long term unsecured issues on debt
• mortgage bonds: long term secured debt, often containing clamins against a specific property
• collateral trust bonds: bonds secured by common stocks of other securities from the borrower
• equipment trust certificate: secured debt generally used to finance railroad equipment
• asset-backed securities (ABS): sale of cash-flows derived directly from a set of bundled assets
• mortgage-backed securities: set of mortgage loans sold, owners recieve a portfion of mortgage payments (off-balance sheeet).
• foreign bond: bonds sold to local investor in another' country's bond market
• yankee bond: bonds sold publicly by a foreign company in the US
• samurai: bonds sold by a foreign firm in Japan
• bulldog: bonds sold ny a foreign firm in the UK
• eurobond: bond demoninated in one country's currency but marketed internationally
• global bonds: very larg bond issues marketed internationally and on individual domestic markets.

A callable bond allows the issuer to call back (repay) the debt before maturity, valuable to reduce the company's leverage, it often happens when interest rates fall.
A puttable (retractable) bond allows the investor to be repaid for the debt, it is a protective covenant for the investor, it often happens when interest rates increase.

A sinking fund is a fund established to retire debt before maturity.

Since invesotrs know that there's risk of default, covenants are used to limit the company default position, for example by:

• debt ratios: limits of further borrowing (senior debt limits senior borrowing, junior debt limits senior and junior borrowing).
• Security: negative pledge: the company promises not to give any of its assets to create a security interest for other lenders, unless the current bondholders are given an equal share of that security.
• Leasing (similar to secured borrowing)
• Dividends

A convertible securty can change during his life: it stars as a bond, but it can be subsequently turned into equity.

• Value of the plain bond (if not converted), think at this values as a lower bound of the price of the convertible bond:

• Value of the converted bond/stock if the bond is converted:

• At maturity, the bondholder can choose to receive the payment of the bond or convert it into common stock:

Instead of selling convertible bonds, firms sometimes sell a package of straight bonds and warrants. Warrants are simply long-term call options that give the investor the right to buy equity.
Warrants are usually issued privately, can be detached, exercised for cash and are usually taxed differently. Note also that warrants can be issued on their own.

• Catastrophe (CAT) bonds: payments are reduced in the event of a specified natural disaster
• Contingent convertibles (CoCos): bonds that convert automatically into equity as the value of the company falls
• Equity-linked bonds: payments are linked to the performance of a stock market index
• Longevity bonds: payments are reduced or eliminated if there's a fall in mortality rates
• Mortality bonds: payments are reduced or elimitated if there's a jump in mortality rates
• Pay-in-find bonds (PKIs): issuer can choose to make interest payments in cash or in more bonds with same face value
• Credit-linked bonds: coupon rate changes with the company's rating
• Reverse floaters (yield-curve notes): floating-rate bonds that pay a higher rate of interest when other interest rates fall (and a lower rate when othe rates rise)
• Set-up bonds: coupon payments increase over time.

Commitment:

• Revolving credit: maximum amount a company can borrow, repay, and re-borrow as needed during the period.
• Evergreen credit: revolving credit without a fixed maturity that automatically renews.

• Bridge loan: short-term loan between permanent finaning or important debt events
• Self-liquidating: loan designed to be repaid by the asset it was used to purchase.
• Term loans: standard loans for a specific amount that are repaid over a set period (usually 1–10 years)

In a Syndicated Loan, a group of banks (the syndicate) works together to provide the funds.

• Lead Bank: Arranges the deal and does the heavy lifting.
• Participants

LIBOR: it was the interbank offered rate, commonly used as the reference for loans. The financial crisis undercut confidence in LIBOR, now it is now longer used.

SOFR (SECURED OVERNIGHT FINANCING RATE): designed to replace LIBOR, it is the average interest rates on overnight Treasury repo transactions (the main difference is that SOFR is transaction-based, not banker-estimated based as the LIBOR).

In an overnight repo transaction, one party sells a security (usually a US Treasury Bond) to another party with a simultaneous agreement to buy it back the very next day at a slightly higher price.

5. Leasing

A lease is a rental agreement that involves a series of fixed paymentsfromthe lessee (user) to the lessor (owner).

• Operating lease: short-term, cancelable. (Historically, these were "off-balance sheet," but modern accounting standards (like IFRS 16) now require to be recognized as liabilities.)
• Financial lease: long-term, non cancelable. (Often, at the end of the term, the lessee often has the option to buy the asset).

Some more possitibilities in leasing include:

• Rental lease (full service): the lessor handles everything, including maintenance, insurance and taxes.
• Net lease: the opposite of full service.
• Direct lease: arrangement where the lessee identifies an asset, and the lessor (often a bank or leasing company) buys it from the manufacturer just to lease it to the lessee.
• Sale and leaseback: A company sells an asset they already own (like a headquarters building) to a buyer and immediately leases it back in order to unlock some capital (liquidity) while still using the asset.
• Leveraged lease: a three-party transaction involving a lessee, a lessor, and a lender. The lessor borrows a significant portion of the asset's cost (usually $60\%$ to $80\%$) to purchase it.

PROs of leasing:

• short-term leases are often convenient
• maintenance is provided
• standardization leads to lower costs
• tax shields/advantages can be used
• leasing preserves capital

CONs of leasing:

• leasing avoid capital expenditures control
• leases may be off-balace sheet financing

What happens if a bankrupt lessee takes a lease? What happens if the lease is rejected?

If the leases is confirmed,the lessee continutes to use the asset and must sustain the payments. If the lease is rejected, the asset is returned to the lessor.
If the value of the returned asset is not enough to cover the remaining payments, the lessor's loss becomes an unsecured claim on the bankrupt firm.

The Equivalent Annual Cost of an asset is the rental payment sufficient to cover the present value of all the costs of owning and operating an asset. The rental payments are hypothetical, (just a way of converting a present value to an annual cost). In the leasing business the payments are real.

If a business/firm needs an asset:

• buy it if the equivalent annual cost of ownership and operating is less than the best lease rate
• if it plans to use it for extended period, usually annual cost of ownership and operating is less than the leasing rate. There are two corner cases here operating lease make even sense despite the higher cost:
• the lessor is able to manage the asset more efficiently/at less expense than the lessee
• operating leases often contain useful options

As mentioned before, historically, operating leases have been off-balance sheet. Consider then the following scenario.

Suppose that, in the past (when leaes were off-balance sheet), a company needed one asset. It has two main options:

• borrow the capital and buy the asset $⟹$ the debt shows up under the liabilities, the bought asset under assets.
• lease the asset $⟹$ the lease rate shows up under expenses in the income statement, no impact on the Balanche Sheet.

Companies usually preferred the secondo option becasue, by keeping the new need off the balance sheet, they showed stronger financial metrics:

• Lower Leverage: Debt-to-Equity ratios look lower
• Higher ROA: Return on Assets ($ROA=\frac{NetIncome}{TotalAssets}$) looks higher because the "Total Assets" denominator is smaller.

According to actual accounting standards however, most leases (even operating ones) must now be recorded on the balance sheet as a Right-of-Use (ROU) Asset and a corresponding Lease Liability.

Suppose then the following example.
Giacomo's GmbH needs to buy a camper-van and asks for a 1-year lease to RoadSurfer GmBh. How much should RoadSurfer charge for that lease?

Knowing all its costs (initial cost, maintenance, tax shields, depreciation) RoadSurfer can then calculate it's break-even rent.

Consider now the following example. Giacomo GmBh is again considering to buy a camper-van worth $100^{\prime }000\text{ CHF}$ with a 8 years life. Roadsurfer offers the 8 years loan at $16.200\text{ CHF}$ per year, but Giacomo remains responsible for maintenance, insurance and operating expenses.

To calculate the Net Present Value of the lease, we have to value the incremental cash flows from the lease and discount them at the after-tax interest rate.

Another financing options would be represented by loan. To compare leasing and loans, we can compare a lease to a loan that has the same impact on future cash flow.

• The lease requires paying $12.80$/year for 7 years.
• We create a hypothetical loan that also requires paying $12.80$/year _("Net cash flow of equivalent loan" row):.

Considering the same interest rate, we then see which one brings the bigger amount of money at time 0:

• The loan gives you $66.86$ today in exchange for those future 12.80 payments.
• The lease gives you $66.20$ (the value of the asset you get to use) for the same future payments.

6. Managing Risk, Options

Reason why risk reduction does NOT add value:

• hedging is a zero sum game
• investors can hedge themself $\to$ they have a do-it yourself alternative

Most businesses face the risk of events that can cause financial stress to them (both financial or business-related risks). The cost and risk of a loss can be shared by others who share the same risk $\to$ the firm can transfer the risk to an insurance company.

Catastrophe bonds (CAT bonds) allow insurers to transfer risk to bonholders by selling bonds whose cash flow payments depend on the level of insurable losses NOT oncurring.
More on CAT bonds here [Investopedia].

• on some CAT bonds (Indemnity Trigger), payments are reduced if claims against the issuer exceed a limit $\to$ the problem is that the insurance company, knowing this, may try to underwrite more counterparties to gain additional premia, therefore creating a problem of moral hazard for the insurance company (since it has less incentives to be careful)
• in some other cases (Index Trigger), payments are reduced if claims against the entire industry exceed a limit $\to$ partial solution to the moral hazard problem

• Derivatives: any financial contract derived from another
• Option: gives the holder the right to buy/sell a security in the future at specified price
• Option Premium: price paid for the option above the price of the underlying
• Intrinsic Value: difference between the strike price and the security price
• Time Premium: value of the option above the intrinsic value
• Exercise Price (Strike): price at which the underlying can be bough/sold
• Expiration Date (Maturity): last date on which the option can be exercised
• American Option: can be exercised any time
• European Option: can. be exercised only on the expiration

• a call option gives the right to buy the underlying.
• a put option gives the right to sell the underlying.

For an European Option:

• $\text{C}$: premium of the call option
• $\text{P}$ premium of the put option
• $PV(K)$: present value of the strike price
• $\text{S}$: underlying price

The idea behind the put-call parity equation is that the two following portfolio must have the same value, otherwise we end up with an arbitrage opportunity:

• Portfolio 1: $\text{Call}+\text{ Money to buy the asset at }K,T$
• Portfolio 2: $\text{Put}+\text{ Asset}$

In case this equation doesn't hold, there's of course an arbitrage opportunity and, to capture a profit, the following strategies can be used:

• $C+PV(K)>S+P$:

  • Reversal (the Call is overpriced):
  • The "synthetic" stock position (the call and the cash) is worth more than the actual stock and the put.
  • Strategy Sell the Call, Borrow the present value of the strike price, Buy the Put, and Buy the Stock.

• $C+PV(K)<S+P$:

  • Conversion (the Put is overpriced):
  • Strategy: Buy the Call, Lend (invest) the present value of the strike price, Sell the Put (Write it), and Short the Stock.

Jack Mining Company is worried about short-term volatility in revnues.
Gold currently seels for USD $1300$/ounce, but the price is volatile and could fall to $1220$ or rise to $1380$ in the next momth. Jack will sell $1000$ ounces to the market in the same period.

1. If Jack remains unhedged (Market Exposure), he remains fully exposed to the "spot" price.

(Where $S$ is the spot price and $Q$ is the quantity of 1,000 ounces)

2. If Jack hedges his position with futures (Price Lock), he eliminates all uncertainty by pre-selling their gold at a fixed price, ensuring a guaranteed revenue regardless of the future price.

(Where $F$ is the locked-in futures price of $1,310)

• in this case, Jack enters a short position on futures (obligation to sell the ounces at a specified price).

3. If Jack hedges with option, he an "insurance" that sets a minimum sale price (strike $K$) while allowing them to benefit from higher market prices, but they must subtract the cost of the insurance (premium) from their total.

(Where $K$ is the strike price of $1,300$ and $P$ is the premium of $110 per ounce)

Generally speaking, a business has:

• Business risk affecting fixed and variable costs and revenues $\to$ operating leverage
• Financial Risk due to IR, FX, commodity price changes etc...

The basic relationship between futures prices and spot prices for equityies:

• $F_t$: futures price on contract of $t$ length
• $S_0$: spot price (today)
• $r_f$: risk-free rate
• $y$: dividend yield

For commodities, the basi relationship becomes:

• The net convenience zield is generally positive and future prices are generally below spot prices. _(This dynamic is called backwardation).
• Sometimes storage prices are high and there's plenty of commodities available, so future prices are above spot prices. _(This dynamic is called contango).

Note that the convenience yield is the implicit, non-monetary benefit of physically holding a commodity compared to owning a futures contract (example: avoiding shortages or ensuring production).

Consider also that the holder of a future contract misses out any dividend or interest payment from the underlying but he doesn't not have to pay for storage costs.

A forward interest rate is a rate for a loan starting in the future. To price it, we use the following formula:

where $r_n$ is the current rate for a $n$-year term and the same applies for $m$.

Some future cash flows are fixed, others may vary depending on the interest rates, rates of exchanes or prices of commodities. In a swap contract, one counterparty exchanges a fixes set of cash for a floaitmg set of cash flow and the second counterparty takes the oppositve position.

A swap uses a Notional Principal ($L$).
This amount is never exchanged between parties; it is simply the "dummy numner" to calculate interest.

• Fixed Rate Payer: Pays an agree and constant interest rate. They are essentially "shorting" interest rates (betting they will go up).
• Floating Rate Payer: Pays a variable market rate (like SOFR). They are "long" interest rates _(betting they will stay low)_A

In practice, only the difference between the two interest amounts is payed (this reduces credit risk for both parties).

• Scenario A (Market Rate < Fixed Rate): the Fixed Payer pays the difference.
• Scenario B (Market Rate > Fixed Rate): the Floating Payer pays the difference.
• Scenario C (Market Rate = Fixed Rate): no money moves _("Wash" scenario)_A

When a swap is created, its Net Present Value (NPV) is $0$. The fixed rate is mathematically "calibrated" with discount factor $Z$ so that the expected value of the floating payments equals the fixed payments today.

To calculate the current value value of an existing swap that changes to a new $r^{\ast }$:

A swap curve (also called the "LIBOR curve/SOFR curve/EURIBOR curve) is the graphical representation of the relationship between swap rates and different maturities (tenors). It's a line that shows you the "fixed rate" the market expects to pay for a swap lasting different maturities.

A currency swap is a contract where two parties exchange cash flows in different currencies over time.

It can be decomposed in:

• a spot FX transaction today
• plus a series of interest payments
• plus a reverse FX transaction at maturity

When a business receive cash flows that depends on interest rate, the firm can manage its risk by buying a bond and matching duration. In this way, exposure to small interest rate changes is zero.

In general, if we want to hedge against changes in the value of asset $A$ (oil) using an offsetting sale of asset $B$ (example: oil futures), we use the following formula:

• $\delta$: sensitivity of $A$ to change in value of $B$ (hedge ratio)
• $\alpha$: unexpected drift/changes

7. International Financial Management

The forward-premium measures whether the market expects a currency to be more expensive or cheaper in the future compared to right now. It is represented by the annualized rate, defined as:

• If the result is Positive (+): the currency is at a Forward Premium (It is expected to become more expensive).
• If the result is Negtative (-): the currency is at a Forward Discount (It is expected to become cheaper).

In general, these relationships are known as the International Fisher Effect (IFE) and Interest Rate Parity (IRP)., that describe the equilibrium between a home/domestic currency ($H$) and a foreign currency ($F$).

The Fisher Effect represents the relationship between nominal interest rates ($r$) and expected inflation (ì$i$). In an efficient market, the ratio of nominal interest rates equals the ratio of expected inflation:

The Interest Parity Equation shows that the difference between the Spot rate ($S$) and the Forward rate ($F$) should offset the difference in interest rates between the two countries to prevent arbitrage:

We can then add a final equation, the Purchasing Power Parity: it explains that the expected change in the exchange rate is driven by the difference in inflation rates between the two countries:

If combine them all, we get the the International Finance Linkages ("Four-Way Equivalence"):

When calculating the cost of capital in an international context, we need to adjust local valuation to account for foreign exchange risk, country risk, and differing inflation rates.

To obtain the required return for a project, the Capital Asset Pricing Model (CAPM) is often the starting point:

To discount the expected cash flows in another currency, we convert the cost of capital from $CHF$ to second currency _($USD$ in the folloeing example)

Note that this formula (or method) doesn't take into account business risk!(every country is exposed to risk, but some parts of the world are more vulnerabil, see the below table).

8. No Lecture

9. Financial Analysis

10. Financial Planning, Working Capital Management

11. Treasury at Holcim / Amrize Case

12. Mergers

13. Corporate Restructuring

14. Financial Crises and Regulatory