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Future value & weighted average rates of return
Old 10-13-2012, 01:23 PM   #1
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Future value & weighted average rates of return

Greetings,

Why is it that Future Value calculations don't seem to handle weighted average rates of return very well? I notice this both in FireCalc and Excel.

For instance:

The future value of $400,000 @ 10% annual rate of return for 30 years is $6,979,760.91.

The future value of $400,000 @ 5% annual rate of return for 30 years is $1,728,776.95.

The sum of these two future values is $8,708,537.86.

However, if we combine these initial amounts at the get-go and use an average annual rate of return, the result is different. The future value of $800,000 @ 7.5% annual rate of return for 30 years is $7,003,964.15!

What is funny about this is that if I look at this on a year over year basis, the returns are identical:


........................Year 1...Year 2....Year 3....Year 4....Year 5
$400000 @ 10% $ 40,000 $ 44,000 $ 48,400 $ 53,240 $ 58,564
$400000 @ 5.0% $ 20,000 $ 22,000 $ 24,200 $ 26,620 $ 29,282
................Total $ 60,000 $ 66,000 $ 72,600 $ 79,860 $ 87,846
$800000 @ 7.5% $ 60,000 $ 66,000 $ 72,600 $ 79,860 $ 87,846

As such, in FireCalc, how does one account for the future value of different asset classes that have unique rates of return, without using a weighted average that is seemingly inaccurate?

Thank you
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Old 10-13-2012, 08:29 PM   #2
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Quote:
Originally Posted by ankos714 View Post
Greetings,

Why is it that Future Value calculations don't seem to handle weighted average rates of return very well? I notice this both in FireCalc and Excel.

For instance:

The future value of $400,000 @ 10% annual rate of return for 30 years is $6,979,760.91.

The future value of $400,000 @ 5% annual rate of return for 30 years is $1,728,776.95.

The sum of these two future values is $8,708,537.86.

However, if we combine these initial amounts at the get-go and use an average annual rate of return, the result is different. The future value of $800,000 @ 7.5% annual rate of return for 30 years is $7,003,964.15!

What is funny about this is that if I look at this on a year over year basis, the returns are identical:

.....

As such, in FireCalc, how does one account for the future value of different asset classes that have unique rates of return, without using a weighted average that is seemingly inaccurate?

Thank you
The difference is the result of compounding. Under the logic you are trying to apply the future value of $400,000 at 10% would only be twice the future value of $400,000 @ 5% and as you can see it is much different.

The three actual FV formulas are:

400,000 * (1+10%)^30
400,000 * (1+5%)^30
800,000* (1+7.5%)^30
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Old 10-13-2012, 09:40 PM   #3
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Can you shed light on why:

[400,000 * (1+10%)^30] + [400,000 * (1+5%)^30] does not equal [800,000* (1+7.5%)^30]

As well as:

How do we incorporate different assets, with different annual rates of return, into FireCalc?

Any additional insights? Thanks
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Old 10-13-2012, 09:46 PM   #4
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Quote:
Originally Posted by ankos714 View Post
How do we incorporate different assets, with different annual rates of return, into FireCalc?
See options under the "Your Portfolio" tab.

If you haven't done so already I highly recommend you spend some time learning the details of how FIRECalc works.
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Old 10-13-2012, 09:51 PM   #5
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Quote:
Originally Posted by ankos714 View Post
Can you shed light on why:

[400,000 * (1+10%)^30] + [400,000 * (1+5%)^30] does not equal [800,000* (1+7.5%)^30]
Due to compounding.


Quote:
Originally Posted by ankos714 View Post
How do we incorporate different assets, with different annual rates of return, into FireCalc?
Have you looked at the options under the Your Portfolio tab? It is fairly flexible albeit not exactly what you are seeking.
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Old 10-14-2012, 11:00 AM   #6
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Yes, I have looked there. Actually, that is what drove me to post here. I was trying to incorporate the appreciation of a multi-family real estate investment property alongside my 401k. To do so, I created a weighted average rate of return that I plugged into the last option in that section: "A portfolio with random performance, with a mean total portfolio return of % and variability (standard deviation) of %. Assume an inflation rate of %."

This lead to a divergence between the weight average annual rate of return and when I calculated the returns individually for each asset class and added them together.

How is real estate appreciate best incorporated into FireCalc?

Thanks so much
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