Finance Ch 5

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  1. There are 2 ways to calculate FVs for multiple cash flows:
    • 1. compound the accumulated balance forward one year at a time or
    • 2. calculate the FV of each CF first and then add these up
  2. PV for multiple cash flows:
    • 1. Discount back one perios at a timeor
    • 2. Calculate the PV individually and add them up

    *the amount that you would need today in order to exactly duplicate those future cash flows (for a given discount rate)
  3. annuity
    a level stream of cash flows for a fixed period of time
  4. PV of an annuity of C dollars per t period
    Annuity PV = C*(1-PVF/r)

    = C*{1-[1/(1+r)^t]/r}
  5. annuity due
    an annuity for which the cash flows occur at the beggining of the month/period

    • ex: Leases
    • any amount that needs to be prepaid the same amount each period

    annuity due value= ordinary annuity value * (1+r)

    • two steps:
    • 1. calc the PV or FV as though it were an ordinary annuity and 2. multiply your answer by (1+r)
  6. Perpetuity
    • level of stream of cash flows continues forever
    • cash flows are perpetual
    • also called consols (in Canada and UK)

    PV for a perpetuity = C/r
  7. preferred stock (preference stock) is an example of a
  8. stated interest rate (quoted interest rate)
    the interest rate expressed in terms of the interest payment made each period
  9. effective annual rate (EAR)
    the interest rate expressed as if it were compunded once per year

    (1+ Quoted rate/m)m - 1

    (1+ APR/12)12 - 1
  10. Annual Percentage Rate (APR)
    the interest charged per period multiplied by the number of periods per year

    also called nominal rate
  11. Payday loan example
    • FV = PV * (1+r)1
    • 120 = 100 * (1+r)1
    • 1.20 = (1+r)
    • r = .20 or 20%

    • APR = .20* 365/18
    • APR = 4.0556 or 405.56%

    • EAR = (1+quoted rate/m)m-1
    • EAR = (1+.20)365/18-1
    • EAR = 39.3292 or 3,932.92%
  12. 3 basic types of loans
    • pure discount
    • interest only
    • amortized
  13. Pure Discount Loans
    simplest form of loan

    borrower received money today and repays a single sum at some time in the future.

    very common when the term is short (one year or less)
  14. Interest Only Loans
    the borrower pays interest each period and to repay the entire principal (the original loan amount) at some point in the future

    (if there is just one period it is the same as a pure discount loan)
  15. amortized loans
    lender may require the borrower to repay parts of the loan amount over time. The process of paying off a loan by making regular principal reductions is called amortizing the loan

    pay interest plus some fixed amount

    common with medium term business loans

    most common (cars and homes)- borrower makes a single fixed payment every period

    • Ex: 5 yr 9% $5,000 loan
    • 5,000 = C * (1-1/1.095)/.09
    •           = C * (1-.6499)/.09

    • C= 5,000/3.8897
    •    = 1,285.46
  16. There are two ways to calculate PV and FV when there are multiple cash flows.
  17. A series of constant cash flows that arrive or are paid at the end of each period is called an
    ordinary annuity
  18. Interest rates can be quoted in a variety of ways. For Financial decisions, it is important that any rates being compared be first converted to effective rates. The relationship between a quoted rate, such as an APR and EAR is given by
    EAR = (1+quoted rate/m)m-1

    m= the # of times per year the money is compounded (or the # of payments per year)

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Finance Ch 5
2012-10-28 19:22:48

Finance Ch 5
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