1. Time Value of Money (TVM)
‍

Concept Explanation:
The concept that money available today is worth more than the same amount in the future due to its earning potential.

‍

Key Formulas:

‍

1. Future Value (FV) - Single Lump Sum: FV = PV * (1 + r)^n
     - PV: Present value.
     - r: Discount or interest rate per period.
     - n: Number of compounding periods.
2. Present Value (PV) - Single Lump Sum: PV = FV / (1 + r)^n
3. Present Value of Annuity (Ordinary): PV = C * [1 - (1 + r)^-n] / r
     - C: Cash flow per period.
4. Present Value of Annuity Due: PV_due = PV_ordinary * (1 + r)
5. Present Value of Perpetuity: PV = C / r
6. Effective Annual Rate (EAR): EAR = (1 + r/m)^m - 1
     - m: Compounding frequency.

‍

‍

2. Capital Budgeting

‍
Concept Explanation:
Capital budgeting involves evaluating and selecting investments or projects that create value for the firm.

Key Formulas:

‍

1. Net Present Value (NPV): NPV = Sum [C_t / (1 + r)^t] - C_0
     - C_t: Cash flow at time t.
     - r: Discount rate.
     - C_0: Initial investment.
2. Internal Rate of Return (IRR): The discount rate where NPV = 0.
3. Profitability Index (PI): PI = PV of Future Cash Flows / Initial Investment.
4. Payback Period: Time required to recover the initial investment from cumulative cash flows.
5. Modified IRR (MIRR): MIRR = [(FV_positive / PV_negative)^(1/n)] - 1
     - FV_positive: Future value of positive cash flows.
     - PV_negative: Present value of negative cash flows.

‍
‍

3. Cost of Capital

‍
Concept Explanation:
The cost of capital is the required return necessary to make a capital budgeting project worthwhile.

‍

Key Formulas:

‍

1. Weighted Average Cost of Capital (WACC): WACC = (E/V) * r_e + (D/V) * r_d * (1 - T)
     - E: Market value of equity.
     - D: Market value of debt.
     - V: Total capital (E + D).
     - r_e: Cost of equity.
     - r_d: Cost of debt.
     - T: Tax rate.
2. Cost of Equity (CAPM): r_e = r_f + Beta * (r_m - r_f)
     - r_f: Risk-free rate.
     - Beta: Systematic risk of the stock.
     - r_m: Expected market return.
3. Cost of Equity (DDM): r_e = D_1 / P_0 + g
     - D_1: Next period's dividend.
     - P_0: Current stock price.
     - g: Growth rate.

‍
‍

‍

4. Valuation

‍
Concept Explanation:
Valuation is the process of determining the present value of an asset or company.

‍

Key Formulas:

‍

1. Enterprise Value (DCF): EV = Sum [FCF_t / (1 + WACC)^t] + [Terminal Value / (1 + WACC)^T]
     - FCF_t: Free cash flow at time t.
     - WACC: Discount rate.
     - T: Final year of forecast.
2. Terminal Value (Gordon Growth): TV = FCF_{T+1} / (WACC - g)
     - FCF_{T+1}: Free cash flow after the forecast period.
     - g: Growth rate.
3. Equity Value: Equity Value = Enterprise Value - Net Debt.

‍
‍

‍

5. Capital Structure

‍
Concept Explanation:
The mix of debt and equity financing used by a firm.

‍

Key Formulas:

‍

1. Levered Beta (Adjusted for Debt): Beta_levered = Beta_unlevered * [1 + (D/E) * (1 - T)]
     - Beta_levered: Beta accounting for leverage.
     - Beta_unlevered: Beta assuming no debt.

‍

‍

6. Dividend Policy

‍
Concept Explanation:
The decision on whether to distribute profits as dividends or reinvest them.

‍

Key Formulas:

‍

1. Retention Ratio (b): b = 1 - Dividend Payout Ratio.
2. Growth Rate (g): g = ROE * b.
     - ROE: Return on equity.

‍

‍

7. Risk and Return

‍
Concept Explanation:
Analyzing the relationship between risk and expected return.

‍

Key Formulas:

‍

1. Portfolio Expected Return: E(R_p) = Sum w_i * E(R_i)
     - w_i: Weight of asset i.
     - E(R_i): Expected return of asset i.
2. Portfolio Variance (Two Assets): Var_p = w_1^2 * Var_1 + w_2^2 * Var_2 + 2 * w_1 * w_2 * Cov_12.

‍

‍

8. Options and Corporate Securities

‍
Concept Explanation:
Contracts offering the right to buy/sell an asset at a specified price.

‍

Key Formula:

• Black-Scholes Model (European Call Option):
  C = S * N(d1) - X * e^(-rT) * N(d2)
  - d1 = [ln(S/X) + (r + sigma^2 / 2)T] / (sigma * sqrt(T))
  - d2 = d1 - sigma * sqrt(T)
  
  Variables:
  - C: Call option price.
  - S: Current stock price.
  - X: Strike price.
  - r: Risk-free rate.
  - T: Time to expiration (in years).
  - sigma: Volatility of the stock's returns.
  - N(d): Cumulative standard normal distribution function.

‍

‍