# Picking a Time Interval for a Cash Flow - PowerPoint PPT Presentation

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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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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

• Ie – daily, weekly, monthly, quarterly, annual?

### 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

### 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

• 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

• 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

• 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

• 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