Key Concepts in Finance and Operating Capital Management

Chapter 10: Historical Volatility and Stock Returns

• Historical Volatility: A key measure of the fluctuations in asset prices over time.

  • Calculating Variance:

  • Formula: Var(R) = rac{1}{T - 1} imes egin{bmatrix}(R1 - R)^2 + (R2 - R)^2 + … + (R_T - R)^2
    ightarrow ext{where } R ext{ is the average return} ext{ and } T ext{ is the total number of returns}\ ext{Standard deviation is calculated as } ext{SD}(R) = ext{sqrt}(Var(R))

• Example Calculation:
  Variance for a set of returns:

  • Returns: -8.71%, 7.19%, 12.99%, 10.55%, -8.32%, 21.08%, 9.10%, -8.89%, 22.88%, 5.67%

  • Result: Var(R) = 0.61872 ext{ and SD}(R) = 1.3727

  • Higher average return tends to correlate with higher volatility.

Confidence Intervals

• 95% Confidence Interval: Understanding the range within which future returns are expected to fall.

  • Formula: CI = R rac{ ext{Confidence level}}{ ext{Standard Error}}

  • Upper range example: 6.35 ext{%} + (2 imes 11.719 ext{%}) = 29.77 ext{%}

  • Lower range example: 6.35 ext{%} - (2 imes 11.719 ext{%}) = -1.07 ext{%}

Risk Types in Investing

• Systematic Risk: Fluctuations in returns due to market-wide factors (e.g., economic change). Commonly known as market risk.

• Unsystematic Risk: Fluctuations due to company-specific factors (e.g., new product launch, poor financial results).

  • More firms involved in a portfolio reduce unsystematic risk due to diversification.

Cash Management Factors

• Importance of cash management: helps to ensure liquidity and fulfill obligations on time.

• Cash Conversion Cycle (CCC): Measures the time it takes for cash to flow through operations.

  • Formula: CCC = ext{Inventory Days} + ext{Accounts Receivable Days} - ext{Accounts Payable Days}

• Negative CCC indicates good cash flow: receives money before paying suppliers.

Free Cash Flow Calculation

• Free Cash Flow (FCF): Key indicator for firm's valuation.

  • Formula: FCF = ext{Net Income} + ext{Depreciation} - ext{Capital Expenditure}

• Example Calculation: If the net income is 19 million and depreciation 5 million with a capital expenditure of 3 million, then:

  • FCF = 19 + 5 - 3 = 21 ext{ million}

• Present Value of Growing Perpetuity Formula: Used to determine value of expected future cash flows with growth.

  • Formula: PV = rac{FCF}{r - g}

  • Where (FCF) is free cash flow, (r) is discount rate, and (g) is growth rate.

Managing Trade Credit

• Trade Credit Dynamics: Understand the impact of taking discount offers on cash flow and costs.

  • Example discount terms: 2/10, net 30 means pay within 10 days to get a 2% discount.

• Effective Annual Cost of Not Taking Discount: Calculated for businesses assessing trade credit terms.

  • Cost calculation example: If you miss the discount on a $100 purchase → ext{Cost} = (1 + ext{Discount})^{ rac{365}{ ext{Difference in days}}} - 1

Inventory Management

• Holding Inventory Benefits: Manage production cycles, prevent stockouts, and meet demand fluctuations.

  • Inventory costs include acquisition costs, ordering costs, storage costs, spoilage, and opportunity costs.

• Just-In-Time (JIT) Inventory: Aims to reduce inventory levels to minimize holding costs, acquiring stock when needed.

Conclusion on Accounts Payable Management

• Stretching Accounts Payable: A strategy where businesses delay payments to manage cash better. Consider benefits vs. potential last payment times.