### Author Topic: Forecasting future values confusion  (Read 3134 times)

#### Ricky

• Pencil Stache
•    • Posts: 842 ##### Forecasting future values confusion
« on: September 30, 2015, 09:50:15 PM »
So, running these numbers have me confused:

A) \$10000 invested per year for 10 years at a return rate of 7% nets \$147,835 at the end of 10 years.

B) \$10000 invested per year for 10 years at an adjusted for inflation rate of 4% nets \$124,863.51 at the end of 10 years.

C) The confusing part is that if you take the present value of \$147,835 at the end of 10 years at a discount rate of 3% (inflation) you get \$110,003.12

Why is the result from C different from B? Isn't B the theoretical present value already since you left off 3%?

 - I did some searching and I didn't realize that it wasn't as simple as just subtracting the inflation rate from the return rate (though I still can't grasp why). But even so, if you rerun "A" with 3.88 instead (the inflation adjusted return), you get \$124,027.82, which is still different from "C". Why the disparities?
« Last Edit: September 30, 2015, 10:09:20 PM by Ricky »

#### MDM

• Walrus Stache
•       • Posts: 9805 ##### Re: Forecasting future values confusion
« Reply #1 on: October 01, 2015, 12:42:17 AM »
A) \$10000 invested per year for 10 years at a return rate of 7% nets \$147,835 at the end of 10 years.

B) \$10000 invested per year for 10 years at an adjusted for inflation rate of 4% nets \$124,863.51 at the end of 10 years.

C) The confusing part is that if you take the present value of \$147,835 at the end of 10 years at a discount rate of 3% (inflation) you get \$110,003.12

What do you get if you take the present value of \$147,835 (\$147,835.99?) 10 years from now, with \$10000 invested per year during those 10 years, at a discount rate of 7%?

What do you get if you take the present value of \$124,863.51 10 years from now, with \$10000 invested per year during those 10 years, at a discount rate of 4%?

#### YoungInvestor

• Bristles
•   • Posts: 407 ##### Re: Forecasting future values confusion
« Reply #2 on: October 01, 2015, 05:54:13 AM »
The adjusted rate. Is 1.07/1.03 -1 = 3.88%.

The reason is simple : say you only buy watermelons. This year, they cost 1\$ each. You take 100 000\$ (which would be 100 000 watermelons) and invest it.

A year from now, your investment is worth 107 000\$ and watermelons now cost 1.03\$. How many watermelons can you buy?

103 883. Therefore, your inflation-adjusted rate of return is 3.883%, as your investment increased the number of watermelons you could buy by this amount.

#### YoungInvestor

• Bristles
•   • Posts: 407 ##### Re: Forecasting future values confusion
« Reply #3 on: October 01, 2015, 06:01:15 AM »
The adjusted rate. Is 1.07/1.03 -1 = 3.88%.

The reason is simple : say you only buy watermelons. This year, they cost 1\$ each. You take 100 000\$ (which would be 100 000 watermelons) and invest it.

A year from now, your investment is worth 107 000\$ and watermelons now cost 1.03\$. How many watermelons can you buy?

103 883. Therefore, your inflation-adjusted rate of return is 3.883%, as your investment increased the number of watermelons you could buy by this amount.

I just realized that this did not answer the original question :

100k * 1.07^10 =196 715\$.
196 715\$ / 1.03^10 = 146 375\$

100k * 1.03883^10 = 146 375\$.

The original post didn't compute its future values correctly.

#### Ricky

• Pencil Stache
•    • Posts: 842 ##### Re: Forecasting future values confusion
« Reply #4 on: October 01, 2015, 06:20:12 AM »
The adjusted rate. Is 1.07/1.03 -1 = 3.88%.

The reason is simple : say you only buy watermelons. This year, they cost 1\$ each. You take 100 000\$ (which would be 100 000 watermelons) and invest it.

A year from now, your investment is worth 107 000\$ and watermelons now cost 1.03\$. How many watermelons can you buy?

103 883. Therefore, your inflation-adjusted rate of return is 3.883%, as your investment increased the number of watermelons you could buy by this amount.

I just realized that this did not answer the original question :

100k * 1.07^10 =196 715\$.
196 715\$ / 1.03^10 = 146 375\$

100k * 1.03883^10 = 146 375\$.

The original post didn't compute its future values correctly.

We're talking about two different things, but maybe we're getting somewhere. I'm not starting with \$100k and making no annual additions - I'm starting with \$0 and adding \$10k every year for 10 years. In your scenario, the numbers make sense, when you're not adding any additional \$ per annum.

The explanation about why you'd use 3.88% is helpful, but still doesn't explain why "C" is different from finding the present value of "A" using a 3.88% discount rate in my scenario.

MDM just threw a curve ball from left field? I'm not sure what he was getting at.
« Last Edit: October 01, 2015, 06:33:36 AM by Ricky »

#### beltim

• Magnum Stache
•      • Posts: 2853 ##### Re: Forecasting future values confusion
« Reply #5 on: October 01, 2015, 06:24:49 AM »
 - I did some searching and I didn't realize that it wasn't as simple as just subtracting the inflation rate from the return rate (though I still can't grasp why). But even so, if you rerun "A" with 3.88 instead (the inflation adjusted return), you get \$124,027.82, which is still different from "C". Why the disparities?

This looks close enough that it might be a case of not using enough digits.  Have you tried using 1.07/1.03 = 1.03883495?

#### Ricky

• Pencil Stache
•    • Posts: 842 ##### Re: Forecasting future values confusion
« Reply #6 on: October 01, 2015, 06:25:47 AM »
 - I did some searching and I didn't realize that it wasn't as simple as just subtracting the inflation rate from the return rate (though I still can't grasp why). But even so, if you rerun "A" with 3.88 instead (the inflation adjusted return), you get \$124,027.82, which is still different from "C". Why the disparities?

This looks close enough that it might be a case of not using enough digits.  Have you tried using 1.07/1.03 = 1.03883495?

Using that number would only further the gap which still wouldn't make sense.

#### MDM

• Walrus Stache
•       • Posts: 9805 ##### Re: Forecasting future values confusion
« Reply #7 on: October 01, 2015, 09:12:47 AM »
MDM just threw a curve ball from left field? I'm not sure what he was getting at.
It's getting at the math behind FV and PV calculations, and when one might expect the PV calculation to "undo" the FV calculation.  What answers do you get to the two questions?

#### Ricky

• Pencil Stache
•    • Posts: 842 ##### Re: Forecasting future values confusion
« Reply #8 on: October 01, 2015, 10:24:56 AM »
MDM just threw a curve ball from left field? I'm not sure what he was getting at.
It's getting at the math behind FV and PV calculations, and when one might expect the PV calculation to "undo" the FV calculation.  What answers do you get to the two questions?

Eh maybe that's the issue - I'm not using the proper formula to find PV when we're talking about \$10k contributions per year.

#### YoungInvestor

• Bristles
•   • Posts: 407 ##### Re: Forecasting future values confusion
« Reply #9 on: October 01, 2015, 11:13:30 AM »
The adjusted rate. Is 1.07/1.03 -1 = 3.88%.

The reason is simple : say you only buy watermelons. This year, they cost 1\$ each. You take 100 000\$ (which would be 100 000 watermelons) and invest it.

A year from now, your investment is worth 107 000\$ and watermelons now cost 1.03\$. How many watermelons can you buy?

103 883. Therefore, your inflation-adjusted rate of return is 3.883%, as your investment increased the number of watermelons you could buy by this amount.

I just realized that this did not answer the original question :

100k * 1.07^10 =196 715\$.
196 715\$ / 1.03^10 = 146 375\$

100k * 1.03883^10 = 146 375\$.

The original post didn't compute its future values correctly.

We're talking about two different things, but maybe we're getting somewhere. I'm not starting with \$100k and making no annual additions - I'm starting with \$0 and adding \$10k every year for 10 years. In your scenario, the numbers make sense, when you're not adding any additional \$ per annum.

The explanation about why you'd use 3.88% is helpful, but still doesn't explain why "C" is different from finding the present value of "A" using a 3.88% discount rate in my scenario.

MDM just threw a curve ball from left field? I'm not sure what he was getting at.

Ah. Your problem is simple. You're discounting the contributions from all 10 years for inflation, whereas you should discount them by the number of years they've been invested.

Applyng 10 years of inflation to your last year's contribution amount is obviously unneeded. Visualize each contribution individually and it should be quite obvious.

#### MDM

• Walrus Stache
•       • Posts: 9805 ##### Re: Forecasting future values confusion
« Reply #10 on: October 01, 2015, 11:27:31 AM »
MDM just threw a curve ball from left field? I'm not sure what he was getting at.
It's getting at the math behind FV and PV calculations, and when one might expect the PV calculation to "undo" the FV calculation.  What answers do you get to the two questions?
Eh maybe that's the issue - I'm not using the proper formula to find PV when we're talking about \$10k contributions per year.

Answer to both questions is \$0 - the same as the starting value for the two FV calculations.  See snapshot below: first two columns in the table are the FV calculations from the OP, and the last column is the PV calculation using the results of the first FV calculation.  Table comes from the 'Misc. calcs' tab on the case study spreadsheet. 