CFA Level 1 - Part 4 Corporate Finance and Portfolio Management

Corporate Finance

Capital Budgeting

  NPV : Σ_t=1ⁿCF_t/(i + r)_t - outlay

  IRR  : Σ_t=1ⁿCF_t/(i + r)_t = outlay

  Payback Period : number of years to recover original investment, based on cashflows

  Discounted Payback Period : number of years to recover original investment, based on discounted cashflows

  NPV profile: shows a project's NPV graph as function of various discount rates

  Profitability Index = PV of future cash flow / initial investment
                                 = 1 +  ( NPV / initial investment )

Cost of Capital
  WACC = w_dr_d(1 + t) + w_pr_p + w_er_e

Cost of Preferred Stock
 P_p = D_p/r_p

Cost of Debt
  calculate the ytm of bond

Cost of Equity
  cost of debt + risk premium
  CPAM: r_i = r_f +  β(r_m-r_f)
  PV model: P₀ = D₁/(r_e-g)

Pure play method
  Unlevered beta of the company:
  β_u,comparable or called β_assets

  Levered beta of the company:
  β_L,comparable or called β_equity 

  Find unlevered beta:
  β_u,comparable = β_L,comparable / [1 + (1 - Tcomparable)Dcomparable/Ecomparable]

  Lever this beta to get β_project
  β_L,project = β_u,comparable [1+ (1 - Tproj)Dproj/Eproj]

Leverage
Degree of Operating Leverage (DOL): measure of operating risk
Operating leverage involves using a large proportion of fixed costs to variable costs in the operations of the firm.


             % change Operating Income
DOL =  -------------------------------------
                % change sales
                     Q(P-V)                 P: price
         = ------------------------     V: variable operating cost
                 Q(P-V) - F               F: Fixed operating cost

   Fixed operating cost, such as factory depreciation

Degree of Financial Leverage (DOL): measure of financial risk

               % change net Income
DFL =  --------------------------------------
              % change Operating Income
                     Q(P-V)                 P: price
         = ------------------------     V: variable operating cost
                 Q(P-V) - F -C          C: Fixed financial cost

  Fixed financial cost, such as interest payment

                  EBIT
DFL = ------------------------
             EBIT - Interest

Since interest is a fixed expense, DFL magnifies returns.

DTL  = DOL x DFL
                     Q(P-V)                 P: price
         = ------------------------     V: variable operating cost
                 Q(P-V) - F -C          F: Fixed operating cost

Break-Even Point         Operating Breakeven Point
                  F + C                                   F
    Qbe = ---------------         Qobe = -----------
                  P - V                                   P - V

Dividend Payment Chronology:
  dividend declaration date:
     the day dividend is declared
  ex-dividend date ( ex-date ) :
     the 1st day that a share trades without dividend
  holder of record date:
     two business days after the ex-dividend date, the date that a shareholder listed in the corp. record will be deemed to have ownership of the shares for purpose of receiving the upcoming dividend
  payment date:
     the day company sends out dividend payment

treasury stock: shares that have been issued and then repurchased

money market yield:
    FV - Price               360
    -------------  * ------------------------------------
        Price           number of days to maturity

bond equiv. yield: state bond yields into annual yield
    FV - Price               365
    -------------  * ------------------------------------
        Price            number of days to maturity

Portfolio risk and return:
                                                Pt + Dt
     holding period return: R = ----------  - 1
                                                    Po

                                                    1
     arithmetic/mean return: R = ---- Σ_t=1^T Rt
                                                    T

     geometric mean return:  R = ^T√π_t=1^T (1+ Rt) - 1

Portfolio Management

For two asset portfolio,

  σ_p ²= w₁²σ₁²+ w₂²σ₂ ² + 2w₁w₂ COV(R1,R2)

  COV(R1,R2) = ρ₁₂σ₁σ₂

Efficient Frontier is combinations of 2 stocks

Utilities Theory and Indifference Curves

Capital Allocation line: risk free asset + risky portfolio
Capital Market line: risk free asset + market portfolio

    E(Rp) = Rf + σ_p/σ_m [E(Rm) - Rf]

CML with different lending and borrowing rates


systematic risk: risk that cannot be avoided
non-systematic risk: risk that is local

total variance = systematic variance + non-systematic variance

beta: it is a measure of volatility or systematic risk, of a security or a portfolio, compared to market as a whole

  βi = ρ_imσ_i/σ_m        E(Ri) = Rf + β_i [E(Rm) - Rf]

Security market line: use systematic risk, applies to any security
CAL, CML: use total risk, applies to efficient portfolio only

Portfolio performance evaluation:
  Sharpe ratio = (Rp-Rf)/σ_p
  Treynor ratio = (Rp-Rf)/β_p
  M-squared(M²) = (Rp - Rf)σ_m/σ_f - [E(Rm) - Rf]
  Jensen's Alpha = Rp - [Rf + β_p(E(Rm) - Rf)]

Application of Sharpe ratio
The greater a portfolio's sharpe ratio, the better its risk adjusted performance has been. If the addition of a new security lowers the sharpe ratio, it should not be added to the portfolio.