DM

Exam Study Notes

Time Value of Money

  • A dollar today is worth more than a dollar received in the future.
  • Three types of interest form the basis of time value of money:
    • Simple interest
    • Compound interest (Future Value)
    • Discounted interest (Present Value)

Compounding Interest

  • Interest earned in the first period is added to the principal.
  • In the second period, interest is earned on the original principal plus the interest from the first period.

Time Line

  • CF_0: Cash Flow at Time 0 (today)
  • CF_1: Cash Flow at Time 1 (end of Period 1, beginning of Period 2)
  • i%: Interest rate

Future Value

  • The future value of an investment can be increased by: Increasing the number of years, Compounding at a higher rate
  • Formula for future value compounded annually:
    • FVn = PV (FVIF{i,n})
    • FV_n = PV(1 + i)^n

Present Value

  • Determining the present value involves inverse compounding.
  • Formula for present value:
    • PV = FV (PVIF_{i,n})
    • PV = FV * (1 / (1 + i)^n)

Annuity

  • An annuity is a series of equal dollar payments for a specified number of years.
  • A compound annuity involves depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow.
  • Formulas:
    • FV = PMT (FVIFA_{i,n})
    • PV = PMT (PVIFA_{i,n})

Annuity Due

  • Annuity due are ordinary annuities with payments shifted forward by one year.
  • Shifts the payments from the end of the year to the beginning.
  • Formulas:
    • FV = PMT (FVIFA_{i,n})(1+i)
    • PV = PMT (PVIFA_{i,n})(1+i)

Perpetuity

  • A perpetuity is an annuity that continues forever.
  • An example is preferred stock with a constant dollar dividend.
  • Formula:
    • PV = PMT/i

Payment More Than Once a Year

  • The existing formulas need modification in terms of interest and periods.
    • FV = PV (FVIF_{i/m, n*m})
    • PV = FV (PVIF_{i/m, n*m})

Valuation of Bond

Key Features of a Bond

  1. Par value: Face amount, typically $1,000, paid at maturity.
  2. Coupon interest rate: Stated interest rate, generally fixed. Multiply by par value to get dollars of interest.
  3. Maturity: Years until the bond must be repaid. Declines over time.
  4. Issue date: Date when the bond was issued.
  5. Default risk: Risk that the issuer will not make interest or principal payments.

Call Provision

  • Allows the issuer to refund the bond if rates decline, benefiting the issuer but hurting the investor.
  • Borrowers are willing to pay more, and lenders require more, on callable bonds.
  • Most bonds have a deferred call and a declining call premium.

Bond Ratings

  • Provide a measure of default risk.
  • Investment Grade:
    • Moody’s: Aaa, Aa, A, Baa
    • S&P: AAA, AA, A, BBB
  • Junk Bonds:
    • Moody’s: Ba, B, Caa, C
    • S&P: BB, B, CCC, D

Factors Affecting Default Risk and Bond Ratings

  • Financial performance
    • Debt ratio
    • Coverage ratios (interest coverage ratio, EBITDA coverage ratio)
    • Current ratios
  • Provisions in the bond contract
    • Secured vs. unsecured debt
    • Senior vs. subordinated debt
    • Guarantee provisions
    • Sinking fund provisions
    • Debt maturity
  • Other factors
    • Earnings stability
    • Regulatory environment
    • Potential product liability
    • Accounting policies

Sinking Fund

  • Provision to pay off a loan over its life rather than all at maturity.
  • Similar to amortization on a term loan.
  • Reduces risk to investor, shortens average maturity.
  • Not good for investors if rates decline after issuance.

Financial Asset Valuation

  • PV = \frac{CF1}{1+r} + \frac{CF2}{(1+r)^2} + … + \frac{CF_n}{(1+r)^n}

Discount Rate

  • The discount rate (r_i) is the opportunity cost of capital.
  • r_i = r^* + IP + LP + MRP + DRP for debt securities.

Bond Valuation Example

  • 10-year, 10% coupon bond, r_d = 10%:
    • V_B = \frac{$100}{1+0.10} + \frac{$100}{(1+0.10)^2} + … + \frac{$100 + $1,000}{(1+0.10)^{10}} = $1,000

Bond Premium and Discount

  • If coupon rate < r_d, bond sells at a discount.
  • If coupon rate = r_d, bond sells at its par value.
  • If coupon rate > r_d, bond sells at a premium.
  • If r_d rises, price falls.
  • Price = par at maturity.

Yield to Maturity (YTM)

  • YTM is the rate of return earned on a bond held to maturity (promised yield).

YTM Example

  • 10-year, 9% coupon, $1,000 par value bond selling for $887:
    • Find r_d that solves the equation:
    • $887 = \frac{$90}{1+rd} + \frac{$90}{(1+rd)^2} + … + \frac{$90 + $1,000}{(1+r_d)^{10}}

Semiannual Bonds

  1. Multiply years by 2 to get periods = 2n.
  2. Divide nominal rate by 2 to get periodic rate = r_d/2.
  3. Divide annual INT by 2 to get PMT = INT/2.

Stock Valuation

Common Stock: Owners, Directors, and Managers

  • Represents ownership.
  • Ownership implies control.
  • Stockholders elect directors.
  • Directors hire management.
  • Managers are "agents" of shareholders, goal: Maximize stock price.

Initial Public Offering (IPO)

  • A firm “goes public” through an IPO when the stock is first offered to the public.
  • Prior to an IPO, shares are typically owned by the firm’s managers, key employees, venture capital providers.

Valuing Common Stocks

  • V{cs} = \frac{D}{K{cs}}, where:
    • D = Dividend
    • P = Price offered
    • K = Required rate of return

Growth (g)

  • Value of stock when the growth rate is zero (g=0).
  • Value of stock when the growth rate is constant.
  • Value of stock when the growth rate is nonconstant.

Growth Rate = 0

  • No increment in yearly dividend.
  • Perpetuity.
  • V{CS} = \frac{D}{K{cs}}

Constant Growth

  • The common dividend increases along with the growth in corporate earnings.

Shareholders Expected Rate of Return

  • The expected rate of return for common stock can be calculated from the valuation equations.

Valuing Preferred Stocks

  • Most preferred stocks are perpetuities (non-maturing).
  • Preferred stock has priority over common stock in bankruptcy.
  • V{ps} = \frac{D}{K{ps}}

Risk and Return

Investment Returns

  • Investment returns measure the financial results of an investment.
  • Returns may be historical or prospective (anticipated).
  • Returns can be expressed in dollar terms or percentage terms.

Return Calculation

  • Return on a $1,000 investment sold for $1,100 after 1 year:
    • Dollar return: $1,100 - $1,000 = $100
    • Percentage return: $100/$1,000 = 0.10 = 10%

Investment Risk

  • Investment risk pertains to the probability of earning a return less than expected.
  • The greater the chance of a return far below the expected return, the greater the risk.

Probability Distribution

  • Compares the risk of Stock X and Stock Y based on rate of return (%) and probability

Investment Alternatives Example

  • Illustrates different investment options with varying returns based on economic conditions.

Unique Aspect of T-Bill Return

  • The T-bill returns 8% regardless of the state of the economy.

Expected Rate of Return Calculation

  • r_{Alta} = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4%

Standard Deviation

  • \sigma = \sqrt{Variance}
  • \sigma = \sqrt{\sum{i=1}^{n}(xi - \hat{r})^2 P_i}

Standard Deviation Results

  • \sigma_{T-bills} = 0.0%
  • \sigma_{Alta} = 20.0%
  • \sigma_{Repo} = 13.4%
  • \sigma_{Am Foam} = 18.8%
  • \sigma_{Market} = 15.3%

Risk Measurement

  • Standard deviation measures the stand-alone risk of an investment.
  • The larger the standard deviation, the higher the probability that returns will be far below the expected return.
  • Coefficient of variation is an alternative measure of stand-alone risk.

Coefficient of Variation (CV)

  • CV = Standard deviation / Expected return.
    • CV_{T-BILLS} = 0.0%/8.0% = 0.0
    • CV_{Alta Inds} = 20.0%/17.4% = 1.1
    • CV_{Repo Men} = 13.4%/1.7%= 7.9

Portfolio Return

  • rp = \sum{i=1}^{n} wi ri
  • r_p = 0.5(17.4%) + 0.5(1.7%) = 9.6%
    • w = weight
    • r = return

Portfolio Standard Deviation

  • \sigmap = \sqrt{\sum{i=1}^{n}(ri - \hat{rp})^2 P_i}
  • The key here is negative correlation.

Portfolio BETA

  • \betap = \sum wi \beta_i
  • Beta is use to calculate the changes of return towards the changes in market return.
    • \beta = 1, if market return increase 10%, Security Return increase 10%
    • \beta = 0, Risk free rate
    • \beta = -1, If market return increase 10%, security return decrease 10%

Risk and Diversification

  • Diversifiable and Market risk.

Stand-Alone Risk

  • Stand-alone risk = Market risk + Diversifiable risk.

Required Rate of Return Concept

  • The investor’s required rate of return is the minimum rate of return necessary to attract an investor.

Capital Asset Pricing Model (CAPM)

  • k = k{rf} + \beta (km – k_{rf})