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## PowerPoint Slideshow about ' Picking a Time Interval for a Cash Flow' - brett-mccarthy

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Presentation Transcript

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
- Your cash flow is really just your mathematical model

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

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