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Picking a Time Interval for a Cash Flow. Need to Get the Cash Flow. Usually starts as a story problem with a bunch of situation data Need to decide who’s pocket you are keeping track of to keep positives and negatives straight Another decision is the degree of detail

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Presentation Transcript
need to get the cash flow
Need to Get the Cash Flow
  • Usually starts as a story problem with a bunch of situation data
  • Need to decide who’s pocket you are keeping track of to keep positives and negatives straight
  • Another decision is the degree of detail
    • Ie – daily, weekly, monthly, quarterly, annual?
how do you decide
How Do You Decide?
  • Look at the data – does it tell about monthly, yearly or what interval data?
  • What can you realistically forecast?
    • Is predicting daily expenses 10 years in advance realistic?
  • What is the interest compounding period
    • Problems are easier if interest compounding period matches the detail of the cash flow
  • You would like a cash flow that matches the interest compounding period and is realistic for what you have to predict or the data you have available
    • Your cash flow is really just your mathematical model
make a decision
Make a Decision
  • With time interval specified all expenses in an interval will be lumped at one point in the interval
  • What time in the interval
    • In this class always at the end (year one expenses all occur exactly at 1 year from time 0)
    • The Beginning
    • Another common choice is the mid point
      • Makes more sense but makes for nasty math
      • IRS does taxes this way
      • We won’t go there.
the time interval match
The Time Interval Match
  • Nice if time interval and interest compounding period match
    • For basic engineering econ books they almost always do
    • When I set up problems for you they most always do.
what if the time interval and compounding period don t match
What if the Time Interval and Compounding Period Don’t Match
  • Remember – by law interest rates are reported on a one year basis in the U.S.
    • If the compounding period is less then you just get the period interest rate
      • Yearly Rate / # of compounding periods each year
  • Two Cases
    • Time interval is shorter than the interest compounding period
    • Time interval is longer than the interest compounding period
time interval is shorter than the compounding period
Time Interval is Shorter than the compounding period
  • Often means cash flow has too much detail and is trying to predict expenses when they don’t change interest.
  • Can ask how interest behaves
    • May only count what is in there at the end and then charge on all of it
      • Definitely favors reducing detail of cash flow
    • May apply a linear fraction of the interest rate to it
      • May make you do a problem with different effective interest rates for each quarter etc.
      • Probably only significant with very short cash flows.
time interval is longer than the compounding period
Time Interval Is Longer than the Compounding Period
  • Compute the Yield for the time interval and use that as an interest rate
  • Example – a loan with daily compounding and monthly payments
    • Say interest rate is 11% compounded daily
    • Get Aprox. Period Interest Rate
      • 11%/ 360 = 0.030556%
    • Now Get Monthly Yield (I’ll model a 30 day month)
      • (1+0.00030556)^30 = 1.009207
      • Subtract the 1 that preserves principle 0.009207
      • Multiply 100 0.9207% monthly
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