Valuation

Value of an asset

 

  • The value of an asset with expected cash flows, CFt, at times, t=1,2,…,n, with required rate of return, r:

Value of a bond

 

  • The value of a bond with coupon interest payments of I per year, maturity value (or par value) of M, maturity of n years, and a required rate of rd:
Annual Coupons:

Beta Coefficient

 

Assets –

Portfolio (Br): The beta coeddicient of an N-asset portfolio with xi invested in asset i with beta equal to Bi :

Capital Asset Pricing Model (CAPM)

 

In equilibrium, the expected return (as well as the required return) (E(Ri)) on asset i having a beta coefficient, βi, is given by:

Where Rf is the rish-free rate of return, and E(Rm) is the expected return on the market portfolio. The term [E(Rm) – Rf] is the expected market risk premium.

Risk

 

  • Single Asset: The risk of a single asset held in isolation is equal to the variance of the returns on the asset, σ2.
  • Portfolio: The risk of aportfolio of assets is given by the variance of the returns in the portfolio, σp2.
  • Single Asset in a Portfolio: The risk of a single asset held as a part of a portfolio of assets is given by the beta coefficient for that asset.
  • Systematic Risk: The portion of the total risk that cannot be eliminated through diversification. The risk is also known as “market” risk. The systematic risk of an asset or portfolio is given by their beta coefficients.
  • Diversifiable Risk: The portion of the total risk of a portfolio that can be eliminated through diversification. Note that:
    Total Risk = Systematic Risk + Diversifiable Risk

Security Market Line (SML)

 

Definition: A graphical representation of the CAPM.
The slope of the SML is equal to [E(Rm)-Rf].

Risk And Return

Retrun

 

  • Expected Return (E(r)) – The expected return of an investment with n possible outcomes, ri, i=1,…,n, each with probability of pi:
  • Variance of Returns (σ2) – The variance of returns of an investment with n possible outcomes and with an expected return, E(r):
  • Standard Deviation (σ):
  • Coefficient of Variation (CV):
  • Covariance of Returns (σij): The covariance between the returns of asset i and asset j, each having n possible outcomes with joint probabilities Ps (ri, rj):
  • Correlation Coefficient (pij):
  • Two-Asset Portfolio:
    • Expected Return ((E(rp) – The expected return on a two-asset porfolio with proportion xi invested in asset i, and xj invested in asset j
    • Variance of Returns p2):
  • N-Asset Portfolio:
    • Expected Return ((E(rp) – The expected retrun on an N-asset portfolio having a proportion xi invested in asset i, i=1,…,N:
    • Variance of Returns (σp2):

Beta Coefficient

 

Assets –

Portfolio (Br): The beta coeddicient of an N-asset portfolio with xi invested in asset i with beta equal to Bi :

Capital Asset Pricing Model (CAPM)

 

In equilibrium, the expected return (as well as the required return) (E(Ri)) on asset i having a beta coefficient, βi, is given by:

Where Rf is the rish-free rate of return, and E(Rm) is the expected return on the market portfolio. The term [E(Rm) – Rf] is the expected market risk premium.

Risk

 

  • Single Asset: The risk of a single asset held in isolation is equal to the variance of the returns on the asset, σ2.
  • Portfolio: The risk of aportfolio of assets is given by the variance of the returns in the portfolio, σp2.
  • Single Asset in a Portfolio: The risk of a single asset held as a part of a portfolio of assets is given by the beta coefficient for that asset.
  • Systematic Risk: The portion of the total risk that cannot be eliminated through diversification. The risk is also known as “market” risk. The systematic risk of an asset or portfolio is given by their beta coefficients.
  • Diversifiable Risk: The portion of the total risk of a portfolio that can be eliminated through diversification. Note that:
    Total Risk = Systematic Risk + Diversifiable Risk

Security Market Line (SML)

 

Definition: A graphical representation of the CAPM.
The slope of the SML is equal to [E(Rm)-Rf].

Time Value of Money

Present Values

 

  • Single Amount: Present Value (PV) of a lump sum (FVn) given at the end of n periods at an interest rate of r%
Annuities

 

  • Ordinary Annuity – Present Value of an ordinary annuity (PVA) of PMT per period for n periods at r % per period:
  • Annuity Due – Present value of an annuity due (PVD) of n cash flows (PMT) at r % per period:
  • Perpetuity: Present value of a perpetuity (PVP) of PMT per period at r % per period: PVP = PMT / r
Series of Cash Flows –

Present value of a series of cash flow (CFt) at times, t = 1,2,…,n, at r %  per period:

Future Values

 

Single Amount –

Future value at the end of n periods (FVn) of a present amount (PV) invested today at r % per period.

Compounded once per period: FVn = PV(1+r)n

Compounded m times per period:

Annuities

Future value at the end of n periods (FVn) of a present amount (PV) invested today at r % per period.

Ordinary Annuity – Future value at the end of n periods of an ordinary annuity (FVA) of PMT per period for n periods at r% per period:

Annuity Due – Future value at the end of n periods of an annuity due of PMT per period at r% per period:

Series of Cash Flows – Future value at the end of n periods of a series of cash flows, CDt2 at times, t 1,2,…,n:

Eddective Annual Rate (EAR)

Annual Percentage Rate (APR)

APR = rate per period x periods per year

Accounting Satetments

Balance Sheet Identity

Assets = Liabilities + Owner’s Equity

Income Statement

Sales

  • Cost of Goods Sold (COGS)
    • =Gross Profit (GP)
      • – Administrative Expenses
      • – Depreciation
      • – Other Expenses
        • = Earning Before Interests and Taxes (EBIT)
            • – Interest
          • = Earnings Before Taxes
            • – Taxes
              • = Net Income  (Net Profit)

Statement of Retained Earnings

Begining Balance Retained Earnings

  • + Net Profit
    • – Dividends on Preferred Stock
    • – Dividends on Common Stock
      • = Ending Balance Retained Earnings

Cash Flow Identity

Cash Flows From Assets = Sum of the Cash Flow paid to the suppliers of capital to the firm

Statement of Cash Flow

Cash Flows from Operations

  • Cash Flows from Investments
    • Cash Flows from Financing
      • Net Increase (or Decrease) in Cash

Financial Ratios

Liquidity

Definiation: Measure of the firm’s ability to meet its short-term obligations.

Leverage

Definiation: Measure of the firm’s degree of indebtedness and its ability to meet longterm obligations.

Activity

Definiation: Measure of the firm’s efficiency in generation sales with its assets.

Profitabiity

Definiation: Measure of the returns on assets and equity.

Dupont System:

ROE = net profit margin x total asset turnover x equity multiplier
or
ROE = ROA x (1 + dept-to-equity ratio)