Analytical Methods

The whole unit on one sheet: time value of money, the risk-and-return statistics, and the ratios the exam loves.

How Does Time Value of Money Work?

• A dollar received today is worth more than a dollar received in the future, because today's dollar can be invested and earn a return. The return you give up by waiting is opportunity cost.
• Net present value (NPV): present value of an investment's future cash inflows minus the initial cost.
  • Formula: NPV = Present Value of Cash Inflows - Initial Investment
  • NPV > 0 = adds value = Accept; NPV < 0 = destroys value = Reject; NPV = 0 = earns exactly the required rate = Indifferent.
• Internal rate of return (IRR): the discount rate that makes NPV of all cash flows equal to zero.
  • Accept if IRR > required rate of return (hurdle rate); reject if IRR < required rate of return.
  • For bonds, IRR equals the yield to maturity (YTM).
• When NPV and IRR conflict on mutually exclusive projects, follow NPV (it measures actual dollar value added). For independent projects they always agree.

Which Measure of Central Tendency Applies?

How Do You Measure Risk and Return?

• Standard deviation: how far individual returns typically deviate from the mean. Measures total risk (systematic + unsystematic). Higher = more volatility = more risk.
• Beta: sensitivity to overall market moves; measures systematic (market) risk only.
  • Beta = 1.0 moves with the market; > 1.0 more volatile (aggressive); < 1.0 less volatile (defensive); 0 no correlation (Treasury bills); < 0 moves opposite the market.
  • A beta of 1.5 is expected to move 1.5% for every 1% market move.
• Alpha: excess return relative to what beta predicted; the primary measure of active management skill. Positive = beat the risk-adjusted benchmark.
  • Jensen's Alpha formula: Alpha = Actual Return - [Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)]
• Sharpe ratio: excess return per unit of total risk.
  • Formula: Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Standard Deviation
  • Higher = better risk-adjusted performance. Uses standard deviation, NOT beta.
  • +1.0 perfect positive (no diversification benefit); 0 no relationship (moderate); -1.0 perfect negative (maximum benefit).
  • Combining low- or negative-correlation assets reduces risk; anything below +1.0 helps.
  • Diversification eliminates unsystematic (company-specific) risk only; systematic (market) risk always remains. Research suggests roughly 30 or more securities diversifies away most unsystematic risk.

Which Ratios Show Liquidity and Leverage?

• Current ratio = Current Assets / Current Liabilities. Current assets include cash, receivables, marketable securities, and inventory. Above 1.0 = adequate liquidity; below 1.0 = may struggle to pay short-term debts.
• Quick ratio (acid-test) = (Current Assets - Inventory) / Current Liabilities. Excludes inventory (the least liquid current asset); more conservative; better gauge of immediate payment ability. 1.0 or higher is generally healthy.
• Debt-to-equity ratio = Total Debt / Shareholders' Equity. Measures financial leverage. Higher = more debt reliance = higher financial risk; leverage amplifies both gains and losses.

What Do the Valuation Ratios Tell You?

• Price-to-earnings (P/E) ratio = Market Price Per Share / Earnings Per Share (EPS). Shows how much investors pay per dollar of earnings; a P/E of 20 = $20 paid per $1 of earnings.
  • High P/E: strong expected growth OR overvalued. Low P/E: possibly undervalued OR declining prospects.
  • Trailing P/E uses past 12 months of actual earnings; forward P/E uses estimated future earnings.
• Price-to-book (P/B) ratio = Market Price Per Share / Book Value Per Share. Book value per common share = (total assets - total liabilities - preferred stock) / common shares outstanding; subtract preferred first.
  • P/B < 1.0 trades below book value (maybe undervalued, maybe impaired assets); P/B > 1.0 market values it above net asset value; P/B = 1.0 price equals book value.
  • Most useful for capital-intensive, asset-heavy industries (banking, insurance, manufacturing, real estate); less useful for asset-light tech and service firms.

Which One-Liners Win Points?

• NPV is a dollar amount; IRR is a percentage. The exam tests whether you can distinguish the two.
• IRR and YTM are the same concept applied differently (YTM is IRR applied to a bond's cash flows).

Which Gotchas Trip Students Up?

• NPV above zero does not mean risk-free. It means expected returns beat the required rate once the discount rate is applied.
• IRR assumes reinvestment at the IRR itself, which is unrealistic for a very high-IRR project.
• A current ratio below 1.0 is a warning sign, not a guarantee of bankruptcy; credit lines and other resources may exist.

One-Breath Recap

Time value of money says a dollar today beats a dollar tomorrow, so value cash flows with future value, net present value (accept when above zero), and internal rate of return, which equals a bond's yield to maturity; when the two conflict on mutually exclusive projects, follow net present value. Standard deviation is total risk, beta is systematic risk only, alpha is manager skill, the Sharpe ratio is return per unit of total risk, and low or negative correlation drives diversification that kills unsystematic but never systematic risk. Financial ratios size up the company (current and quick for liquidity, debt-to-equity for leverage) and valuation ratios ask whether the price is right (price-to-earnings, price-to-book against net asset value), but every ratio is meaningless in isolation, so always compare to peers, competitors, and history.

Need more than the recap? Read the full Analytical Methods unit.