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Picking a Time Interval for a Cash Flow

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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Picking a Time Interval for a Cash Flow

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  1. Picking a Time Interval for a Cash Flow

  2. 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?

  3. 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

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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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