Financial Management Review — Key Formulas for CPA, CFA & Finance Exams

1. Series Summary

Chapter	Topic	Key content
1	Time Value of Money	PV, FV, annuities
2	Capital Budgeting	NPV, IRR, PI, Payback Period
3	Risk and Return	Portfolio theory, CAPM, Beta
4	Capital Structure	MM Theorem, WACC, Leverage
5	Dividend Policy	MM dividend irrelevance, payout ratio, buybacks
6	Bond Pricing	Rate-price relationship, YTM, Duration
7	Stock Valuation	DDM, P/E, P/B, EV/EBITDA
8	Derivatives	Futures, options, swaps, hedging
9	Working Capital	CCC, EOQ, 5 Cs of credit
10	Comprehensive Review	Formula memorization

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2. Complete Formula Reference

(1) Time Value of Money

$$\begin{aligned} FV &= PV \times (1 + r)^n \\ PV &= \frac{FV}{1 + r}^n \\ \text{Annuity PV} &= C \times [1 − (1 + r)^(−n)] / r \\ \text{Perpetuity PV} &= \frac{C}{r} \\ \text{Growing Perpetuity} &= \frac{C}{r − g} \end{aligned}$$

(2) Capital Budgeting

$$\begin{aligned} NPV &= \sum \frac{CF_t}{1 + r}^t − \text{Initial Investment} \\ PI &= PV(CF) / \text{Initial Investment} \\ IRR: \text{The rate} r \text{at which NPV} &= 0 \end{aligned}$$

(3) CAPM

$$E(R_i) = R_f + \beta_i \times [E(R_m) − R_f]$$

(4) WACC

$$WACC = R_E \times (\frac{E}{V}) + R_D \times (1 − T_c) \times (\frac{D}{V})$$

(5) MM Theorem

$$\begin{aligned} \text{No taxes}: V_L &= V_U \\ \text{With taxes}: V_L &= V_U + T_c \times D \end{aligned}$$

(6) Dividend Valuation

$$P_0 = \frac{D_1}{r_E − g} [\text{Gordon Growth Model}]$$

(7) Bonds

$$\text{Bond Price} = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{FV}{(1+r)^n} \qquad \frac{\Delta P}{P} \approx -D^* \times \Delta r \ \ \text{(Modified Duration)}$$

(8) Working Capital

$$\begin{aligned} CCC &= DIO + DSO − DPO \\ EOQ &= \sqrt(\frac{2DO}{H}) \end{aligned}$$

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3. Capital Budgeting Methods Compared

Method	Strengths	Weaknesses
NPV	Directly measures value creation; theoretically superior	Requires estimating cost of capital
IRR	Intuitive as a rate of return	Multiple IRRs possible; conflicts with NPV on mutually exclusive projects
PI	Useful for ranking under capital constraints	Ignores absolute scale
Payback Period	Simple; emphasizes liquidity	Ignores time value; ignores cash flows after payback

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4. MM Theorem Summary

Assumption	Conclusion
Perfect market (no taxes)	V_L = V_U (capital structure irrelevant)
With corporate taxes	V_L = V_U + T_c × D (debt is beneficial)
Taxes + bankruptcy costs	Optimal capital structure exists (Trade-Off Theory)

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5. Risk Summary

• Total Risk = Systematic Risk + Unsystematic Risk
• Systematic Risk: Measured by Beta (β); cannot be diversified away
• Unsystematic Risk: Can be eliminated through diversification

CAPM: Only systematic risk is priced → Unsystematic risk earns no extra return (because it can be diversified away)

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6. Exam Relevance by Credential

(1) CPA Exam (Business Environment & Concepts / Financial Accounting)

High-Weight Topics:

1. Capital Budgeting (NPV, IRR) — ~30%
2. Capital Structure (MM, WACC) — ~25%
3. Risk and Return (CAPM, Beta) — ~20%
4. Bond & Stock Valuation — ~15%
5. Working Capital & Dividends — ~10%

(2) CFA Level 1 (Corporate Finance / Portfolio Management)

Additional Topics:

• Capital Market Line (CML) vs Security Market Line (SML)
• Efficient Market Hypothesis (EMH)
• Corporate Governance
• Options pricing (Black-Scholes overview)
• M&A and corporate restructuring

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7. Common Exam Traps

1. Beta > 1 means the stock outperforms the market? (FALSE)

• Higher beta simply means higher required return. Actual returns vary.

2. Bond price and YTM move in the same direction? (FALSE)

• They move inversely (rates ↑ → price ↓).

3. If NPV > 0, IRR always exceeds the cost of capital? (TRUE — for a single project)

• On mutually exclusive projects, NPV and IRR rankings can diverge.

4. In a perfect market, a stock buyback = cash dividend in terms of shareholder wealth? (TRUE)

• MM dividend irrelevance theorem.

5. Greater diversification always lowers beta? (FALSE)

• Beta measures systematic risk. Diversification eliminates unsystematic risk, not beta.

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8. Comprehensive Practice Quiz

Q. Risk-free rate = 3%, market risk premium = 7%, β = 1.2. Use CAPM to find the required return; then use DDM to price the stock with D₁ = $0.60 and g = 3%.

CAPM: E(R) = 3% + 1.2 × 7% = 3% + 8.4% = 11.4% DDM: P₀ = $0.60 / (0.114 − 0.03) = $0.60 / 0.084 ≈ $7.14

Q. NPV and IRR give conflicting rankings on mutually exclusive projects. Which rule should you follow and why?

Follow NPV. NPV directly measures the dollar increase in shareholder wealth. IRR is a percentage return that ignores the scale of investment. To maximize shareholder value, always choose the project with the highest positive NPV.