Picking a time interval for a cash flow
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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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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 Match

  • 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 Match

  • 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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