Corporate Finance¶

Why This Matters¶

Every business decision eventually comes down to money: should we build a new factory, acquire a competitor, or return cash to shareholders? Corporate Finance gives you the toolkit to answer these questions rigorously. It is the discipline of evaluating investments, valuing businesses, and deciding how to finance them. If Financial Accounting tells you where the money went, and Operational Finance tells you how efficiently the business runs, Corporate Finance tells you whether the business is creating or destroying value -- and what to do about it.

At its heart, the course asks three questions. First, is this project worth doing? You learn to forecast the cash a project will generate, discount those cash flows to today's value, and compare that value against the cost. Second, what is this company worth? You learn two methods -- Discounted Cash Flow (DCF) and multiples -- and discover that each has strengths and blind spots. Third, how should we pay for it? You learn that the mix of debt and equity a company uses is not neutral: it changes the company's risk, its tax bill, and ultimately its value.

What makes this course challenging is that every answer depends on assumptions about the future. A small change in the discount rate or the growth forecast can swing a valuation by millions. The course teaches you not just to calculate, but to exercise judgment: to stress-test your assumptions, to think about what could go wrong, and to recognize when the numbers are telling you something your gut does not want to hear.

How It All Connects¶

The four modules of this course build on each other like floors of a building.

Module 1 (Project Evaluation) lays the foundation. You learn the mechanics of Net Present Value (NPV), Internal Rate of Return (IRR), and Payback Period. These are the tools you will use to decide whether any single investment is worth pursuing. The key insight: a dollar today is worth more than a dollar tomorrow, so you must discount future cash flows to compare them fairly.

Module 2 (Business Valuation) scales up from projects to entire companies. You learn to value a firm using DCF -- essentially treating the whole company as one giant project -- and using multiples, which compare your company to similar firms the market has already priced. This module also tackles M&A (asking "what is the target worth to us?"), the debt-versus-equity decision, and private equity.

Module 3 (Financing and Cost of Capital) answers the question that Modules 1 and 2 left open: what discount rate should you use? You learn the Capital Asset Pricing Model (CAPM) to estimate the cost of equity, and the Weighted Average Cost of Capital (WACC) to blend the costs of all financing sources. You also learn how to adjust for different capital structures by unlevering and relevering beta.

Module 4 (Advanced Topics) applies everything you have learned to real-world transactions. You analyze dividend policy (should we pay shareholders or reinvest?), IPOs (Initial Public Offerings), green finance, and LBOs (Leveraged Buyouts). Each topic forces you to integrate project evaluation, valuation, and cost-of-capital analysis into a single decision framework.

The throughline is this: NPV requires a discount rate; the discount rate requires WACC; WACC requires an understanding of risk, beta, and capital structure; and all of these feed back into how you value companies and structure transactions.

Lesson 1: Project Evaluation -- NPV and the Investment Decision¶

Sessions 1-2. Technical Note: FN-650-E. Case: HIFU TAOC.

The Big Idea¶

Project evaluation -- also called capital budgeting -- is the process of deciding whether to invest money today in exchange for uncertain cash flows tomorrow. It is the most fundamental skill in corporate finance, because every strategic decision a company makes (building a plant, launching a product, acquiring a competitor) is ultimately an investment project.

The key principle is the time value of money: a euro received today is worth more than a euro received next year, because today's euro can be invested to earn a return. To compare cash flows that arrive at different times, you must discount them -- that is, translate future cash flows back into their present-day equivalent.

Present Value and Discounted Cash Flow¶

The Present Value (PV) of a stream of future cash flows is calculated by discounting each cash flow at rate r:

PV = CF₁/(1+r)¹ + CF₂/(1+r)² + CF₃/(1+r)³ + ... + CFₙ/(1+r)ⁿ

The Intuition: Think of the discount rate as a currency exchange rate -- but instead of converting euros to dollars, you are converting "future euros" to "present euros." A future euro is cheaper than a present euro because of the risk and delay involved in collecting it. The further into the future a cash flow sits, the more heavily it gets discounted.

Quick Mental Math: At a 10% discount rate, a cash flow doubles in value roughly every 7 years (the Rule of 72). Conversely, a cash flow 7 years out is worth about half its face value today.

Net Present Value (NPV)¶

NPV compares the present value of all future cash flows against the initial investment:

NPV = -CF₀ + Σ CFₜ/(1+r)ᵗ

Decision Rule: Invest if NPV > 0. For mutually exclusive projects, choose the one with the highest NPV.

The Intuition: NPV tells you how much richer this project makes you, in today's money. An NPV of 5 million euros means that after paying for the investment, paying back your investors at their required rate, and adjusting for risk, you still have 5 million euros of value left over. A negative NPV means the project earns less than your investors demand -- you would literally be better off putting the money in financial markets.

Useful For: Every investment decision a manager faces -- new product launches, capacity expansions, technology upgrades, acquisitions. NPV is the gold standard of project evaluation.

Internal Rate of Return (IRR)¶

The IRR is the discount rate that makes the NPV exactly equal to zero:

0 = -CF₀ + CF₁/(1+IRR)¹ + CF₂/(1+IRR)² + ... + CFₙ/(1+IRR)ⁿ

Decision Rule: Invest if IRR > required rate of return (r).

The Intuition: If an investment has an IRR of 25%, think of it as a machine that converts every 100 euros you invest today into 125 euros one year later. If your company's required return is only 10%, that machine is clearly worth running -- you are earning 25% on money that only costs you 10%.

Quick Mental Math: IRR is the "break-even discount rate." If someone asks "how high would rates have to go before this project stops making sense?" the answer is the IRR.

Caution -- IRR Has Limitations:

1. Projects with non-conventional cash flows (outflows followed by inflows followed by more outflows) can produce multiple IRRs, making the rule impossible to apply.
2. When comparing mutually exclusive projects, IRR can give the wrong answer. A small project with a high IRR may create less value than a large project with a lower IRR. Always defer to NPV when IRR and NPV conflict.

Payback Period¶

Payback = Initial Investment / Annual Cash Flow (for even cash flows)

Decision Rule: Invest if payback < required payback period.

The Intuition: Payback answers a simple question: how long until I get my money back? It is a measure of liquidity risk rather than profitability. A project that pays back in 2 years is less risky than one that takes 8 years, simply because less can go wrong in the shorter timeframe.

Caution: Payback ignores the time value of money and ignores all cash flows after the payback period. A project that pays back in 3 years but generates enormous cash flows for the next 20 years looks identical to one that stops producing cash on day 1,096. Use payback only as a complement to NPV and IRR, never as a standalone rule.

The Gordon Growth Model (Perpetuity)¶

When cash flows are expected to grow at a constant rate forever, you can use the growing perpetuity formula:

PV = CF₁ / (r - g)

The Intuition: This formula captures an infinite stream of growing cash flows in a single fraction. It works because as cash flows grow further into the future, the discount factor shrinks even faster (as long as r > g), making the sum converge to a finite number. This is the same formula used in the Gordon Growth Model for stock valuation, where CF₁ is replaced by D₁ (next year's dividend): P = D₁/(r - g).

Cross-reference: The time value of money is also covered in Decision Analysis, where you use discount rates to evaluate decision trees and calculate Expected Monetary Value (EMV).

Lesson 2: Project Evaluation -- Methodology¶

Session 3. Case: AZA Group Hotel.

The Big Idea¶

Knowing the formulas is necessary but not sufficient. This lesson teaches you a structured 9-step methodology for evaluating real-world investment projects, moving from back-of-the-envelope calculations to rigorous analysis.

Free Cash Flow (FCF) and Equity Cash Flow (ECF)¶

The cash flows you discount in an NPV analysis are not accounting profits -- they are free cash flows. The distinction matters enormously.

Free Cash Flow (FCF):

FCF = EBIT × (1 - T) - Change in Net Assets

The Intuition: FCF measures the cash generated by the project's assets, as if the project were entirely equity-financed (no debt). It strips out financing decisions to isolate the operational performance of the investment. FCF is the cash available to pay all capital providers -- both debt holders and equity holders.

Equity Cash Flow (ECF):

ECF = Net Income - Change in Net Assets + Change in Net Debt

The Intuition: ECF is the cash that remains after paying everyone else -- lenders, suppliers, employees, the government. It is the cash available exclusively to equity holders. When there is no debt, ECF = FCF after taxes. The difference between ECF and FCF after taxes reveals the effect of leverage (debt) on shareholder returns.

Cross-reference: The concepts of EBIT, Net Income, and Net Working Capital (called NFO at IESE) come directly from Financial Accounting (the income statement and balance sheet) and Operational Finance (where you learn to forecast these items and diagnose problems using balance sheet differences).

The 9-Step Methodology¶

1. General Analysis: What is the product? Who are the customers? What does the competitive landscape look like?
2. Forecast P&L and Balance Sheet: Project revenues, costs, and balance sheet items for T years, where T is the number of years of high growth. After year T, assume growth converges to 2-3% (long-term inflation).
3. Calculate FCF and ECF: Use the formulas above. Include a terminal value to capture cash flows from year T+1 onward.
4. Determine the Discount Rate: Use the risk premium approach or WACC (covered in detail in Lessons 9-11).
5. Calculate NPV, IRR, and Payback: Compute all three using both FCF and ECF. Compare the two sets of results to isolate the effect of leverage.
6. Sensitivity Analysis: Identify the key risk factors. Model best-case and worst-case scenarios. How sensitive is the NPV to changes in revenue growth? Discount rate? Operating margins?
7. Project vs. Shareholder Analysis: Account for sunk costs (ignore them -- they are gone), transfer prices, and cannibalization (does this new product steal sales from our existing products?).
8. Other Criteria: Strategic fit, soft information, personal motivations. Consider these factors, but only after the quantitative analysis is complete. If you start by deciding "this is a strategic project," you will spend the rest of the analysis confirming your bias.
9. Decision and Action Plan: Synthesize all information. Decide whether to invest, and if so, develop an implementation plan.

Cross-reference: The sensitivity analysis in Step 6 connects directly to Decision Analysis, where you build decision trees and calculate the value of additional information. The forecasting in Step 2 draws on the methods taught in Operational Finance (FN-629-E), particularly the balance sheet difference technique for diagnosing financial problems.

Back-of-Napkin DCF -- Three Numbers You Need¶

In practice, you often need a rough valuation before building a full model. A napkin DCF requires just three inputs:

1. FCF (Free Cash Flow): What the business generates in cash after all reinvestment. Use last year's, or a normalized average.
2. g (Growth Rate): How fast FCF will grow. For mature businesses, use GDP growth (2-3%). For growing businesses, use revenue growth tempered by margin compression.
3. r (Discount Rate): Your WACC or required return. Typically 8-12% for most businesses.

Perpetuity Value = FCF₁ / (r − g)

The Intuition: Small changes in r and g cause enormous swings in value. The gap between r and g is what matters -- it is the denominator. When r − g = 10%, value = 10× FCF. When r − g = 4%, value = 25× FCF. This is why growth companies trade at seemingly insane multiples -- investors are betting on a small r − g gap.

The Rule of 72: To estimate how long it takes money to double, divide 72 by the annual rate. - At 6% → doubles in 12 years - At 10% → doubles in 7.2 years - At 15% → doubles in 4.8 years

Cross-reference: Revenue projections in this DCF often start with market sizing. See Marketing Management, Lesson 2 for the TAM (Total Addressable Market) → SAM (Serviceable Addressable Market) → SOM (Serviceable Obtainable Market) funnel, which disciplines your top-line assumptions.

Lesson 3: Business Valuation with DCF¶

Sessions 4-5. Case: NVIDIA. Technical Note: FN-628-E.

The Big Idea¶

Valuing an entire company is conceptually identical to valuing a single project: you forecast the company's future cash flows and discount them to the present. The difference is scale and complexity. A company is a portfolio of existing projects plus the option to pursue future ones.

Enterprise Value and Equity Value¶

Before diving into valuation methods, you must understand the relationship between Enterprise Value (EV) and Equity Value:

Enterprise Value (EV) = Market Value of Equity + Net Debt

Or equivalently:

Equity Value = Enterprise Value - Net Debt

Where Net Debt = Total Debt - Cash and Cash Equivalents.

The Intuition: Think of buying a house. Enterprise Value is the price of the house. If the house has a mortgage (debt), you do not keep the full price when you sell -- you must first pay off the mortgage. What remains is your equity. Similarly, Enterprise Value is the "price tag" on the whole business; Equity Value is what belongs to shareholders after paying off debt.

DCF Valuation in Two Steps¶

Step 1 -- Forecast Period: Project FCF for each year of the explicit forecast period (typically 5-10 years of above-average growth).

Step 2 -- Terminal Value: At the end of the forecast period, estimate the present value of all remaining cash flows using the perpetuity formula:

Terminal Value = FCFₜ₊₁ / (WACC - g)

The total Enterprise Value is then:

EV = Σ FCFₜ/(1+WACC)ᵗ + Terminal Value/(1+WACC)ᵀ

Quick Mental Math: The terminal value typically accounts for 60-80% of total enterprise value. This means your long-term growth assumption (g) and discount rate (WACC) matter enormously. A 1% change in either can swing the valuation by 20% or more. This is why sensitivity analysis (varying g and WACC in a matrix) is essential.

Useful For: Valuing companies for acquisition, IPO pricing, strategic planning, and any situation where you need an intrinsic (fundamental) estimate of what a business is worth.

Lesson 4: Valuation with Multiples¶

Session 6. Case: Volkswagen AG 2009.

The Big Idea¶

DCF valuation is rigorous but time-consuming and highly sensitive to assumptions. Multiples valuation offers a faster, market-based alternative: instead of building a financial model from scratch, you look at what the market is already paying for similar companies and apply that pricing to your target.

The Core Formula¶

(Value of Firm XYZ) = (Multiple of Comparable Firms) x (Financial Metric of Firm XYZ)

Key Multiples¶

Equity-Based Multiples:

P/E = Stock Price / Earnings Per Share (EPS)

The Intuition: The P/E ratio tells you how many euros investors are willing to pay for one euro of current earnings. A P/E of 20 means investors pay 20 euros for every euro of earnings -- they expect those earnings to grow enough to justify the premium. High P/E = high growth expectations. Low P/E = low growth expectations or high risk.

Caution: P/E is affected by capital structure (debt levels), accounting policies, and non-recurring items. It is difficult to compare companies with very different leverage ratios.

Enterprise Value-Based Multiples:

EV/EBITDA = Enterprise Value / Earnings Before Interest, Taxes, Depreciation, and Amortization

EV/Sales = Enterprise Value / Revenue

The Intuition: EV/EBITDA is the workhorse multiple of corporate finance. Because EBITDA is a pre-financing, pre-depreciation cash flow measure, it strips out the effects of capital structure and accounting for depreciation. This makes it ideal for comparing companies with different debt levels. An EV/EBITDA of 8x means you are paying 8 euros for every euro of operating cash flow the business generates.

Quick Mental Math: A typical industrial company trades at 6-10x EV/EBITDA. High-growth tech companies can trade at 20-40x. If a company trades significantly above or below its peers, ask why -- it usually signals either superior growth prospects, higher risk, or market mispricing.

Trading Multiples vs. Transaction Multiples¶

Transaction multiples are inherently higher than trading multiples because they include the control premium -- the extra amount a buyer must pay to gain control of a company's cash flows and strategy.

Identifying Comparable Firms¶

Good comparables share the same industry, similar size, similar growth, and similar profitability. The process involves: (1) start with an industry classification (SIC or GICS codes), (2) narrow by business focus and size, (3) test for similar growth and profitability, (4) cross-check against analyst reports.

Sector-Specific Multiples: In some industries, standard multiples do not capture what matters. Airlines use EV/Sales per Seat Mile. Hotels use EV/Number of Beds. Internet retailers use EV/Number of Customers. Always choose a multiple that reflects the key value driver of the industry.

Cross-reference: The financial metrics used in multiples (EBITDA, Net Income, Revenue) come from Financial Accounting. The operational metrics (customers, subscribers, beds) connect to Operations Strategy's focus on industry-specific performance measures.

Back-of-Napkin Valuation -- Is This Deal Overpriced?¶

When you hear "Company X was acquired for €500M," your first reaction should be: relative to what?

Quick EV/EBITDA Sanity Check:

EV (Enterprise Value) = Equity Value + Net Debt EBITDA (Earnings Before Interest, Taxes, Depreciation, and Amortization) = Operating profit + D&A (Depreciation and Amortization)

The Intuition: EV/EBITDA tells you: "How many years of current cash earnings am I paying for this business?" An 8× multiple means you are paying 8 years' worth of EBITDA. If you believe the business will grow, 8 years is cheap. If it is declining, 8 years is expensive.

Quick Mental Math: - Acquisition price ÷ EBITDA = the multiple. Compare to sector norms above. - If the acquirer is paying a 30% premium to the current market price, there should be at least 30% in synergies or growth to justify it. - "Synergies" are often overestimated. Rule of thumb: assume you will capture 50-70% of projected synergies.

Cross-reference: EBITDA connects to Financial Accounting, Lesson 2 where you learned how the income statement is constructed. Enterprise Value connects to the balance sheet (Financial Accounting, Lesson 1) -- you need net debt from there.

Lesson 5: M&A -- Deal Valuation¶

Session 7. Case: Warehouse Industries 2017.

The Big Idea¶

When one company acquires another, the buyer must determine what the target is worth -- not just its standalone value, but its value including the synergies the combination will create. Overpaying destroys value for the buyer's shareholders; underpaying means the deal will not happen.

Valuing an Acquisition Target¶

M&A valuation uses both DCF and multiples, but adds two critical layers:

1. Standalone Value: What is the target worth on its own? Use DCF (project the target's FCF, discount at the target's WACC) and trading multiples as a cross-check.

2. Synergy Value: What additional value does the combination create?

• Cost synergies (highly probable): Eliminating duplicate headquarters, reducing headcount, negotiating bulk purchasing discounts.
• Revenue synergies (speculative): Cross-selling products to the other company's customers, entering new markets using the combined platform. Model these conservatively.

Maximum Acquisition Price = Standalone Value + PV of Synergies

If you pay more than this, you are destroying value for your own shareholders.

The Control Premium¶

When buying a public company, you must pay a premium over the current stock price (typically 20-30%). This is because public market prices reflect a minority, passive stake. To gain control -- the right to appoint management, set strategy, and redirect cash flows -- you must pay extra.

Goodwill in Accounting¶

When the purchase price exceeds the fair value of the target's identifiable net assets, the difference is recorded as Goodwill on the buyer's balance sheet. Goodwill captures synergies, control premium, workforce value, and brand reputation. Under IFRS and US GAAP, goodwill is not amortized but must be tested for impairment annually.

Cross-reference: The accounting treatment of acquisitions (consolidation, goodwill, impairment) is covered in detail in Financial Accounting. The operational due diligence that identifies synergies connects to Operations Strategy and Managerial Accounting (cost analysis for identifying redundancies).

Lesson 6: Debt vs. Equity -- The Capital Structure Decision¶

Session 8. Case: LogisTech.

The Big Idea¶

How a company finances itself -- the mix of debt and equity -- is not a neutral choice. Debt brings tax advantages and discipline but increases the risk of financial distress. Equity is flexible and permanent but dilutes existing owners and sends negative signals to the market. The optimal capital structure balances these forces.

Why Debt Is Attractive¶

1. Lower cost: Debt holders take less risk (they get paid first in bankruptcy), so they demand lower returns than equity holders.
2. Tax shield: Interest payments on debt are tax-deductible. Dividends to equity holders are not. This subsidy from the government makes debt cheaper still.
3. No dilution: Borrowing does not reduce existing shareholders' ownership percentage.
4. Managerial discipline: The obligation to make fixed interest and principal payments forces managers to operate efficiently and avoid wasteful spending.

Why Equity Is Necessary¶

1. No bankruptcy risk: Equity has no mandatory payments. You cannot default on a dividend.
2. Flexibility: In downturns, you can cut dividends. You cannot cut interest payments without defaulting.
3. Capacity for growth: Some investments are too risky for debt financing. Fast-growing companies with volatile cash flows often need equity.

The Signaling Problem¶

When a company announces a new equity issue, its stock price typically drops 3-4%. The market interprets the announcement as a signal that management believes the stock is overvalued (otherwise, why sell?). This is called the adverse selection or information asymmetry problem.

Capital Structure Theories¶

Modigliani-Miller (MM) Irrelevance (No Taxes): In a perfect market with no taxes and no bankruptcy costs, capital structure does not matter. The value of the firm depends only on its assets and cash flows, not on how it is financed.

MM with Taxes: Once you introduce corporate taxes, debt becomes valuable because of the interest tax shield. Under this strict model, the firm should finance with 100% debt to maximize value.

Trade-Off Theory: In reality, the benefits of the tax shield must be balanced against the costs of financial distress (legal fees, lost customers, lost suppliers, fire-sale asset prices). The optimal capital structure is the point where the marginal benefit of additional tax shield equals the marginal cost of increased distress probability.

Pecking Order Theory: Managers prefer financing sources in this order: (1) retained earnings, (2) debt, (3) equity. This hierarchy minimizes information asymmetry costs and negative signaling.

Quick Mental Math: As a rule of thumb, a healthy industrial company should maintain an equity ratio (equity / total assets) between 40% and 60%. Below 40%, the firm is over-leveraged and should repay debt before paying dividends. Above 60%, it may not be fully exploiting the tax shield.

Lesson 7: Private Equity¶

Session 9. Case: Riverside -- Euromed.

The Big Idea¶

Private equity (PE) firms acquire companies using significant amounts of debt, improve their operations, and sell them for a profit -- typically within 4-7 years. The PE model is a concentrated application of everything covered so far: project evaluation, valuation, leverage, and capital structure.

How a PE Deal Works¶

1. Sourcing and Screening: PE firms identify undervalued or underperforming companies with stable cash flows and potential for operational improvement.
2. Valuation: The PE firm values the target using DCF, multiples, and LBO analysis (see Lesson 13).
3. Structuring: The acquisition is typically financed with 60-80% debt and 20-40% equity from the PE fund.
4. Value Creation: The PE firm actively manages the portfolio company, implementing operational improvements, strategic repositioning, and sometimes add-on acquisitions.
5. Exit: After 4-7 years, the PE firm sells the company (via IPO, sale to another PE firm, or sale to a strategic buyer) and distributes proceeds to its investors.

Key Metrics¶

IRR (Internal Rate of Return): PE sponsors typically target an IRR of 20-25% on their equity investment. This high bar reflects the illiquidity, risk, and active management required.

MOIC (Multiple on Invested Capital): How many times you get your money back. A 3x MOIC over 5 years corresponds to approximately a 25% IRR.

Lesson 8: Cost of Equity and Cost of Debt¶

Session 12. Case: Novartis/Sandoz Spin-Off. Technical Note: FN-604-E.

The Big Idea¶

Now that you know how to calculate NPV (Lessons 1-2) and how to forecast cash flows (Lessons 3-5), you face the critical question: what discount rate should you use? The answer is the cost of capital -- the minimum return the company must earn to satisfy its investors. This lesson breaks the cost of capital into its two components: the cost of equity and the cost of debt.

The Capital Asset Pricing Model (CAPM)¶

The cost of equity is the return that shareholders demand for investing in a particular stock. The CAPM provides the standard formula:

rₑ = rƒ + β × (rₘ - rƒ)

The Intuition: CAPM says that the return you should demand from any investment has two parts. The first is the risk-free rate -- the return you could earn by doing nothing risky at all (buying government bonds). The second is a premium for taking on risk, which depends on how much the stock moves with the overall market (beta) multiplied by the price of risk in the market (the risk premium).

If beta = 0, the stock has no systematic risk, and investors should demand only the risk-free rate. If beta = 1, the stock has the same risk as the market, and investors should demand the market return. If beta = 1.5, the stock is 50% riskier than the market, and investors demand a proportionally higher return.

Quick Mental Math: With rƒ = 4% and a market risk premium of 6%, every 0.1 increase in beta adds 0.6% to the cost of equity. A stock with beta = 1.2 has a cost of equity of 4% + 1.2 x 6% = 11.2%.

Understanding Beta¶

β = Cov(Rᵢ, Rₘ) / Var(Rₘ)

The Intuition: Beta measures sensitivity to the market. A stock with beta 1.5 tends to rise 15% when the market rises 10% and fall 15% when the market falls 10%. High beta = higher expected return but more volatile ride. Beta captures only systematic risk (market-wide, non-diversifiable risk). Firm-specific risk (unsystematic risk) can be eliminated through diversification and is therefore not rewarded by the market.

Determinants of Beta:

1. Cyclicality of revenues: Companies whose sales swing with the business cycle (luxury goods, construction) have higher betas than those with stable demand (utilities, consumer staples).
2. Operating leverage: Companies with high fixed costs and low variable costs have higher betas because small changes in revenue cause large swings in profits.
3. Financial leverage: Companies with more debt have higher equity betas because the fixed interest payments amplify the volatility of equity returns. (See Lesson 10 on unlevering and relevering.)

The Cost of Debt¶

The cost of debt is more straightforward than the cost of equity:

r_d = rƒ + Company's Debt Premium (Credit Spread)

The after-tax cost of debt accounts for the tax deductibility of interest:

After-tax cost of debt = r_d × (1 - T)

The Intuition: Lenders demand a premium above the risk-free rate that reflects the company's probability of default. A highly-rated company (AAA) pays a small spread; a junk-rated company (BB) pays a large one. Because interest is tax-deductible, the government effectively subsidizes part of the cost. If the interest rate is 6% and the tax rate is 25%, the after-tax cost is only 4.5%.

Risk and Return: The Foundations¶

Before applying CAPM, you must understand the statistical building blocks:

Diversification and the Efficient Frontier¶

As long as the correlation between two assets is less than +1 (that is, they do not move in perfect lockstep), combining them in a portfolio reduces the overall risk below the weighted average of their individual risks. This is the diversification effect.

The efficient frontier is the set of portfolios that offer the highest expected return for each level of risk. Rational investors choose only portfolios on this frontier. Adding a risk-free asset creates the Capital Market Line (CML), which dominates the efficient frontier because investors can now lend (buy risk-free bonds) or borrow (use leverage) to reach any desired risk-return combination along a straight line.

Cross-reference: The statistical concepts (variance, standard deviation, expected value) are also used in Decision Analysis. The concept of diversification connects to Operations Strategy's discussion of risk management through geographic and product diversification.

Lesson 9: Estimating the WACC¶

Session 13. Case: Novartis (continued).

The Big Idea¶

The Weighted Average Cost of Capital (WACC) blends the cost of equity and the after-tax cost of debt into a single discount rate. It represents the average return the company must earn on its existing assets to satisfy all of its investors -- both shareholders and lenders.

The WACC Formula¶

WACC = (E/V) × rₑ + (D/V) × r_d × (1 - T)

The Intuition: Imagine you run a business financed with 60% equity and 40% debt. Your shareholders demand 12% and your lenders charge 6% (before tax). With a 25% tax rate, the after-tax cost of debt is 4.5%. Your WACC is:

WACC = 0.60 × 12% + 0.40 × 6% × (1 - 0.25) = 7.2% + 1.8% = 9.0%

This means every project you undertake must earn at least 9% to satisfy both shareholders and lenders. If a project earns 11%, the NPV is positive and you should do it. If it earns 7%, you are destroying value.

Including Preferred Stock: If the company also uses preferred stock, the formula expands to:

WACC = (E/V) × rₑ + (D/V) × r_d × (1 - T) + (P/V) × rₚ

Where P is the market value of preferred stock and rₚ is its cost.

When to Use the Firm's WACC vs. a Project-Specific Rate¶

The firm's WACC is the correct discount rate only when the project has the same risk and the same capital structure as the firm as a whole. If the project is riskier (e.g., a publishing company entering the software business), you must use a higher discount rate -- typically based on the average beta of the project's industry. Using the firm's WACC for all projects leads to systematic errors: you will accept too many high-risk projects (because you are underpricing their risk) and reject too many low-risk projects (because you are overpricing their risk).

Computing WACC -- Step by Step¶

1. Estimate E: Stock price x number of shares outstanding.
2. Estimate D: Use book value of debt as a proxy for market value.
3. Calculate weights: E/V and D/V.
4. Estimate rₑ: Use CAPM with an industry beta (more reliable than firm-specific beta due to less measurement error). Use a market risk premium of approximately 6-9.5% (historical averages).
5. Estimate r_d: Risk-free rate + the company's credit spread.
6. Determine T: The effective corporate tax rate.
7. Plug and calculate.

Quick Mental Math: For a company with a 50/50 debt-equity split, a 12% cost of equity, a 6% cost of debt, and a 25% tax rate: WACC = 0.5 x 12% + 0.5 x 6% x 0.75 = 6% + 2.25% = 8.25%.

Back-of-Napkin WACC -- When You Do Not Have Time for CAPM¶

Sometimes you need a discount rate fast. Here are rules of thumb:

The Intuition: WACC is the "hurdle rate" -- the minimum return a project must earn to justify the capital used. Using too low a WACC makes bad projects look good. Using too high a WACC kills good projects. When in doubt, run the NPV at three rates (low/base/high) and see if the conclusion changes. If it only works at 7% but dies at 10%, it is a fragile bet.

Cross-reference: For the full WACC derivation, see the existing formula above. The cost of equity component uses CAPM, which relies on beta -- a concept that also appears in Competitive Strategy when analyzing how industry risk affects strategic choices.

Lesson 10: Unlevering and Relevering Returns¶

Session 14. Technical Note: FN-604-E.

The Big Idea¶

When you look up a company's beta on Bloomberg, you are seeing its equity beta -- a number that reflects both the underlying operational risk of the business and the additional financial risk created by debt. If you want to compare the operational riskiness of two companies with different capital structures, or if you want to estimate the cost of equity for a company that is about to change its capital structure, you must first strip out the effect of debt (unlever), and then add back the effect of the new debt level (relever).

Step 1: Unlever -- Find the Asset Beta (or Asset Return)¶

The unlevered beta (also called asset beta, βᵤ) measures the pure operational risk of the business, as if it had no debt at all.

βᵤ = βₗ / [1 + (D/E) × (1 - T)]

Or equivalently, using returns:

Rₐ = [E / (E + D(1-T))] × Rₑ + [D(1-T) / (E + D(1-T))] × R_d

The Intuition: Think of a company as a person carrying a backpack. The person's strength (operational risk) stays the same regardless of how heavy the backpack is. But the heavier the backpack (more debt), the more the person sways when walking (higher equity beta). Unlevering removes the backpack so you can see the person's natural gait.

Step 2: Relever -- Calculate the New Equity Beta¶

Once you know the asset beta, you can relever it for any target capital structure:

βₗ = βᵤ × [1 + (D/E) × (1 - T)]

Or equivalently, using returns:

Rₑ = Rₐ + (Rₐ - R_d) × (D/E) × (1 - T)

The Intuition: Adding debt to a company amplifies the risk to equity holders -- they now bear both the operational risk and the risk that the company might not be able to meet its debt payments. The (1-T) term reflects the tax shield: because interest is tax-deductible, the government absorbs some of the financial risk, so the increase in equity beta is not as dramatic as it would be in a no-tax world.

Practical Application¶

Suppose you want to estimate the WACC for a new project in an industry different from your company. You would:

1. Find comparable companies in the target industry.
2. Look up their equity betas.
3. Unlever each beta to remove the effect of their capital structures.
4. Average the unlevered betas to get a clean estimate of the industry's operational risk.
5. Relever the average unlevered beta using your company's target capital structure.
6. Plug the relevered beta into CAPM to get the cost of equity.
7. Calculate WACC using this project-specific cost of equity.

This two-step method must be used whenever the leverage ratio differs from the one used to calculate the original cost of equity. This is the single most important conclusion from the WACC technical note (FN-604-E).

Lesson 11: Dividend Policy¶

Session 15. Case: eBay.

The Big Idea¶

Once a company generates profits, it faces a fundamental choice: reinvest the cash in new projects or return it to shareholders. Dividend policy addresses how much cash to return, and in what form -- dividends, share buybacks, or some combination.

Three Competing Theories¶

1. MM Dividend Irrelevance: In a perfect market (no taxes, no transaction costs, perfect information), dividend policy does not matter. The value of the firm depends entirely on its investment decisions, not on how it distributes cash. If shareholders want cash but the company retains it, they can simply sell a few shares to create a "homemade dividend."

2. Bird-in-the-Hand Theory (Gordon/Lintner): Investors prefer the certainty of a cash dividend today over the uncertain promise of future capital gains. Because dividends reduce investor uncertainty, companies that pay high dividends should have a lower cost of equity and a higher stock price.

3. Tax Preference Theory: In most tax jurisdictions, dividends are taxed at higher rates than capital gains, and capital gains taxes are deferred until the investor sells. Investors therefore prefer companies to retain earnings (or buy back shares) rather than pay dividends, because it minimizes their tax bill.

Dividends vs. Share Buybacks¶

Practical Guidance:

1. Before returning cash, check your capital structure. If equity ratio < 40%, use the cash to repay debt instead.
2. Set a sustainable dividend policy aligned with long-term profitability. Avoid erratic dividends -- markets punish cuts severely.
3. If excess cash remains, choose between buybacks and extra dividends based primarily on tax considerations.
4. Execute buybacks slowly over a long period to avoid driving up the purchase price against yourself.

Lesson 12: Initial Public Offerings (IPOs)¶

Session 16. Case: Jose Cuervo. Reading: RWJ Chapter 19.

The Big Idea¶

An Initial Public Offering (IPO) is the first time a company sells equity to the public. Going public provides access to a vast pool of capital, creates liquidity for founders and early investors, and establishes a public market price for the company's shares. But it is expensive, complex, and fundamentally changes how the company operates.

The IPO Process¶

1. Preunderwriting: Negotiate with investment banks (underwriters), build a syndicate, obtain board approval.
2. Registration: File a registration statement with the securities regulator (SEC in the US). During the 20-day waiting period, distribute a preliminary prospectus (the "red herring"). No shares can be sold yet.
3. Pricing: On the effective date, set the final offering price based on investor demand and market conditions.
4. Public Offering and Sale: The underwriter sells shares to institutional and retail investors.
5. Market Stabilization: For approximately 30 days after the offering, the underwriter may place buy orders to support the stock price.

The Role of Underwriters¶

Underwriters provide four functions: certification (assuring investors the price is fair), monitoring (ongoing oversight of management), marketing (selling the shares), and risk bearing.

Firm Commitment: The underwriter buys the entire issue from the company at a discount and resells it to investors at the offering price, bearing 100% of the risk. Standard for large issues.

Best Efforts: The underwriter acts as an agent, receiving a commission for each share sold but taking no risk. Standard for smaller IPOs.

The Spread: The difference between the price the underwriter pays and the public offering price. This is the underwriter's primary compensation.

Green Shoe Provision: An option allowing the underwriter to buy up to 15% additional shares at the offering price to cover excess demand.

IPO Underpricing¶

IPOs are systematically underpriced -- the average firm-commitment IPO rises approximately 15% on its first day of trading. This is not accidental; it is a deliberate strategy to counteract the Winner's Curse.

The Winner's Curse Explained: Informed investors know which IPOs are underpriced and swarm to buy them, leaving uninformed investors with smaller allocations in good IPOs and full allocations in bad ones. If IPOs were priced at fair value, uninformed investors would realize they consistently "win" only the losers and would leave the market. Underpricing ensures that even uninformed investors earn a positive average return, keeping them in the game.

The True Cost of Going Public¶

These costs exhibit significant economies of scale -- larger offerings have lower percentage costs. For very small IPOs (< $10M), total direct costs can exceed 17%.

Useful For: Understanding when going public makes sense (and when it does not), evaluating IPO pricing, and recognizing the information asymmetry dynamics in capital markets.

Lesson 13: LBO Valuation¶

Session 18. Case: Hoffmann Saveurs.

The Big Idea¶

A Leveraged Buyout (LBO) is the acquisition of a company using a large proportion of borrowed money (typically 60-80% debt, 20-40% equity). The financial sponsor (private equity firm) uses the target company's own cash flows to service and pay down the debt, amplifying equity returns through financial leverage. LBO valuation is a specialized application of DCF, project evaluation, and capital structure theory.

The Four Steps of an LBO Model¶

Step 1 -- Entry Valuation: Determine the purchase price, typically calculated as a multiple of EBITDA.

Purchase Price (EV) = Entry Multiple x EBITDA

Step 2 -- Financing Structure: Determine the debt/equity split. Example: For a company with 10M EBITDA purchased at 5x (50M EV), 70% debt = 35M borrowed, 15M equity check.

Step 3 -- Operating Model and Debt Paydown: Project the company's P&L and FCF over the holding period (typically 5-7 years). Every dollar of FCF is used to pay down debt. As debt decreases, the equity value mechanically increases dollar-for-dollar, even if the enterprise value stays flat.

Step 4 -- Exit and Returns:

Exit EV = Exit Multiple x Final Year EBITDA

Equity at Exit = Exit EV - Remaining Debt

Sponsor IRR: The IRR on the equity investment. PE sponsors typically target 20-25% IRR.

The Intuition: The magic of an LBO is the leverage effect. If you buy a company for 100, put up 30 of equity and borrow 70, and the company's value rises to 130, your equity is now worth 60 (130 - 70 debt). Your equity doubled (from 30 to 60) even though the company's value rose only 30%. This is the power of leverage -- and its danger in reverse.

Three Levers of Value Creation in an LBO:

1. EBITDA growth: Grow the business through revenue increases or margin improvement.
2. Debt paydown: Use cash flow to reduce debt, mechanically increasing equity value.
3. Multiple expansion: Sell at a higher multiple than you paid. This is the least reliable lever -- never build a business plan on the assumption that the market will pay you more per dollar of EBITDA than you paid.

Quick Mental Math: To double your money in 5 years, you need roughly a 15% IRR. To triple it, you need about 25%. PE sponsors aiming for 3x MOIC over 5 years need all three levers working.

Back-of-Napkin LBO -- Can This Deal Work?¶

PE (Private Equity) firms buy companies with mostly debt, improve them, and sell. The napkin test:

Entry: Buy at 8× EBITDA. EBITDA = €50M. Price = €400M. Fund with 60% debt (€240M) and 40% equity (€160M).

Hold period (5 years): Pay down €100M of debt from cash flows. Grow EBITDA from €50M to €65M (5% annual growth).

Exit: Sell at 8× EBITDA = 8 × €65M = €520M. Subtract remaining debt (€140M). Equity value = €380M.

Return: Invested €160M equity, got back €380M. That is a 2.4× MOIC (Multiple on Invested Capital) in 5 years, which is roughly a 19% IRR (Internal Rate of Return).

The Three Levers of LBO Returns: 1. Multiple expansion: Buy at 6×, sell at 8× (market timing / repositioning) 2. EBITDA growth: Grow the business (revenue growth + margin improvement) 3. Debt paydown: Use cash flows to repay debt, so more of the exit value goes to equity

Quick Mental Math: - A 2× MOIC in 5 years ≈ 15% IRR - A 3× MOIC in 5 years ≈ 25% IRR - PE firms target 20%+ IRR, so they need roughly 2.5-3× in 5 years - If EBITDA is not growing and multiples are not expanding, the only return comes from debt paydown -- which alone rarely gets you to 2×

Cross-reference: This napkin LBO synthesizes concepts from across the course: entry valuation uses multiples (Lesson 4), the financing structure applies capital structure theory (Lesson 6), EBITDA growth connects to the FCF forecasting methodology (Lesson 2), and the target IRR is the equity investor's cost of capital (Lesson 8).

Lesson 14: Green Finance¶

Session 17. Case: Shell.

The Big Idea¶

Green finance integrates environmental, social, and governance (ESG) considerations into corporate finance decisions. It asks whether a company's financial strategy is consistent with long-term sustainability -- and whether sustainability can itself be a source of financial value.

Key Concepts¶

Green Bonds: Debt instruments whose proceeds are earmarked exclusively for environmentally beneficial projects (renewable energy, energy efficiency, clean transportation). Green bonds typically price at a slight premium (lower yield) compared to conventional bonds -- the "greenium" -- because ESG-focused investors accept a marginally lower return.

Double Materiality (EU CSRD Framework): Companies must report on two dimensions: (1) how their activities affect the environment and society (outward impact), and (2) how ESG factors affect their own financial performance (inward impact on cash flows, financial position, and market value).

Scope 3 Emissions: The CSRD expands reporting boundaries to include emissions from the entire value chain -- upstream (suppliers) and downstream (end users) -- not just the company's own direct operations.

The Financial Logic¶

ESG is not just ethics; it connects directly to financial value through multiple channels:

• Cost of capital: Companies with strong ESG profiles can access cheaper financing (green bonds, ESG-linked loans).
• Risk management: Companies that manage environmental and social risks reduce the probability of regulatory fines, lawsuits, and reputational damage.
• Revenue growth: Sustainability can open new markets and attract customers willing to pay a premium for responsible products.
• Operating efficiency: Environmental targets (reducing energy use, minimizing waste) often drive operational cost savings.

Caution -- Greenwashing: Superficial sustainability claims without genuine operational changes. Greenwashing destroys market trust and exposes the company to regulatory and reputational risk.

Cross-reference: The ESG reporting frameworks connect to Financial Accounting (sustainability reporting standards), Operations Strategy (sustainable supply chains), and Business Ethics (the stakeholder model vs. shareholder model).

Lesson 15: What Every Manager Should Know About Corporate Finance¶

Session 21.

The Big Idea¶

This capstone session integrates all four modules into a unified mental model for financial decision-making. The key takeaways:

1. Value creation is the objective. Every decision should increase the NPV of the firm. If an investment does not earn above the cost of capital, it destroys value.

2. Cash is king. Accounting profits can be manipulated; cash flows cannot. Always focus on FCF, not reported earnings.

3. Risk and return are inseparable. Higher returns require higher risk. The CAPM and WACC give you a disciplined way to price that risk.

4. Capital structure matters -- but not as much as operations. The tax shield from debt adds value, but the primary driver of firm value is the quality of the business and its investments, not financial engineering.

5. Markets are smarter than you think -- but not always right. Market prices reflect collective information and expectations. Betting against the market requires a clear informational advantage and the humility to recognize when you might be wrong.

Quick Reference¶

The 10 Essential Formulas¶

Five Rules of Thumb¶

1. Rule of 72: Divide 72 by the growth rate to estimate doubling time. At 10%, money doubles in ~7.2 years.
2. Terminal value dominance: Terminal value typically represents 60-80% of enterprise value. Stress-test your growth and discount rate assumptions.
3. WACC sensitivity: A 1% change in WACC can swing a valuation by 15-25%.
4. The 40/60 capital structure rule: Keep equity ratio between 40% and 60% for most industrial companies.
5. IPO cost reality: Plan for total issuance costs of ~23% of the amount raised (11% direct + 12% underpricing).

Glossary¶