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2015-03-02 21:25:21

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  1. Placing a value on a security
    Attempting to determine the worth of a stream of future Cash flows
  2. $ valued higher the earlier it is received
    $ now is worth more than $ later
  3. Time Value of Money
    Deals with equivalence relationships between cash flows with different dates.
  4. Discount
    Reduce value based on how much time passes before money is paid.

    I.e. receive 9,500 dollars today in exchange for 10,000 one year from now. You discount the 10,000 based on the one year threshold before the money is repaid.
  5. Interest Rate ( r ) Definition
    Rate of return that reflects the relationship between differently dated cash flows.
  6. Interest Rates can be thought of in 3 ways:
    • 1. Rate of Return - minimum rate of return an investor must receive in order to accept the investment.
    • 2. Discount rate - rate at which we would discount a future amount to find its value today
    • 3. Opportunity Cost - If instead of investing the 9,500, the investor decided to spend it, he would loose the interest rate earned over that period.
  7. Opportunity Cost
    Value that investors forgo by choosing a particular course of action.
  8. Interest Rate ( r ) Formula
    Real Risk Free Interest rate + Inflation Premium + Default Risk Premium + Liquidity Premium + Maturity Premium
  9. Interest Rates (Economics)
    Set by the marketplace by the forces of supply (investors) and demand (borrowers) of funds.
  10. Real Risk-free Interest rate
    Single-period interest rate for a completely risk-free security if no inflation were expected. Reflects the time preferences of individuals for current versus future consumption
  11. Inflation Premium
    Compensates investors for expected inflation.Reflects the average inflation rate expected over the maturity of the debt.
  12. Inflation
    Reduces purchasing power of a unit of currency - the amount of goods one can buy with a unit of currency.
  13. Nominal risk-free interest rate
    • Real risk free interest rate + Inflation premium. Typically the interest rate for short term government debt (US T-BILL).
    • 90 day t bill represents the nominal risk free interest rate over 90 days.
  14. Default risk premium
    Compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount.
  15. Liquidity premium
    Compensates investors for the risk of loss relative to an investment's fair value if the investment needs to be converted to cash quickly.

    US T bills do not have a liquidity premium because they can be bought and sold in large amounts without affecting their market price.
  16. Liquidity premium on financial instruments
    Many bonds of small issuers trade infrequently after they are issued. The interest rate on such bonds includes a liquidity premium reflecting the relatively high costs of selling a position (including the impact on price)
  17. Maturity premium
    Compensates investors for the increased sensitivity of the MV of debt to a change in market interest rates as maturity is extended.

    The difference between the interest rate on longer maturity treasury debt vs. short term treasury debt reflects a positive maturity premium for the longer term debt and possibly a different inflation premium as well.
  18. Future Value of a Single Cash Flow (one period)


    • PV = Present value of investment
    • FV = future value of investment
    • N = # of periods from today
    • r = rate of interest per period
  19. Simple Interest
    Interest rate * principal (interest earned on principal investment)
  20. Principal
    Amount of funds originally invested
  21. Compounding
    Interest earned on interest
  22. Future Value of a Like Cash Flow (multiple periods) - Compounding


    • PV = present value of investment
    • FV = future value of investment
    • N = # of compounding periods
    • r = rate of interest per period

    ** Stated interest rate and compounding periods must be compatible (i.e. annual interest rate to annual compounding periods)
  23. Future Value Factor
    Links today's present value with tomorrow's future value.

     Future value to be received 5 periods from today (N = 5).

    PV and FV are separated in time through the factor 
  24. PV & FV separated in time has 3 important consequences:
    • 1. Can add amounts of money only if they are indexed at the same point in time
    • 2. For a given interest rate, the FV increases with the number of periods
    • 3. For a given # of periods, the FV increases with the interest rate
  25. Stated Annual Interest Rate ()
    Also known as the quoted annual interest rate. Rate quoted by bank on an annual basis. Normally quoted on annual basis even if instrument compounds more frequently.

    Rate is strictly a quoting convention as often times the actual monthly rate x 12 will not be exactly the stated amount.
  26. Future Value w/ more than one compounding period (i.e. semi-annual, quarterly):


    •  = stated annual interest rate
    • m = number of compounding periods per year (monthly, daily, etc.)
    • N = # of years

    *Periodic rate and the # of compounding periods must be compatible (yearly to yearly)
  27. Continuous Compounding Truism
    When number of compounding periods is infinite. The more frequent the compounding, the larger ending amount.
  28. Effective Annual Rate (EAR)
    The actual rate of interest earned after compounding is taken into account (vs. stated annual rate).

    i.e. $1 earning 8.16% interest annual compounding earns the same as $1 earning 8% interest semi-annual compounding.
  29. Continuous Compounding


     = e (2.7182818) raised to the stated annual interest rate () * the number of years (N)
  30. Effective Annual Rate (EAR)


    Periodic interest rate = Stated annual interest rate divided by m

    m = # of compounding periods in the year
  31. EAR with continuous compounding

  32. Annuity
    finite set of level sequential cash flows
  33. Ordinary Annuity
    Annuity that has first cash flow at one period from now (t=1)
  34. Annuity Due
    Annuity that has first cash flow that occurs immediately (t=0)
  35. Perpetuity
    Perpetual annuity. Set of level never-ending sequential cash flows with the first cash flow occurring one period from now.
  36. Future Value of Ordinary Annuity


    Term in brackets = future value annuity factor

    • A = annuity amount
    • r= interest rate per period
    • N = number of time periods
  37. Present Value Factor


    Discounts future value to present value.
  38. Present Values - Relation to discount rate & # of periods.
    1. For a given discount rate, the farther in the future the amount to be received, the smaller that amount's present value.

    2. Holding time constant, the larger the discount rate, the smaller the present value of the future amount.
  39. Quoted interest rate.

    # of periodic interest rate payments * the number of compounding periods in the year.
  40. Present value w/ compounding


    • m = # of compounding periods in the year
    •  = quoted annual interest rate
    • N = number of years
  41. PV of a series of equal cash flows (present value of annuity)


    Value in brackets = present value annuity factor

    • A = annuity amount
    • r = interest rate per period (must correspond to frequency of annuity payments (annual, quarterly)
    • N = # of annuity payments
  42. PV of infinite series of equal cash flows (perpetuity)


    • A = Annuity
    • R = return

    Only works when interest rates are positive.

    Only valid for perpetuity with level payments (some government bonds and preferred stocks can fit perpetuity)
  43. PV of series of unequal cash flows
    Must find PV of each cash flow and add the results.
  44. Growth Rate


    • 1/N = square root
    • N = # of years
  45. Cash Flow Additivity Principal
    Important for solving for uneven cash flows. Says that dollar amounts indexed at the same point in time are additive.
  46. PV & FV are same measures separated in time.
    PV & FV are same measures separated in time.

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