CFA (Chartered Financial Analyst) Equity and Fixed Income Investments Syllabus

Compare public equity with private equity along liquidity, disclosure, and pricing.

Public equity is exchange-traded, highly liquid, subject to mandatory disclosure, and continuously priced by the market. Private equity is illiquid, has limited disclosure, is negotiated/infrequently priced, and typically involves a longer investment horizon and active ownership.

Name three main forms (strategies) of private equity investment.

Venture capital (financing early-stage/start-up companies), leveraged buyouts (acquiring mature companies using significant debt), and development/growth capital (financing expansion of established firms).

What is the intrinsic value of a stock and how does it relate to market price?

Intrinsic (fundamental) value is the value an investor estimates after fully and correctly analyzing all characteristics of the asset. If market price differs from intrinsic value, there is a mispricing: $\text{Mispricing} = (V_{\text{actual}} - P) - (V_{\text{estimate}} - V_{\text{actual}})$.

List the three major categories of equity valuation models.

(1) Present value (absolute) models—DDM, FCFF/FCFE, residual income; (2) multiplier (market-based/relative) models—P/E, P/B, P/S, EV/EBITDA; (3) asset-based valuation models using the firm's net asset value.

State the general dividend discount model (DDM) for a stock's value.

$$V_{0} = \sum_{t=1}^{\infty} \frac{D_{t}}{(1+r)^{t}}$$ where $D_{t}$ is the expected dividend in period $t$ and $r$ is the required return on equity.

State the Gordon (constant) growth dividend discount model and its key assumption.

$$V_{0} = \frac{D_{1}}{r - g} = \frac{D_{0}(1+g)}{r - g}$$ It assumes dividends grow at a constant rate $g$ in perpetuity, with $r > g$.

In the Gordon growth model, how is the sustainable (implied) dividend growth rate estimated?

$$g = b \times \text{ROE} = (1 - \text{payout ratio}) \times \text{ROE}$$ where $b$ is the earnings retention ratio.

What is the terminal (continuing) value in a two-stage DDM and how is it discounted?

At the end of the high-growth stage $n$, terminal value uses the Gordon model on the first stable-growth dividend: $$V_{n} = \frac{D_{n+1}}{r - g_{L}}$$ It is then discounted back to today along with the stage-one dividends: $V_{0} = \sum_{t=1}^{n}\frac{D_t}{(1+r)^t} + \frac{V_n}{(1+r)^n}$.

Define free cash flow to the firm (FCFF) starting from net income.

$$\text{FCFF} = \text{NI} + \text{NCC} + \text{Int}(1 - \text{tax}) - \text{FCInv} - \text{WCInv}$$ where NCC is non-cash charges, Int is interest expense, FCInv is fixed capital investment, and WCInv is working capital investment.

Define free cash flow to equity (FCFE) from FCFF and from net income.

From FCFF: $$\text{FCFE} = \text{FCFF} - \text{Int}(1-\text{tax}) + \text{Net borrowing}$$ From net income: $$\text{FCFE} = \text{NI} + \text{NCC} - \text{FCInv} - \text{WCInv} + \text{Net borrowing}$$

How are firm value and equity value computed in the single-stage FCFF and FCFE models?

Firm value $= \dfrac{\text{FCFF}_{1}}{\text{WACC} - g}$, and equity value $=$ firm value $-$ market value of debt. Equity value directly $= \dfrac{\text{FCFE}_{1}}{r - g}$, discounting FCFE at the required return on equity.

When is a free cash flow model preferred over a dividend discount model?

When the firm pays no dividends, when dividends differ substantially from the company's capacity to pay, when free cash flows align with profitability, or when an investor takes a control perspective (can influence dividend policy).

State the residual income (RI) for a single period.

$$\text{RI}_{t} = E_{t} - r \cdot B_{t-1}$$ Residual income equals net income minus an equity charge equal to the required return on equity times beginning book value of equity.

State the residual income valuation model.

$$V_{0} = B_{0} + \sum_{t=1}^{\infty} \frac{E_{t} - r B_{t-1}}{(1+r)^{t}} = B_{0} + \sum_{t=1}^{\infty} \frac{(\text{ROE}_t - r)B_{t-1}}{(1+r)^{t}}$$ Value equals current book value plus the present value of expected future residual income.

What is the key advantage and a key weakness of the residual income model?

Advantage: it recognizes value (book value) early and is useful for firms paying no dividends or having negative early free cash flow. Weakness: it relies on accounting (book value, clean-surplus) data that can be manipulated and requires adjustments.

What is the clean surplus relation underlying residual income valuation?

$$B_{t} = B_{t-1} + E_{t} - D_{t}$$ Ending book value equals beginning book value plus earnings minus dividends; all changes in equity (other than transactions with owners) flow through the income statement.

Compare trailing versus leading (forward) P/E ratios.

Trailing P/E uses the most recent four quarters of actual EPS: $\frac{P_{0}}{\text{EPS}_{0}}$. Leading (forward) P/E uses next-period forecast EPS: $\frac{P_{0}}{\text{EPS}_{1}}$. Forward P/E is preferred when past earnings are non-representative.

Derive the justified leading P/E from the Gordon growth model.

Dividing $V_0 = \frac{D_1}{r-g}$ by $E_1$ and using $D_1/E_1 = $ payout ratio: $$\frac{P_{0}}{E_{1}} = \frac{1 - b}{r - g}$$ where $1-b$ is the dividend payout ratio.

What does the PEG ratio measure and how is it interpreted?

$$\text{PEG} = \frac{\text{P/E}}{g\,(\%)}$$ It standardizes the P/E for expected earnings growth; lower PEG suggests a stock is relatively undervalued, but it assumes a linear P/E–growth relationship and ignores risk.

Define enterprise value (EV) and the EV/EBITDA multiple.

$$\text{EV} = \text{Market value of equity} + \text{Market value of debt} - \text{Cash and investments}$$ EV/EBITDA $= \frac{\text{EV}}{\text{EBITDA}}$; it is useful for comparing firms with different capital structures because EBITDA is pre-interest and pre-tax.

What are the three major approaches to private company valuation?

The income approach (DCF of expected cash flows), the market approach (multiples from comparable public companies or transactions), and the asset-based approach (fair value of assets minus liabilities).

In private company valuation, distinguish a discount for lack of control (DLOC) from a discount for lack of marketability (DLOM).

DLOC reduces value for a non-controlling (minority) interest that cannot direct firm policy; it is derived from the control premium. DLOM reduces value because private shares cannot be readily sold. They are multiplicative: $\text{Total discount} = 1 - (1-\text{DLOC})(1-\text{DLOM})$.

State the equity risk premium and its role in the required return on equity.

The equity risk premium (ERP) is the expected return on equities above the risk-free rate. Required return $= R_f + \text{ERP} \times \beta$ (CAPM) or, for a market portfolio, $R_f + \text{ERP}$.

Write the Gordon growth (supply-side / forward-looking) estimate of the equity risk premium.

$$\text{ERP} = \frac{D_{1}}{P_{0}} + g - R_{f}$$ the forward dividend yield plus the long-term earnings/dividend growth rate, minus the long-term risk-free rate.

State the build-up method and bond-yield-plus-risk-premium method for required return on equity.

Build-up: $r = R_{f} + \text{ERP} + \text{size premium} + \text{specific-company premium}$ (no beta). Bond-yield-plus-risk-premium: $r = \text{YTM on the firm's long-term debt} + \text{equity risk premium}$.

Define the par value, coupon rate, and tenor (term to maturity) of a fixed-income security.

Par (face/principal) value is the amount repaid at maturity. The coupon rate is the annual interest rate applied to par to determine periodic coupon payments. Tenor/term to maturity is the remaining time until the final principal repayment.

State the price of a fixed-coupon bond as the present value of its cash flows.

$$P = \sum_{t=1}^{N} \frac{C}{(1+r)^{t}} + \frac{\text{FV}}{(1+r)^{N}}$$ where $C$ is the periodic coupon, FV is par, $r$ is the periodic market discount rate, and $N$ is the number of periods.

State the inverse price-yield relationship and the premium/par/discount rules.

Bond price moves inversely to its yield (market discount rate). If coupon $>$ yield, the bond trades at a premium; if coupon $=$ yield, at par; if coupon $<$ yield, at a discount.

Differentiate a spot rate from a forward rate.

A spot rate is the yield (discount rate) today on a single cash flow received at one future date (a zero-coupon rate). A forward rate is an interest rate agreed today for a loan beginning at a future date and ending later; e.g., the 1-year rate one year from now, $f(1,1)$.

Give the no-arbitrage relationship linking two-period spot and forward rates.

$$(1+z_{2})^{2} = (1+z_{1})\,[1 + f(1,1)]$$ where $z_1, z_2$ are 1- and 2-year spot rates and $f(1,1)$ is the implied 1-year forward rate one year forward.

Distinguish current yield, yield to maturity (YTM), and yield to call (YTC).

Current yield $= \frac{\text{annual coupon}}{\text{price}}$ (ignores capital gain/loss and reinvestment). YTM is the IRR equating price to all cash flows held to maturity. YTC is the IRR assuming the bond is called at the first/next call date and price.

Define a covenant and contrast affirmative with negative covenants.

A covenant is a legally enforceable term in the bond indenture. Affirmative (positive) covenants require the issuer to do things (e.g., pay taxes, maintain assets, supply financials). Negative (restrictive) covenants prohibit actions (e.g., limit additional debt, restrict dividends, restrict asset sales) to protect bondholders.

Compare a bullet bond, an amortizing bond, and a sinking fund provision.

A bullet bond pays only coupons until maturity, then repays full principal at maturity. A fully amortizing bond repays principal gradually through each payment so nothing is owed at maturity. A sinking fund requires the issuer to retire portions of the principal on a schedule before maturity.

Differentiate ABS, MBS, and a CDO in structured finance.

An asset-backed security (ABS) is backed by a pool of financial assets (auto loans, credit-card receivables). A mortgage-backed security (MBS) is an ABS backed specifically by mortgage loans. A collateralized debt obligation (CDO) repackages a pool of debt into tranches with different risk/return, paid via a waterfall.

What is a special purpose entity (SPE/SPV) and why is it used in securitization?

An SPE is a bankruptcy-remote legal entity that buys the pooled assets from the originator and issues the ABS. It isolates the assets from the originator's credit risk, so investors bear the risk of the assets, not the originator's bankruptcy.

Explain credit tranching and time tranching in structured securities.

Credit tranching distributes credit (default) risk: senior tranches absorb losses last, subordinated/junior tranches absorb losses first. Time tranching distributes prepayment risk by directing principal repayments to tranches sequentially (e.g., CMO classes A, B, C).

What is prepayment risk in MBS, and define contraction and extension risk?

Prepayment risk is uncertainty in cash flow timing from borrowers repaying principal early. Contraction risk: when rates fall, prepayments speed up and the security shortens (reinvestment at lower rates). Extension risk: when rates rise, prepayments slow and the security lengthens.

Distinguish the roles of bond market issuance in the primary market: underwritten versus best-efforts offerings.

In an underwritten (firm-commitment) offering, the investment bank buys the entire issue and resells it, bearing the risk of unsold bonds. In a best-efforts offering, the bank acts only as an agent and is not obligated to buy unsold securities, so the issuer bears placement risk.

What is a repurchase agreement (repo) and the repo rate?

A repo is the sale of a security with an agreement to repurchase it later at a higher price; it is effectively a collateralized short-term loan. The repo rate is the implied interest rate—the difference between the sale and repurchase prices, annualized—affected by collateral quality and term.