Finance Course by Olivier LevynE

Olivier Levyne is a Finance professor with almost 30 years experience in teaching in the field of finance at HEC, ESCP and ISC universities in Paris, as well as practice in the field of mergers and acquisitions at an investment bank. The professor offers courses in both English and French to interested students that include a range of material: from handouts, summary sheets and slides to models designed for financial simulations and short films that further explain the models in Excel.

Principles of Corporate Finance


This part covers the following topics:
1. Refresher on financial analysis
2. Cash management
3. Principles of trading on options
4. Capital budgeting: Net Present Value (NPV), Internal Rate of Return (IRR), etc.
5. Leverage effect principle
6. Cost of equity
7. Weighted Average Cost of Capital (WACC)

It provides a summary of the most important principles of corporate finance and prepares you to dive deeper into the world of Mergers and Acquisitions.

Posted on Thursday, March 26, 2020.

Financial options

the course

An option is a right to buy (call) or to sell (put) an underlying asset, on the expiration date (European option) or during a given period (American option) at a price which is known in advance (Strike price). It enables various trading strategies in order to speculate on:
• the increase of the price of the underlying asset
• the decrease of the price of the underlying asset
• the volatility of the price of the underlying asset
• the stability of the price of the underlying asset.

Some combinations of options enable to make profits if the underlying asset's price is stable while having a floor for losses in case of volatilty: butterflies and condors.

The combination of positions on options and futures enables aribtrages, namely strategies the results of which do not depend on the price of the underlying asset and are therefore known in advance: reverse conversion and conversion. The box spread is an arbitrage which relies only on options: it does not use any future contract. Such derivative products can be valued in discrete time (Cox-Ross-Rubinstien) or in continuous time (Black & Scholes).
Such principles are detailed in the following handout:

Cox-Ross-Rubinstein's Option Pricing Model

Cox, Ross and Rubinstein have proposed, in 1979, an option pricing model in discrete time. Their 2 main assumptions are the following ones:

• The time t between the option's valuation date and its expiration date can be divided into n periods
• During a given period, the underlying asset's spot price either goes up (and is mutiplied by a number equal to u), or goes down (and is multiplied by a number equal to d). Assuming k upward moves and n-k downward moves, the generic spot price of the underlying asset on expiration date is: u^(k) x d^(n-k) x S where k is a natural number taking its values in the [0,n] interval

On expiration date of the call, its premium (Cn) is equal to its intrinsic value (IV) which can be calculated for each possible spot price of the underlying asset: Cn=max(0;uk.dn-k.S -E). Then, the method consists in going backward till the valuation date to get the call's premium. This is based on a tree, in which each node is the value of a call that is defined by:
C=1/(1+r)^(t/n) x [p x Cu + (1-p) x Cd]
r = risk free rate
p = probability of an upward move during a period
Cu = premium of the call at the end of the next period, assuming an upward move
Cd = premium of the call at the end of the next period, assuming a downward move
p= probability of an upward move during a period

The evidence of the formula and of the useful intermediary results is detailed in the first Handout of this page. The following handout describes, step by step, the Cox-Ross-Rubinstein's valuation of the call's premium based on an illustrative example:

Greek Letters

Partial derivatives of the Black & Scholes formula enable to get sensivities of options premiums to 4 paramters. These sensitivites are often named by Greek letters.

• Delta for the sensivitity to a change in the spot price of the underlying asset
• Vega for the sensivitity to a change in the volatility of the underlying asset
• Theta for the sensitiity to a change in time to expiration
• Rhô for the sensivitity to a change in the risk free rate.The delta also enables to calibrate a hedging strategy. But, as the delta depends on the spot price of the underlying asset, which is changing everyday, the delta is also changing and the hedging has to be adapted accordingly.

The Gamma provides a measure of the sensitivity of the delta to changes in the spot price of the underlying asset. The following slides present the various Greek letters with an illustrative example:

Posted on Thursday, April 2, 2020.

real options


Real options enable us to solve corporate finance problems with customary financial options pricing models (Black& Scholes and Merton in continuous time, Cox-Ross-Rubinstein in discrete time). Specific real options models were also developed with examples such as Dixit and Pindyck's model, which helps options with no expiration date to find the best time for investment. The slides and the underlying excel model that are provided below correspond to a slight extract of a more detailed Real Options course. This course has been been taught for more than seven years in the Master of International Finance at HEC Paris.

Detailed Content​

1. Equity valuation
2. Growth option
3. Value of a patent in the pharma industry
4. Pricing of an oil concession
5. Breakdown of the debt value taking LGD into account

Userful Papers On Options​

Fischer Black and Myron Scholes explain in their seminal paper, published in 1973 by the Journal of Political Economy, that the shareholders have an option on their firm's assets. In other terms, the equity value is the call premium on the firm's assets, the strike price being the face value of debt ie the amount to be repaid: "The Pricing of Options and Corporate Liabilities"​

Robert Merton proposes a formula to calculate the risk premium of a corporate debt in a paper published in 1973 by the Journal of Finance: "On the Pricing of Corporate Debt: the Risk Structure of Interest Rates"

Posted on Thursday, April 9, 2020.

mergers and acquisitions

Corporate Valuation​

As taught in Master in Financial Economics and CEMS at HEC Paris:
1. Listed peers
2. M&A peers
3. DCF
4. Net asset value and Sum of the Parts

Tender Offers

1. Paid in cash
2. Paid in shares
3. Mixed offers

Fine-Tuning Of The Perpetuity Growth Rate

The final perpetuity growth rate in a DCF can't necesserally be looked uon as the GDP's. Indeed, the expected growth of the firm is not that of the economy. The following document explains how to have a perpetuity growth rate in line with the company's (or industry's) expected growth rate by the market

Listed Peers Approach

Preliminary valuation approach of Swatch based on a simple sample of 2 listed peers: LVMH and Richemont.

The excel file below includes financial information, based on a Reuters' consensus of brokers, for the firm to be valued and its peers. The brokers consensus is taken from the Zonebourse website and calculation of customary multiples (EV/Sales, EV/EBITDA, EV/EBIT, P/E) and application to the corresponding aggregates of the firm to be valued.

The slides provide a justification of the peers' selection, reminding that Swatch is a luxury group, and not only the manufacturer and distributor of plastic watches and the presentation of the outputs, in a table and in a graph, and provision of comments on the discrepancies between the outputs of the various valuations.

The video below presents how to prepare a graph to summarize the outputs


It is often hard, for the external advisor, to assess the synergies that will be developed after a contemplated deal. These synergies will be estimated in the background of workshops that will be attended by the bidder's and the target's professionals. However, it is possible to determine the required pre-tax synergies to get an EPS accretive deal. These preliminary synergies will have to be validated by the bidder's management

Leveraged buyout (LBO)

The following videos encompass information about the structuring of a LBO:

Target’s income statement with no interests (as they depend on the net debt which will be in the balance sheet to come)
This income statement is based on a Reuter’s consensus of brokers from sales to EBIT. The assumptions for the soft landing are:
a. Linear phasing of the growth of sales
b. Sustainability of the EBITDA margin and the D&A ratio of the brokers’ last year
c. 25% corporate tax rate

Cash flow statement to be looked upon as the change in net debt
Cash Flow = Net Income – Dividends based on a 100% payout rate applied to the previous year’s net income + D&A – Net Capex – Change in WCR
For Capex: linear phasing
For WCR in the balance sheet: sustainability of the 2018 WCR/sales ratio
Then preparation of the balance sheet.

Business plan of the holding company
This includes the search of the appropriate maximum acquisition debt which enables the holding’s cash balance to be always positive.
Otherwise (negative cash balance), thé holding runs into debt via an overdraft which is not possible based on the loan agreement.

Calibration of the holding’s capital subscribed by the PE fund so that its IRR is 20% over 3 years

Posted on Thursday, April 16, 2020.

financial institutions

General principles

Financial institutions (banks and insurance companies) have to abide by regulations which focus on their solvency:
• For banks and other credit institutions (consumer credit, leasing, factoring...) : Basel 3
• For insurance and reinsurance companies: Solvency 2

The calculation of these ratios is based on restated consolidated aggregates.

Custodians and asset managers often have a banking licence. In that case, they have to abide by the Basel 3 regulation.

For each country the regulation is performed by a domestic watchdog. In France, the ACPR (Autorité de Contrôle Prudentiel et de Résolution) monitors the solvency of financial institutions.

30 banks are looked upon as systemic ones. In other words, the bankruptcy of one of them would generate a systemic crisis for global finance. In that context, 8 European banks are regulated by the European Central Bank.

30 banks are looked upon as systemic ones. In other words, the bankruptcy of one of them would generate a systemic crisis for global finance. In that context, 8 European banks are regulated by the European Central Bank. The 30 systematic banks are:

Europe and UK:
• 4 in France: BNP Paribas, BPCE, Crédit agricole & Société générale
• 1 in Germany: Deutsche Bank
• 1 in the Netherlands: ING
• 1 in Spain: Santander
• 1 in Italy: Unicredit
• 2 in Switzerland: Crédit suisse & UBS
• 3 in the United Kingdom: Barclays, HSBC & Standard Chartered

North America:
• 8 in the USA: Bank of America, Bank of New York Mellon, Citigroup, Goldman Sachs, JP Morgan Chase, Morgan Stanley, State Street & Wells Fargo
• 2 in Canada Banque: Toronto-Dominion & RBC

• 4 in China: Agricultural Bank of China, Bank of China, CCB & ICBC
• 3 in Japan: Mitsubishi UFJ, Mizuho & Sumitomo Mitsui


Each bank has to respect regulatory ratios, among which a Core Equity Tier 1 (CET1) ratio = CET1 / RWA where:
CET1 = shareholders equity - intangible assets including goodwill - shareholdings in other financial institutions
RWA = Risks Weighted Assets. The RWA correspond to the commitments that are undertaken by the bank, the main ones being the loans granted to retail and corporate clients.

The weighting coefficients are generally calculated thanks to the bank's internal system that is closely monitored by the regulator(s). The weigthing coefficient is the more important as the risk of default of the borrower is high. Since 2019, according to the Bank for International Settlements (BIS), the minimum CET1 ratio is 7.0% = 4.5% + 2.5% (capital conservation buffer) before taking a 0.0%-2.5% countercycle buffer which is applied when credit growth is judged to result in an unacceptable build-up of systematic risk. A target CET1 ratio is prescribed to each bank by its regulator(s).

Given the magnitude of the CET1 ratio, it is systematically embedded in the valuation of a bank:
• The bank's equity value is equal to the sum of present values of future dividends that correspond to forecasted levels of excess equity. Excess equity correspond to the maximum dividend that could be paid out to the bank's shareholders taking the target CET1 constraint into account. This is the reason why the valuation of a bank is based on a Dividend Discount Model (instead of DCF model) • A listed peers and/or M&A peers approach can also be conducted. The 3 main multiples are generally taken into account: P/E, P/BV (= market cap / book value of consolidated equity, group share), P/TBV (= market cap / book value of consolidated tangible equity, group share) & ROE correlated P/BV
An alternative approach which is also based on a multiple, but which includes only the specificities of the company to be valued, consists in applyig the (ROE - g) / (k - g) multiple to its CET1 or, by approximation, to its TBV.
The following slides present a detailed example:

insurance companies

Insurance and reinsurance companies calculate a Solvency 2 ratio. The defintion of the Solvency 2 ratio is : Equity / SCR

• As for banks, the equity which is taken into account is reduced by goodwills and intangible assets
• The SCR corresponds to the Solvency Capital Requirements. It includes 5 risks: Underwriting risk in life, non life and health, Market risk, Counterparty risk, Risk relative to intangible assets & Operational risk. It is reduced by diversification benefits as the SCR includes coefficients of correlation between the various risks that may be negative or equal to 0.

The Solvency 2 ratio has to be at least equal to 1. However, most global players (Axa, Allianz, Generali...) post a Solvency 2 ratio that is generally higher than 150%. The higher the Solvency 2 ratio is, the lower the cost of reinsurance contract is and the higher the technical profitability is.
The following document proposes a focus on SCR. It underlines the principle of their calculation in the Solvency 2 environment and the implied calculation of benefits of diversification for an insurance or a reinsurance company:

Posted on Thursday, April 23, 2020.

models and other tools


1. Equity value and Black & Scholes

2. LGD and spread on debt

3. Patent value

4. Option to abandon

5. Oil concession valuation

6. Cox-Ross-Rubinstein option model

7. DCF valuation

8. M&A peers

9. NAV and SotP


The professor mentions important tools related to market risk premium, brokers' forecasts, etc. that can be useful to those interested in finance. An extended list of these can be found on the professor's website through the link below:

Posted on Thursday, April 30, 2020.