the discount rate to figure out the time value of money of buying lettuce and tomatoes and beef and selling them the next week
What has this to do with O's chart, or anything else for that matter?
It is what you would do with the tools you are advocating using
Do elaborate....
You live in a city of 1 million people.......5 years from now the population is estimated to grow to 1.38 million...
What tool would you use to determine the suggested annual growth rate?
A) No, you didn't
B) No, it isn't
C) A tvm calculator
You made the assumption the growth is going to be constant. The irony is typically analysis would be the reverse, you'd have an expected growth rate and use that to calculate the expected population. But fine, let's go with your scenario.
The tool I would use is Excel and I would take the fifth root of 1.38 and subtract 1. It's a simple math formula, why would you bother with a more complex solution?
That gives you BTW 6.6537%
You made the assumption the growth is going to be constant.
Not at all.....I am looking for the COMPOUND AVERAGE RATE OF GROWTH over the period....I can break down the sub periods to whatever scale you prefer, assuming I have beginning and ending values for such increments....each increment may show a different rate.
If I aggregate them, they will combine to the same 6.6537%/yr...
Wrong, that's not a mathematical property. You can't just take the averages, it gives you different results.
Try this in your calculator.
Take the 6.6537% I gave you as the answer and do a two year calculation where first you enter 1/2 * 6.6537% and the second year you take 3/2 * 6.6537%. The average would be the same as both years at 6.6537%. But note you get a different population with each calculation. The number isn't too far off, but when you're doing more years at more different rates it stops being close very quickly.
BTW, in addition to a Michigan MBA, I was a Math and Computer Science double major at Maryland. Also have a masters in Computer Science from Virginia Tech.
Just so you know, in the real world, we do actually create all these models in Excel. It makes it easy to keep changing parameters as we do real analysis on various options. It also is easier to verify what we are doing is correct, like realizing what you just said was wrong, you can't just average the numbers.
No one uses TVM calculators other than financial sales people and marketers. The real business people use Excel. We even have a saying, Corporate America runs on Excel. And damn it's true