Corporate Finance

Project Discount Rate – Core Rule

Discount a project at the expected return on a financial asset of comparable risk or shareholders could take the cash as a dividend and invest it themselves, so the project must beat that alternative.

The return investors require IS the firm's cost of capital; anything raising one raises the other.

3 Determinants of Beta

Cyclicality of revenues (sales that track the business cycle → higher beta)

Operating leverage (high fixed production costs → magnifies cyclicality → higher beta)

Financial leverage (debt = fixed finance costs → higher equity beta)

Cyclicality vs Variability (Trap!)

Cyclicality: how much revenues move WITH the business cycle, driving beta.

Variability: total ups and downs (standard deviation), which can be firm-specific.

Operating Leverage High vs Low

Firms with high fixed costs and low variable costs have high operating leverage and vice versa.

Operating vs Financial Leverage

Operating leverage: fixed costs of PRODUCTION.

Financial leverage: fixed costs of FINANCE (interest is due regardless of sales).

Asset Beta vs Equity Beta

Asset beta: business risk only = beta the shares would have if 100% equity financed.

Equity beta: business risk + financial risk (debt).

$\beta_A = \frac{E}{D+E}\beta_E + \frac{D}{D+E}\beta_D$, a portfolio of all the firm's debt and equity.

With debt (and $\beta_D = 0$), $\beta_E > \beta_A$.

Effect of More Debt on Betas and Cost of Equity

Asset beta: stays the SAME (same business, same business risk).

Equity beta: rises (shareholders carry more financial risk).

Cost of equity: rises through the CAPM as a result of above.

Firm vs Project Discount Rate and consequences

Discount each project at a rate matching ITS OWN risk (beta), not the firm's.

WACC is only right when the project has the same risk as the firm AND the firm keeps its target financing mix (I.e., stable D/E ratio)

Otherwise the firm may accept too many unprofitable high-risk projects, rejects too many profitable low-risk ones.

Converting D/E into WACC Weights (Trap!)

To weights: $\frac{D}{V} = \frac{D/E}{1 + D/E}$ and $\frac{E}{V} = \frac{1}{1 + D/E}$

Back to D/E: $\frac{D}{E} = \frac{D/V}{1 - D/V}$

Always use MARKET values, never book values.

Cost of Debt in the WACC (Trap!)

Rule: use the YTM on the firm's bonds, NOT the coupon rate.

Exception: bond selling at par → YTM = coupon.

Several bond types: each gets its own YTM and its own weight.

Tax Shield in the WACC – Which Parts? (Trap!)

Gets $(1-T_C)$: debt only (coupon AND zero-coupon bonds), because interest is tax-deductible.

No tax adjustment: common equity and preferred shares (dividends aren't deductible).

Preferred shares: cost = dividend ÷ MARKET price, with the dividend based on PAR value.

Effect of Issuing Debt on WACC

**Equity side**: D/E ↑ → equity beta ↑ → $R_E$ ↑ (asset beta unchanged).

**Debt side**: more weight on cheaper debt.

**With taxes**: WACC falls slightly, driven by the interest tax shield.

**Without taxes**: the two effects cancel exactly → WACC unchanged (MM, Week 2).

Liquidity and the Cost of Capital

**Rule**: lower liquidity (higher trading costs) → investors demand a higher expected return → higher cost of capital.

**3 trading costs**: brokerage fees, bid–ask spread, market impact costs.

**Key point**: a firm's risk is hard to change, but its liquidity is easier to improve.

Adverse Selection and the Cost of Capital

**Problem**: informed traders "pick off" counterparties who lack their information.

**Chain**: more informed traders → wider bid–ask spread → higher trading costs for ALL → higher required return → higher cost of capital.

**Rule**: the spread rises with the ratio of informed to uninformed traders.

2 Ways to Lower the Cost of Capital (Liquidity)

**Attract uninformed investors** (stock split → shares more affordable → more small investors → less adverse selection → narrower spread)

**Disclose more information** (segment data, management forecasts, analyst coverage → smaller info gap → narrower spread)

A stock split doesn't change value directly; any gain comes through the lower cost of equity.

Levered Project NPV – Roadmap

**Step 0**: market values of E and D.

**Step 1**: gear up the asset beta to the equity beta.

**Step 2**: CAPM → $R_E$.

**Step 3**: WACC (cost of debt = YTM).

**Step 4**: discount project cash flows at the WACC → NPV.

Capital Structure and Shareholder Wealth

**Rule**: a capital structure change helps shareholders IF AND ONLY IF firm value $(V = D + E)$ rises.

**Takeaway**: managers should pick the debt–equity ratio that makes the "pie" biggest.

**MM view (no taxes)**: slicing the pie differently doesn't change its size.

Effect of Leverage on EPS and ROE

**High EBI (good times)**: leverage BOOSTS EPS & ROE.

**Low EBI (bad times)**: leverage CUTS EPS & ROE, since interest is fixed.

**ROA**: NOT affected by leverage (measured before interest).

EPS vs EBI Graph

**Levered line**: lower intercept (negative EPS at EBI = 0, because of interest) but STEEPER slope (fewer shares).

**Unlevered line**: starts at the origin, flatter.

**Slope**: = risk to shareholders (how strongly EPS reacts to EBI).

**Lines cross**: at the break-even EBI.

Break-even EBI (Debt vs Equity Plan)

**Solve**: set EPS equal, $\frac{EBI(1-T_C)}{N_{equity\ plan}} = \frac{(EBI - \text{Interest})(1-T_C)}{N_{debt\ plan}}$

**Trap**: $(1-T_C)$ cancels, so taxes don't change the break-even EBI.

**Above break-even**: debt plan gives higher EPS. **Below**: equity plan is better.

**Intuition**: at break-even, ROA = cost of debt; debt helps EPS only when ROA > $R_D$.

Levered vs Unlevered Equity – Which Is Better?

**Levered equity**: higher EXPECTED EPS & ROE, but worse in bad times → riskier.

**Unlevered equity**: lower expected return, but safer.

**MM answer**: neither; investors are indifferent because they can create or undo leverage themselves at the same cost.

MM Proposition I (No Taxes)

**Statement**: $V_L = V_U$; capital structure does not affect firm value.

**Intuition**: investors can copy OR undo corporate leverage on their own (homemade leverage).

**Analogy**: cutting a pizza into more slices gives more pieces, not more pizza.

Homemade Leverage – Borrow vs Lend

**To ADD leverage** (copy levered shares): BORROW personally so your D/E matches the firm's, and buy extra unlevered shares.

**To REMOVE leverage** (undo it): sell part of your levered shares and LEND the cash.

**Amount to lend**: firm's D/V × your total investment.

Homemade Leverage – Sense Check

**Same cost**: your net initial outlay must match the strategy you're copying.

**Same payoff**: identical € earnings in EVERY economic state.

**Unlevered position**: total payoff = your ownership % × firm's EBI.

Arbitrage Behind MM I

**If** $V_L > V_U$: levered shares overpriced → sell them, borrow & buy unlevered shares → same payoff, cheaper.

**If** $V_L < V_U$: sell unlevered shares, buy levered shares & lend.

**Process stops**: when $V_L = V_U$ and no cheaper route is left.

Valuing Firms in MM Questions (No Taxes)

**Unlevered**: $V_U = E_U = \frac{EBI}{R_A}$ (perpetuity).

**Levered**: $V_L = V_U$, so levered equity $E_L = V_L - D$.

**Levered cost of equity**: $R_E = \frac{EBI - R_D \times D}{E_L}$

MM Assumptions and Why They Fail

**Assumptions**: no taxes, no transaction or bankruptcy costs, individuals borrow at the same rate as firms.

**If individuals pay more to borrow**: corporate leverage CAN add value.

**Reality**: industries stick to typical D/E ratios (banks high, pharma low) → taxes & bankruptcy costs matter (Week 3+).

MM Proposition II (No Taxes) – Logic

**Meaning**: the cost of equity rises LINEARLY with D/E.

**Why**: more debt → equity holders bear more financial risk → demand a higher return.

**Requires**: $R_A > R_D$ (even unlevered equity is riskier than debt).

**Formula sheet**: $R_0 = R_A$ (all-equity cost of capital); set $t_C = 0$ for no-tax questions.

WACC Without Taxes (Trap!)

**Rule (MM)**: $R_{WACC} = R_A$ at ANY debt–equity ratio.

**Trap**: debt is cheaper than equity, so adding debt LOOKS like it lowers the WACC.

**Reality**: the remaining equity gets riskier, $R_E$ rises, and this exactly offsets the cheaper debt.

MM II Graph

**$R_E$**: upward-sloping straight line vs D/E (slope = $R_A - R_D$).

**$R_{WACC}$**: flat line at $R_A$.

**$R_D$**: flat line (debt treated as riskless).

**$R_A$**: a single POINT (at D/E = 0), not a line.

MM II and Beta – Same Idea

**Week 1**: leverage raises the equity beta; asset beta stays fixed.

**Week 2**: leverage raises $R_E$ (MM II); $R_A$ stays fixed.

**Link**: higher equity beta in the CAPM = higher $R_E$; two views of the same financial risk.

Share Price Around Financing Decisions (MM)

**Announcement**: price jumps by project NPV ÷ shares outstanding (efficient markets).

**At the issue itself**: price does NOT move, whether debt or equity is issued (no new info).

**Debt-financed buyback**: price unchanged; shares repurchased = debt raised ÷ share pri