Sources and References

Primary textbook — Berk, J., DeMarzo, P., and Stangeland, D. Corporate Finance, Sixth Canadian Edition. Pearson Canada, 2024.

Supplementary — Ross, S. A., Westerfield, R. W., and Jordan, B. D. Fundamentals of Corporate Finance, 13th Edition. McGraw-Hill, 2022. | Brealey, R. A., Myers, S. C., and Allen, F. Principles of Corporate Finance, 13th Edition. McGraw-Hill, 2020.

Online resources — MIT OpenCourseWare 15.401 Finance Theory I; CFA Institute curriculum on capital structure and valuation; Bank of Canada monetary policy publications.

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Chapter 1: Risk and Return — Foundations

1.1 The Risk-Return Tradeoff

Every financial decision begins with a fundamental tradeoff: to earn higher expected returns, an investor must accept greater risk. This principle governs not only individual investment decisions but also corporate financial policy. A firm’s cost of capital — the rate of return demanded by investors — depends directly on the riskiness of the firm’s assets and cash flows.

1.2 Systematic vs. Idiosyncratic Risk

Financial risk decomposes into two components. Systematic risk (also called market risk or undiversifiable risk) arises from economy-wide forces such as recessions, changes in interest rates, and inflation. Because systematic risk affects all firms simultaneously, it cannot be eliminated by diversification. Idiosyncratic risk (firm-specific or unsystematic risk) arises from events unique to a company, such as a product recall or executive departure. Holding a diversified portfolio causes idiosyncratic risks to cancel out.

The total risk of any asset can be decomposed as:

\[ \text{Total Risk} = \text{Systematic Risk} + \text{Idiosyncratic Risk} \]

As the number of assets in a portfolio grows, the idiosyncratic component of portfolio variance approaches zero, leaving only systematic risk.

1.3 Portfolio Theory and Diversification

Harry Markowitz demonstrated that combining assets whose returns are not perfectly correlated reduces portfolio variance. For a two-asset portfolio:

\[ \sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_{12} \]

where \(\sigma_{12} = \rho_{12} \sigma_1 \sigma_2\) is the covariance between assets 1 and 2. The lower the correlation \(\rho_{12}\), the greater the diversification benefit. When \(\rho_{12} = -1\), a perfect hedge is theoretically achievable.

1.4 The Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM), developed by William Sharpe (1964) and John Lintner (1965), provides a precise relationship between systematic risk and required return. The CAPM rests on assumptions of mean-variance optimization, homogeneous expectations, and frictionless markets.

1.4.1 Estimating Beta

In practice, beta is estimated by regressing a stock’s historical excess returns on the market’s excess returns over a sample period (typically 60 monthly observations):

\[ r_i - r_f = \alpha_i + \beta_i (r_m - r_f) + \varepsilon_i \]

The slope coefficient \(\hat{\beta}_i\) is the estimated beta. Betas are typically published by financial data providers (Bloomberg, Refinitiv). Because raw betas revert toward 1.0 over time, practitioners often use adjusted betas:

\[ \beta_{\text{adjusted}} = \frac{2}{3} \hat{\beta} + \frac{1}{3}(1.0) \]

Sector	Typical Beta Range
Utilities	0.3 – 0.7
Consumer staples	0.5 – 0.8
Financial services	0.9 – 1.3
Technology	1.0 – 1.8
Biotechnology	1.2 – 2.0

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Chapter 2: Capital Structure in Perfect Capital Markets

2.1 The Modigliani-Miller Propositions

In 1958, Franco Modigliani and Merton Miller (MM) posed a deceptively simple question: does the way a firm finances itself affect its total value? Under idealized conditions — no taxes, no bankruptcy costs, no information asymmetries, and complete markets — the answer is no.

The intuition is an arbitrage argument. If a levered firm traded at a different price than an equivalent unlevered firm, investors could replicate the payoff of one using the other plus personal borrowing or lending (“homemade leverage”), eliminating any price difference.

As debt increases, equity holders face more financial risk (their residual claim is more volatile), so they demand a higher expected return. The WACC remains constant regardless of leverage:

\[ \text{WACC} = \frac{E}{V} r_E + \frac{D}{V} r_D \]

2.2 Homemade Leverage

A key implication of MM is that individual investors can undo any capital structure decision made by the firm. If a firm is unlevered but an investor wants the payoff of a levered investment, they can borrow personally and buy more of the unlevered firm’s equity. Conversely, if a firm is levered but the investor prefers an unlevered payoff, they can lend (buy government bonds) alongside holding the levered equity.

2.3 Why Perfect Markets Are a Starting Point

The MM framework is valuable precisely because it identifies the conditions under which capital structure would be irrelevant. In reality, taxes, financial distress costs, and information asymmetries make capital structure matter enormously. The subsequent chapters relax each assumption in turn to understand what drives real-world capital structure decisions.

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Chapter 3: Debt and Taxes

3.1 The Interest Tax Shield

The Canadian Income Tax Act (and its counterparts worldwide) allows corporations to deduct interest expense before calculating taxable income. Dividends paid to equity holders are not deductible. This asymmetry gives debt a tax advantage.

3.2 The WACC with Taxes

When taxes are present, the after-tax cost of debt is \(r_D (1 - \tau_c)\), giving:

\[ \text{WACC} = \frac{E}{V} r_E + \frac{D}{V} r_D (1 - \tau_c) \]

The tax shield effectively lowers the WACC, which raises firm value when future free cash flows are discounted at the lower rate. This is a departure from the perfect-markets MM world where WACC was constant.

3.3 MM Proposition II with Taxes

With corporate taxes, the required return on equity in a levered firm becomes:

\[ r_E = r_U + \frac{D}{E}(1 - \tau_c)(r_U - r_D) \]

Notice that the leverage premium is now scaled by \((1-\tau_c)\), so the increase in required equity return is smaller than in the no-tax case. The tax shield partially cushions the increased financial risk borne by equity holders.

3.4 Personal Taxes

Miller (1977) extended the analysis to include personal taxes. Investors pay taxes on interest income at the personal rate \(\tau_{pD}\) and on equity income (dividends and capital gains) at an effective rate \(\tau_{pE}\). The net tax advantage of debt relative to equity is:

\[ \text{Net Tax Advantage} = 1 - \frac{(1-\tau_c)(1-\tau_{pE})}{(1-\tau_{pD})} \]

In Canada, the dividend tax credit and the preferential treatment of capital gains (only 50% of capital gains are included in taxable income) reduce but typically do not eliminate the tax advantage of corporate debt. The effective Canadian personal tax rates on equity income are meaningfully lower than those on interest income, which partially offsets the corporate-level benefit of debt.

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Chapter 4: Financial Distress, Managerial Incentives, and Information

4.1 Costs of Financial Distress

As leverage rises, the probability that a firm cannot meet its debt obligations increases. Financial distress — the situation where cash flows may be insufficient to service debt — imposes real costs that offset the tax shield benefit.

Direct costs include legal fees, administrative costs of bankruptcy proceedings, and management time diverted to financial restructuring rather than value creation. Studies estimate direct costs at 3–5% of pre-distress firm value for large firms, and proportionally higher for small firms.

Indirect costs are often much larger:

• Underinvestment (debt overhang): When a firm is in financial distress, shareholders may refuse to fund positive-NPV projects if the gains accrue primarily to bondholders. This “debt overhang” problem (Myers, 1977) destroys value.
• Asset substitution (risk shifting): Levered equity holders have an incentive to take on excessive risk, because they capture the upside while bondholders bear more of the downside. This transfers wealth from creditors to shareholders.
• Loss of customers and suppliers: Customers of distressed firms may lose confidence in future warranty and service commitments. Suppliers may demand cash payment rather than extending trade credit.
• Management distraction: Executives spend time on lender negotiations rather than value creation.

4.2 The Trade-Off Theory of Capital Structure

The trade-off theory predicts that:

1. Firms with stable, predictable cash flows (e.g., utilities, consumer staples) can sustain higher leverage because default probability is low.
2. Firms with valuable intangible assets (e.g., growth firms in technology) should use less debt, because intangibles lose value quickly in distress.
3. The optimal debt ratio increases with the tax rate and decreases with the probability of distress.

4.3 Agency Costs and Capital Structure

Agency costs of equity arise from separation of ownership and control. Managers (agents) may consume perquisites, pursue empire building, or underperform when shareholders (principals) cannot perfectly monitor them. Leverage mitigates some of these costs by:

• Reducing free cash flow available for wasteful spending (Jensen, 1986 free cash flow hypothesis)
• Subjecting management to market discipline — a firm that cannot service its debt faces takeover or bankruptcy

Agency costs of debt take the form of underinvestment and asset substitution problems. Protective covenants in bond indentures restrict dividend payments, additional borrowing, and asset sales to partially address these problems.

4.4 The Pecking Order Theory

The reason: equity issuance signals to the market that management believes the stock is overvalued (managers have superior information about true firm value), causing the stock price to fall. Debt does not convey this negative signal as strongly. Therefore, in the presence of information asymmetry, firms follow a hierarchy of financing preferences rather than targeting an optimal leverage ratio.

Pecking order predictions:

• Profitable firms accumulate retained earnings and have lower debt ratios
• Firms issue equity when other sources are exhausted or when asymmetric information is low
• Dividend smoothing creates “financial slack” that reduces reliance on costly external financing

Theory	Primary Driver	Key Prediction
Trade-Off Theory	Tax shields vs. distress costs	Firms have target leverage ratios
Pecking Order Theory	Information asymmetry	No target ratio; equity last resort
Market Timing Theory	Mispricing	Firms issue equity when overvalued
Agency Theory	Manager-shareholder conflicts	Leverage disciplines management

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Chapter 5: Payout Policy

5.1 Forms of Payout

A firm distributes cash to shareholders primarily through dividends and share repurchases. The choice between these mechanisms has important implications for taxes, signaling, and financial flexibility.

In Canada, eligible dividends from Canadian-controlled private corporations (CCPCs) and public corporations receive a dividend tax credit (DTC) that partially offsets the double taxation effect (corporate tax paid, then personal dividend tax). The enhanced dividend tax credit rate as of 2024 is approximately 15.02% federally on grossed-up dividends.

5.2 The MM Dividend Irrelevance Theorem

Under the same idealized conditions as MM capital structure irrelevance, Modigliani and Miller (1961) showed that dividend policy is also irrelevant to firm value given a fixed investment policy.

The logic: Any dollar paid as a dividend reduces retained earnings by a dollar, requiring the firm to raise an additional dollar from the capital market. The new shares issued dilute existing shareholders exactly enough to offset the dividend received. Net wealth of existing shareholders is unchanged.

5.3 Why Dividends Matter in Practice

In practice, dividends matter for several reasons:

1. Tax effects: Differential personal taxation of dividends and capital gains creates payout preferences. High-tax-bracket investors prefer capital gains (deferred, lower rate); low-tax-bracket investors (e.g., pension funds, RRSPs) may prefer dividends.
2. Clientele effect: Different investor clienteles prefer different payout policies. Retirees seeking current income prefer dividends; growth-oriented institutional investors may prefer share repurchases.
3. Signaling: Dividend increases convey management’s confidence in sustained future earnings. Dividend cuts are associated with sharp negative stock price reactions (average −15 to −20%).
4. Agency costs: Regular dividends commit firms to distributing cash, reducing the free cash flow available for wasteful managerial spending.

5.4 Dividend Smoothing

The dividend smoothing phenomenon is well-documented: firms adjust dividends gradually toward a target payout ratio, as modeled by Lintner (1956):

\[ \Delta DIV_t = \text{SOA} \times \left[ \text{Target Payout} \times EPS_t - DIV_{t-1} \right] \]

where SOA (speed of adjustment) is typically 0.3 to 0.5 for large North American firms. Firms are reluctant to cut dividends, so they raise them cautiously when earnings improve.

5.5 Share Repurchases vs. Dividends

Feature	Cash Dividend	Share Repurchase
Tax treatment	Taxed as dividend income	Capital gains (deferred, lower rate)
Flexibility	Commitment signal; cuts are costly	Flexible; no expectation created
Share price reaction	Falls by approximately dividend amount on ex-date	Positive (signal of undervaluation)
Effect on EPS	No effect on shares outstanding	Increases EPS (fewer shares)
Appropriate when	Stable, mature firms with steady cash flow	Firm believes stock is undervalued

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Chapter 6: Capital Budgeting and Valuation with Leverage

6.1 Interactions Between Financing and Investment

When firms partially finance projects with debt, the tax shield on interest creates value that must be captured in the project’s valuation. Two principal methods handle this: the WACC method and the Adjusted Present Value (APV) method.

6.2 The WACC Method

The most common approach discounts unlevered free cash flows at the after-tax WACC:

\[ V_L = \sum_{t=1}^{T} \frac{FCF_t}{(1 + \text{WACC})^t} + \frac{TV_T}{(1+\text{WACC})^T} \]

where \(TV_T\) is the terminal value at the end of the explicit forecast horizon. This approach implicitly assumes the firm rebalances debt continuously to maintain a constant debt-to-value ratio. The tax shield is embedded in the discount rate rather than valued separately.

6.3 The Adjusted Present Value (APV) Method

The APV method, developed by Stewart Myers (1974), separates the base-case value from financing effects:

\[ APV = V_U + PV(\text{Tax Shield}) - PV(\text{Financial Distress Costs}) \]

The base-case value \(V_U\) is computed by discounting FCF at the unlevered cost of equity \(r_U\), reflecting the risk of assets alone without any financing benefit. Then each financing side-effect is valued and added or subtracted separately.

APV is particularly useful when the debt level is predetermined (not rebalanced with firm value), such as in leveraged buyouts (LBOs) where large amounts of fixed debt are scheduled for repayment.

6.4 Beta, Leverage, and the Hamada Equation

When a firm changes its capital structure, both its equity beta and the risk perceived by equity investors change. The relationship between asset (unlevered) beta and equity (levered) beta is given by the Hamada equation:

\[ \beta_E = \beta_U \left( 1 + \frac{D(1-\tau_c)}{E} \right) \]

Conversely, to unlever an observed equity beta:

\[ \beta_U = \frac{\beta_E}{1 + \frac{D(1-\tau_c)}{E}} \]

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Chapter 7: Equity Financing

7.1 Sources of Equity Capital

Firms raise equity at various stages of their life cycle, from seed capital through public markets.

Private Equity (PE) firms in leveraged buyouts (LBOs) use high levels of debt to acquire mature firms, seeking value through operational improvements, debt pay-down, and subsequent sale or IPO.

7.2 Initial Public Offerings

A firm raises external equity for the first time through an Initial Public Offering (IPO).

7.2.1 The IPO Process

1. Selection of underwriters: Investment banks advise on timing and pricing, and conduct the sale. Most IPOs use firm-commitment underwriting, where the bank guarantees a price and bears the residual risk. In a best-efforts arrangement, the bank acts as agent only.
2. Registration and prospectus: Securities regulators (in Canada, provincial commissions coordinated by the CSA) require a prospectus — a detailed disclosure covering financial history, use of proceeds, and risk factors.
3. Roadshow and book-building: The underwriter solicits indications of interest from institutional investors to gauge demand and set the offering price.
4. Greenshoe option (over-allotment): Underwriters receive an option to sell up to 15% additional shares, used to stabilize the aftermarket price.

7.2.2 IPO Underpricing

A robust empirical finding is that IPO shares are systematically underpriced — the first-day closing price typically exceeds the offer price. Average first-day returns in Canada and the US range from 10 to 20%.

Explanations include:

• Rock’s winner’s curse: Uninformed investors receive more shares in overpriced IPOs (informed investors avoid them), so uninformed investors must be compensated with underpricing to participate.
• Signaling: High-quality firms underprice as a costly signal to distinguish themselves from low-quality firms (who cannot afford to leave money on the table).
• Underwriter incentives: Underwriters benefit from loyal institutional clients who receive underpriced shares.

7.2.3 Seasoned Equity Offerings

After going public, a firm may raise additional equity through a Seasoned Equity Offering (SEO). SEO announcements typically cause stock prices to fall 2–3%, consistent with signaling theories. In a rights offering, existing shareholders receive subscription rights allowing them to purchase new shares at a discount, preserving proportional ownership.

7.3 Private Placements and Shelf Registration

Experienced issuers can use shelf registration (SEC Rule 415 in the US; comparable Canadian equivalents) to register a large block of securities in advance and issue them in tranches as market conditions allow. Private placements to accredited investors (Rule 144A in the US) bypass public registration requirements but restrict resale.

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Chapter 8: Debt Financing

8.1 Types of Debt Securities

Corporate debt ranges from short-term commercial paper to long-term bonds. Key characteristics include face value (par), coupon rate, maturity, seniority, and covenants.

In the priority waterfall at bankruptcy, secured creditors are paid first, followed by senior unsecured creditors, subordinated (junior) debt holders, preferred shareholders, and finally common equity holders.

8.2 Bond Pricing

A bond’s price equals the present value of its future cash flows:

\[ P = \sum_{t=1}^{T} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^T} = C \times \frac{1 - (1+y)^{-T}}{y} + \frac{F}{(1+y)^T} \]

where \(C\) is the periodic coupon payment, \(F\) is face value, \(y\) is the yield to maturity (YTM), and \(T\) is the number of periods.

Key bond price relationships:

• When YTM > coupon rate, the bond trades at a discount (price < par).
• When YTM < coupon rate, the bond trades at a premium (price > par).
• When YTM = coupon rate, the bond trades at par.
• Bond prices and yields move inversely.

8.3 Duration and Interest Rate Sensitivity

A bond’s Macaulay duration measures the weighted average time to receive cash flows, where weights are the present value of each cash flow as a fraction of the total price:

\[ D = \frac{\sum_{t=1}^{T} t \times \frac{C/(1+y)^t + F/(1+y)^T \cdot \mathbf{1}_{t=T}}{P}}{1} \]

Modified duration approximates the percentage price change for a small change in yield:

\[ D^* = \frac{D}{1+y} \]\[ \frac{\Delta P}{P} \approx -D^* \times \Delta y \]

8.4 Zero-Coupon Bonds

Zero-coupon bonds pay no periodic interest, returning only face value at maturity. They are issued at a deep discount:

\[ P = \frac{F}{(1+y)^T} \]

Zero-coupon bonds have duration equal to their maturity, making them the most interest-rate sensitive bonds for a given term. Strip bonds (created by separating coupon and principal cash flows of government bonds) are the most common form.

8.5 Bond Covenants

Types of covenants:

• Affirmative covenants: Firm must maintain minimum financial ratios (e.g., interest coverage ratio ≥ 3.0×) and provide regular financial statements.
• Negative covenants: Firm may not pay dividends above a threshold, issue additional senior debt, sell major assets, or engage in mergers without bondholder consent.
• Call provisions: Allow the firm to repurchase bonds before maturity at a preset call price, giving flexibility if interest rates fall. Callable bonds offer higher coupons to compensate investors for the call risk.
• Convertible provisions: Allow bondholders to convert to equity at a preset conversion ratio. Conversion is attractive when the stock price exceeds the conversion price.

8.6 Credit Risk and Credit Ratings

Credit rating agencies (Moody’s, S&P, DBRS Morningstar in Canada) assign ratings from AAA/Aaa (highest quality) to D (default). The credit spread — the yield differential between a corporate bond and a government bond of the same maturity — compensates investors for default risk, liquidity risk, and taxation differences.

S&P Rating	Moody’s	Description
AAA	Aaa	Highest quality, minimal credit risk
AA	Aa	High quality, very low credit risk
A	A	Strong capacity to meet obligations
BBB	Baa	Adequate protection; investment grade cutoff
BB	Ba	Speculative; subject to substantial risk
B	B	Speculative; high credit risk
CCC	Caa	Substantial risk; near default
D	C	In default

Bonds rated BBB/Baa and above are investment grade. Those below are speculative grade (high-yield or “junk” bonds). Many institutional investors (pension funds, insurance companies) are restricted to holding investment-grade securities.

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Chapter 9: Time Value of Money — Review and Extensions

9.1 Present Value and Future Value

The foundation of all financial valuation is the time value of money: a dollar received today is worth more than a dollar received in the future because it can be invested to earn a return.

9.2 Annuities

9.3 Perpetuities

9.4 Effective Annual Rate vs. Stated Rate

When interest is compounded more frequently than annually, the effective annual rate (EAR) exceeds the stated (nominal) annual rate:

\[ EAR = \left(1 + \frac{r_{\text{stated}}}{m}\right)^m - 1 \]

where \(m\) is the number of compounding periods per year.

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Chapter 10: Capital Budgeting

10.1 Net Present Value (NPV)

NPV is the theoretically correct investment criterion because it:

1. Uses all cash flows over the project’s life
2. Properly discounts cash flows to reflect the time value of money and risk
3. Gives the direct dollar increase in shareholder wealth from accepting the project

10.2 Internal Rate of Return (IRR)

10.2.1 Limitations of IRR

Despite its intuitive appeal, IRR has several important limitations:

1. Multiple IRRs: When cash flows change sign more than once (e.g., a project with clean-up costs at end), there may be multiple IRRs or none. NPV is unambiguous.
2. Scale problem: For mutually exclusive projects of different sizes, IRR can lead to incorrect ranking. A small project with a high IRR may have a lower NPV than a large project with a lower IRR.
3. Timing problem: IRR implicitly assumes that interim cash flows are reinvested at the IRR. NPV assumes reinvestment at the cost of capital, which is more realistic.
4. Non-conventional cash flows: IRR analysis can be misleading when initial inflows are followed by outflows.

10.3 Payback Period

Limitations: Ignores time value of money, ignores cash flows after payback, cutoff is arbitrary. The discounted payback period addresses the first limitation by discounting each cash flow before computing the cumulative total, but still ignores post-payback cash flows.

10.4 Profitability Index

10.5 Mutually Exclusive Projects and Capital Rationing

When projects are mutually exclusive (only one can be chosen), use NPV rather than IRR to rank. The incremental (differential) IRR approach can resolve ranking conflicts: compute the IRR on the incremental cash flows between the two projects; if incremental IRR > hurdle rate, choose the larger project.

Under capital rationing (limited investment budget), select projects to maximize total NPV subject to the budget constraint. For independent projects, rank by PI and select down the list until the budget is exhausted. For complex combinations with integer constraints, use integer programming.

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Chapter 11: Stock Valuation

11.1 The Dividend Discount Model (DDM)

The intrinsic value of a stock equals the present value of all expected future dividends:

\[ P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1+r_E)^t} \]

where \(D_t\) is the dividend per share in period \(t\) and \(r_E\) is the required return on equity.

11.1.1 Constant Growth DDM (Gordon Growth Model)

If dividends grow at a constant rate \(g\) forever (\(r_E > g\)):

\[ P_0 = \frac{D_1}{r_E - g} \]

Implied required return: If the current price and next dividend are observable, solve for \(r_E\):

\[ r_E = \frac{D_1}{P_0} + g = \text{Dividend yield} + \text{Capital gains yield} \]

11.1.2 Multi-Stage DDM

For firms with non-constant growth, the DDM is applied in two (or more) stages:

1. Forecast dividends explicitly during the high-growth phase (years 1 through \(n\))
2. Apply the Gordon Growth Model to estimate the terminal value at year \(n\) using a long-run sustainable growth rate

\[ P_0 = \sum_{t=1}^{n} \frac{D_t}{(1+r_E)^t} + \frac{1}{(1+r_E)^n} \times \frac{D_{n+1}}{r_E - g_{\infty}} \]

11.2 Free Cash Flow to Equity (FCFE) Model

When a firm does not pay dividends matching its free cash flow, the FCFE model values the equity based on the cash available to equity holders after all debt obligations:

\[ FCFE = Net Income + Depreciation - CAPEX - \Delta NWC - \text{Debt repayments} + \text{New borrowings} \]\[ P_0 = \sum_{t=1}^{\infty} \frac{FCFE_t}{(1+r_E)^t} \]

11.3 Comparable Company Analysis (Multiples)

Relative valuation benchmarks a firm’s value against comparable firms using market multiples.

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Chapter 12: Cost of Capital — WACC

12.1 Overview of the WACC

The Weighted Average Cost of Capital (WACC) is the minimum return a firm must earn on its existing assets to satisfy all capital providers — both debt and equity holders. It serves as the discount rate for evaluating new investments with the same risk profile as the firm’s existing assets.

\[ \text{WACC} = \frac{E}{V} r_E + \frac{P}{V} r_P + \frac{D}{V} r_D (1-\tau_c) \]

where:

• \(E\) = market value of equity, \(D\) = market value of debt, \(P\) = market value of preferred shares, \(V = E + D + P\)
• \(r_E\) = cost of equity, \(r_P\) = cost of preferred shares, \(r_D\) = cost of debt
• \(\tau_c\) = corporate marginal tax rate
• Weights are based on market values, not book values

12.2 Cost of Equity (via CAPM)

The most common approach is to use the CAPM:

\[ r_E = r_f + \beta_E (r_m - r_f) \]

Steps:

1. Determine the risk-free rate (typically 10-year Government of Canada bond yield)
2. Estimate the equity risk premium (ERP), typically 4–6% for Canadian markets
3. Estimate beta from regression of stock returns on market returns, or use industry beta

12.3 Cost of Preferred Shares

Preferred shares pay a fixed dividend \(D_P\) and are typically perpetual. Their cost is:

\[ r_P = \frac{D_P}{P_P} \]

where \(P_P\) is the current market price of the preferred share. Note that preferred dividends are not tax-deductible in Canada, so no tax adjustment is applied to \(r_P\).

12.4 Cost of Debt

The pre-tax cost of debt is estimated as the yield to maturity on the firm’s existing long-term debt. The after-tax cost of debt is:

\[ r_D^{\text{after-tax}} = r_D \times (1 - \tau_c) \]

If the firm has no publicly traded bonds, the cost of debt can be estimated by looking at the yields on bonds of comparable firms with the same credit rating.

12.5 Full WACC Example

12.6 Divisional WACC and Pure-Play Method

When a firm operates in multiple business segments with different risk profiles, using a single firm-wide WACC leads to misallocation of capital: too many low-risk projects are rejected (their true hurdle rate is lower) and too many high-risk projects are accepted.

The pure-play method estimates a separate cost of capital for each division:

1. Identify publicly traded firms that operate solely in the division’s industry.
2. Unlever their equity betas to obtain asset betas.
3. Relever the asset beta to the target division’s capital structure.
4. Apply CAPM to get the divisional cost of equity and compute divisional WACC.

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Chapter 13: Working Capital Management

13.1 The Cash Conversion Cycle

Working capital is the excess of current assets over current liabilities. Effective management requires understanding the cash conversion cycle (CCC):

\[ CCC = DIO + DSO - DPO \]

A shorter CCC implies the firm needs less permanent working capital investment. Firms aim to minimize DIO and DSO while maximizing DPO (within the limits set by supplier terms).

13.2 Cash Management

Firms hold cash for three reasons (Keynes): (1) transactions — to meet day-to-day payment obligations; (2) precautionary — as a buffer against unexpected cash shortfalls; and (3) speculative — to exploit investment opportunities quickly.

The Baumol model treats cash management as an EOQ (economic order quantity) problem: the firm periodically liquidates marketable securities to replenish its cash balance, trading off transaction costs against the opportunity cost of holding cash. The optimal cash balance is:

\[ C^* = \sqrt{\frac{2TF}{r}} \]

where \(T\) is the total annual cash disbursements, \(F\) is the fixed cost per securities transaction, and \(r\) is the opportunity cost (short-term interest rate).

13.3 Receivables Management

Extending trade credit to customers is effectively a short-term investment. The firm must evaluate the credit terms offered and the creditworthiness of customers. Credit decisions involve:

1. Credit standards: Which customers qualify? Evaluated using the five C’s of credit: Character, Capacity, Capital, Collateral, Conditions.
2. Credit terms: The “2/10 net 30” convention means a 2% discount if paid within 10 days, otherwise full payment due in 30 days.
3. Collection policy: Procedures for pursuing late payers (reminder statements, collection agencies, legal action).

The cost of trade credit discount to a customer who forgoes the early-payment discount and pays at the net date:

\[ \text{Annualized Cost} = \left(1 + \frac{d}{1-d}\right)^{365/N} - 1 \]

where \(d\) is the discount percentage and \(N\) is the extra days gained by delaying payment.

13.4 Inventory Management

Inventory represents a significant investment for manufacturing and retail firms. The Economic Order Quantity (EOQ) model determines the optimal order size that minimizes total annual inventory costs:

\[ EOQ = \sqrt{\frac{2DS}{H}} \]

where \(D\) is annual demand (units), \(S\) is the fixed cost per order (ordering cost), and \(H\) is the holding cost per unit per year.

Just-in-Time (JIT) inventory management aims to minimize inventory by receiving materials exactly when needed, reducing DIO and carrying costs. JIT requires close coordination with suppliers and exposes the firm to supply chain disruptions (as evidenced during the COVID-19 pandemic).

13.5 Short-Term Financing Sources

Trade credit is the implicit financing obtained by delaying payment to suppliers. The firm benefits by extending DPO, but must weigh this against relationship costs and the annualized cost of forgone discounts.

Bank lines of credit — revolving or committed credit facilities — provide flexible short-term financing. A revolving credit facility allows the firm to draw, repay, and redraw up to the credit limit. A committed facility guarantees availability in exchange for a commitment fee.

Commercial paper is short-term (typically 30 to 270 days in the US, up to 365 days in Canada) unsecured notes issued by high-credit-quality firms directly in the money market, bypassing banks. Rates are typically below bank prime lending rates.

Factoring involves selling accounts receivable to a financial intermediary (factor) at a discount, converting receivables to immediate cash. The factor assumes the credit risk (non-recourse factoring) or the firm retains it (recourse factoring).

Short-Term Financing Source	Typical Cost	Key Feature
Trade credit (forgoing discount)	Very high (40%+ annualized)	Readily available; no negotiation needed
Bank line of credit	Prime + 1–3%	Flexible; availability depends on credit
Commercial paper	Near T-bill rate	Available only to high-rated firms
Factoring	2–5% of receivables	Immediate cash; transfers credit risk

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Chapter 14: Integrative Topics

14.1 Free Cash Flow and Firm Valuation — A Complete Example

14.2 Connecting CAPM, WACC, and Capital Budgeting

The chain of logic in corporate finance is:

1. CAPM uses beta to translate systematic risk into required return: \(r_E = r_f + \beta(r_m - r_f)\)
2. WACC blends the cost of equity, preferred, and after-tax debt based on capital structure weights
3. NPV uses WACC as the discount rate to evaluate investment projects
4. Positive NPV projects create shareholder value; accepting them increases stock price
5. Optimal capital structure minimizes WACC (after accounting for taxes and distress costs), maximizing firm value

14.3 Summary Table — Capital Budgeting Decision Rules

Method	Decision Rule	Strengths	Weaknesses
NPV	Accept if NPV > 0	Theoretically correct; maximizes value	Requires precise cash flow and discount rate estimates
IRR	Accept if IRR > hurdle rate	Intuitive percentage return	Multiple IRRs; scale/timing problems
Payback	Accept if payback ≤ cutoff	Simple; liquidity-focused	Ignores TVM; ignores post-payback flows
Discounted Payback	Accept if discounted payback ≤ cutoff	Incorporates TVM	Still ignores post-payback flows
Profitability Index	Accept if PI > 1	Useful for capital rationing	Cannot directly compare different-scale projects
MIRR	Accept if MIRR > hurdle rate	Addresses IRR reinvestment assumption	Less common in practice

14.4 Key Formulas Reference

Time Value of Money

\[ FV = PV(1+r)^n \qquad PV = \frac{FV}{(1+r)^n} \]\[ PV_{\text{annuity}} = C \times \frac{1-(1+r)^{-n}}{r} \qquad PV_{\text{perpetuity}} = \frac{C}{r} \qquad PV_{\text{growing perpetuity}} = \frac{C_1}{r-g} \]

Risk and Return

\[ E[r] = \sum_s p_s r_s \qquad \sigma^2 = \sum_s p_s(r_s - E[r])^2 \qquad \beta = \frac{\text{Cov}(r_i, r_m)}{\sigma_m^2} \]\[ r_i = r_f + \beta_i(r_m - r_f) \quad \text{(CAPM/SML)} \]

Capital Structure

\[ V_L = V_U \quad \text{(MM I, no taxes)} \qquad V_L = V_U + \tau_c D \quad \text{(MM I, with taxes)} \]\[ r_E = r_U + \frac{D}{E}(r_U - r_D) \quad \text{(MM II, no taxes)} \]\[ \text{WACC} = \frac{E}{V}r_E + \frac{D}{V}r_D(1-\tau_c) \]

Bond Pricing

\[ P = C \times \frac{1-(1+y)^{-T}}{y} + \frac{F}{(1+y)^T} \qquad \frac{\Delta P}{P} \approx -D^* \times \Delta y \]

Dividend Discount Model

\[ P_0 = \frac{D_1}{r_E - g} \quad \text{(constant growth)} \qquad r_E = \frac{D_1}{P_0} + g \]

Working Capital

\[ CCC = DIO + DSO - DPO \]\[ \text{Cost of trade credit} = \left(1 + \frac{d}{1-d}\right)^{365/N} - 1 \]

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Summary

AFM 274 traces the corporate finance decision framework across three interconnected pillars: valuation, capital structure, and financial management.

Valuation begins with the time value of money and progresses through bond pricing (coupon bonds, zero-coupon bonds, YTM, duration), stock valuation (DDM, FCFE, comparable multiples), and full discounted cash flow (DCF) analysis using free cash flows. The NPV rule is the theoretically correct investment criterion, supported by IRR, payback, and profitability index as supplementary tools.

Capital structure begins with the elegant irrelevance propositions of Modigliani and Miller, which establish a benchmark for thinking about when and why financing decisions create value. Introducing corporate taxes reveals the interest tax shield and the incentive to use debt. Introducing financial distress costs establishes the trade-off theory with an interior optimum. Agency costs and information asymmetry further enrich the analysis through pecking order theory and signaling.

Payout policy echoes the MM framework: in perfect markets, how firms return cash to shareholders is irrelevant. In reality, tax asymmetries, the clientele effect, signaling, and agency costs all make the choice between dividends and repurchases consequential.

Working capital management ensures that the firm’s short-term financial health supports its long-term value creation — managing the cash conversion cycle, receivables, inventory, and short-term financing sources to minimize the cost of operating the business on a day-to-day basis.

The central thread throughout is that corporate financial decisions should be evaluated by their impact on firm value, measured through the NPV framework with a risk-adjusted discount rate grounded in the CAPM. Managers who internalize this framework — accepting all positive-NPV projects at the correct hurdle rate, financing at the minimum WACC, distributing excess cash efficiently, and managing working capital rigorously — maximize long-run shareholder value.