CFA (Chartered Financial Analyst) Corporate Issuers Syllabus

When can NPV and IRR give conflicting rankings for mutually exclusive projects, and which rule is preferred?

They can conflict when projects differ in scale or in the timing/pattern of cash flows. NPV is preferred because it measures the absolute increase in shareholder wealth and assumes reinvestment at the cost of capital, whereas IRR assumes reinvestment at the IRR.

What problems can arise with the IRR method?

Multiple IRRs (or no IRR) when cash flow signs change more than once (non-conventional cash flows), and incorrect rankings for mutually exclusive projects due to scale or timing differences.

Define a real option in capital budgeting and name common types.

A real option is the right (not obligation) to alter a project as conditions change, adding flexibility/value. Types: timing (delay) options, abandonment options, expansion (growth) options, flexibility (e.g., price-setting or production) options, and fundamental options.

How does the existence of real options affect a project's NPV?

$$NPV_{overall} = NPV_{(without\ option)} - cost\ of\ option + value\ of\ option.$$ Valuable flexibility (e.g., to expand or abandon) raises the project's overall value above the static NPV.

What is the cost of capital, and why does a firm use it?

The cost of capital is the rate of return required by the firm's suppliers of capital; it is the marginal cost of raising new funds and serves as the discount rate (hurdle rate) for evaluating average-risk investments.

State the formula for the weighted average cost of capital (WACC).

$$WACC = w_{d}\,r_{d}(1-t) + w_{p}\,r_{p} + w_{e}\,r_{e}$$ where $w$ are the market-value weights of debt, preferred, and equity; $r_d, r_p, r_e$ are their costs; and $t$ is the marginal tax rate applied to debt.

Why is the after-tax cost of debt used in WACC, and what is its formula?

Interest is tax-deductible, providing a tax shield, so the relevant cost is after-tax: $$r_{d}(1-t).$$ Only debt receives this adjustment because dividends are not tax-deductible.

What weights should be used in WACC, and why?

Target (or market-value) capital structure weights, because WACC reflects the marginal cost of raising new capital in the proportions the firm intends to maintain, not historical book values.

State the CAPM formula for the cost of equity.

$$r_{e} = R_{f} + \beta\,(E[R_{m}] - R_{f})$$ where $R_f$ is the risk-free rate, $\beta$ is the stock's systematic risk, and $(E[R_m]-R_f)$ is the equity risk premium.

Give the dividend discount (Gordon growth) model formula for the cost of equity.

$$r_{e} = \frac{D_{1}}{P_{0}} + g$$ where $D_1$ is next year's expected dividend, $P_0$ is the current price, and $g$ is the constant dividend growth rate.

What is the bond-yield-plus-risk-premium approach to cost of equity?

$$r_{e} = r_{d} + \text{risk premium},$$ where the firm's before-tax cost of debt (bond yield) is increased by a risk premium (often 3%-5%) to reflect equity's higher risk.

How is the cost of preferred stock (non-callable, non-convertible) calculated?

$$r_{p} = \frac{D_{p}}{P_{p}}$$ where $D_p$ is the fixed preferred dividend and $P_p$ is the current preferred share price. No tax adjustment because dividends are not tax-deductible.

What is the country risk premium (CRP), and how is it added to the cost of equity?

An extra premium for the political/economic risk of an emerging market. It is added to the equity risk premium: $$r_{e} = R_{f} + \beta\,[\,(E[R_{m}]-R_{f}) + CRP\,].$$

Give a common formula for estimating the country risk premium.

$$CRP = \text{Sovereign yield spread} \times \frac{\sigma_{Equity}}{\sigma_{Bond}}$$ i.e., the sovereign yield spread scaled by the ratio of the annualized standard deviation of the local equity market to that of the local sovereign bond market.

What is the difference between a levered beta and an unlevered (asset) beta?

Levered (equity) beta reflects both business and financial (leverage) risk; unlevered/asset beta reflects only business risk. They relate via $$\beta_{asset} = \frac{\beta_{equity}}{1 + (1-t)\frac{D}{E}}.$$

State Modigliani-Miller Proposition I without taxes.

In a perfect market with no taxes, capital structure is irrelevant: firm value is independent of its debt-equity mix, $V_L = V_U$. Value depends only on the firm's assets and operating cash flows.

State Modigliani-Miller Proposition II without taxes.

The cost of equity rises linearly with leverage: $$r_{e} = r_{0} + (r_{0} - r_{d})\frac{D}{E},$$ so WACC stays constant. The benefit of cheaper debt is exactly offset by higher equity cost.

How does MM Proposition I change when corporate taxes are introduced?

Debt creates a tax shield, so value rises with leverage: $$V_{L} = V_{U} + t\,D,$$ where $tD$ is the present value of the interest tax shield. This implies a theoretically optimal structure of nearly 100% debt absent other costs.

According to the static trade-off theory, what determines the optimal capital structure?

The balance between the tax benefits of debt and the costs of financial distress (and agency costs). Optimal leverage is where the marginal value of the tax shield equals the marginal expected cost of financial distress, minimizing WACC and maximizing firm value.

What does the pecking order theory say about financing preferences?

Due to asymmetric information, managers prefer financing in order: internal funds (retained earnings) first, then debt, and external equity only as a last resort. Issuing equity signals overvaluation, so it is least preferred.

Define the degree of operating leverage (DOL) and give its formula.

DOL measures the sensitivity of operating income (EBIT) to changes in units sold (or sales): $$DOL = \frac{\%\Delta EBIT}{\%\Delta Q} = \frac{Q(P - V)}{Q(P - V) - F}.$$

Define the degree of financial leverage (DFL) and give its formula.

DFL measures the sensitivity of net income (or EPS) to changes in EBIT: $$DFL = \frac{\%\Delta EPS}{\%\Delta EBIT} = \frac{EBIT}{EBIT - I},$$ where $I$ is interest expense.

Define the degree of total leverage (DTL) and its relationship to DOL and DFL.

DTL measures the sensitivity of net income/EPS to changes in units sold: $$DTL = DOL \times DFL = \frac{\%\Delta EPS}{\%\Delta Q}.$$ It combines operating and financial leverage.

What is the breakeven quantity of sales, and give its formula.

The number of units at which net income (or operating income) is zero. Operating breakeven: $$Q_{OBE} = \frac{F}{P - V}.$$ Including fixed financing costs: $$Q_{BE} = \frac{F + I}{P - V}.$$

Define net working capital and the cash conversion cycle.

Net working capital = current assets - current liabilities. The cash conversion cycle = Days of Inventory Outstanding + Days of Sales Outstanding - Days of Payables Outstanding; it measures days between paying for inputs and collecting from customers.

What is the difference between liquidity ratios and a firm's primary vs secondary sources of liquidity?

Liquidity ratios (current, quick, cash) measure ability to meet short-term obligations. Primary sources are readily available funds (cash, short-term credit lines); secondary sources (asset sales, debt restructuring, bankruptcy) may threaten operations or signal distress.

State the current ratio and the quick (acid-test) ratio formulas.

$$\text{Current ratio} = \frac{\text{Current assets}}{\text{Current liabilities}}; \quad \text{Quick ratio} = \frac{\text{Cash} + \text{Marketable securities} + \text{Receivables}}{\text{Current liabilities}}.$$

What is the difference between an aggressive and a conservative working capital (financing) policy?

An aggressive policy finances more current assets with short-term debt—higher return but higher liquidity/refinancing risk. A conservative policy uses more long-term financing—lower risk but typically lower return (higher financing cost).

What practical factors influence a firm's actual capital structure decisions beyond MM theory?

Target debt ratios, business risk and earnings stability, asset tangibility (collateral), tax position, financial flexibility, market conditions, agency costs, debt covenants, the firm's life-cycle stage, and signaling considerations.

Define corporate restructuring and name its three broad categories.

Material changes to a company's composition, structure, or operations. Categories: (1) investment actions that grow the firm (e.g., acquisitions), (2) divestment actions that shrink it (e.g., divestitures, spin-offs), and (3) restructuring of capital/ownership (e.g., leveraged recapitalizations, bankruptcy reorganization).

Distinguish a horizontal, vertical, and conglomerate merger.

Horizontal—combining firms in the same industry/business (seeking economies of scale, market power). Vertical—combining firms at different stages of the same production chain (e.g., supplier and producer). Conglomerate—combining firms in unrelated businesses (diversification).

Differentiate a divestiture, a spin-off, and a carve-out.

Divestiture—selling a division/asset to a third party for cash. Spin-off—distributing shares of a subsidiary to existing shareholders, creating a new independent public company with no cash raised. Carve-out (equity carve-out)—selling a minority stake in a subsidiary via IPO to outside investors, raising cash.