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– 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