What is the present value of future payments?

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Kelly
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What is the present value of future payments?

Post by Kelly »

Folks,

Can someone please double check my math?

Scenario is two streams of income. $1000 per year. One stream is inflation adjusted (real payments) one is a nominal payment. Both go on for 30 years. I assumed each these payments are risk free so the appropriate discount rate is inflation.

What is the value today of those two streams? This is how I did it: I put the first nominal payment in the first row of the spreadsheet. Each sequential payment was divided by the trailing years inflation rate. I then summed those 30 payments. That is the value today of those 30 nominal payments.

The value today for the real payments is simply $30,000.

Is this correct?

Many thanks

Kelly
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bobcat2
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Re: What is the present value of future payments?

Post by bobcat2 »

One stream is inflation adjusted (real payments) one is a nominal payment. Both go on for 30 years. I assumed each these payments are risk free so the appropriate discount rate is inflation. ...Is this correct?
No. The appropriate discount rate is not the inflation rate. The appropriate 30 year risk free rates are the rates on nominal 30 year Treasuries and 30 year TIPS.

Currently 30 year nominal Treasuries are yielding about 3.1% and 30 year TIPS are yielding about 1.0%.

The inflation rate per se is never the risk free rate. The riskless asset is the security that offers a perfectly predictable rate of return in terms of the selected unit of account and the length of the investor's decision horizon. In this case the selected units of account are nominal and real US dollars and the length of the investor's decision horizon is 30 years.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Topic Author
Kelly
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Re: What is the present value of future payments?

Post by Kelly »

Thanks Bobcat.

I'm trying to simulate how an annuity with a guarantee withdrawal benefit would have performed during period 1968 to 1997. This was the worst retirement period according to the 1992 Bengen study that gave us the 4% withdrawal rate. The annuity allows you to withdraw 5% of the account value in year one and each year thereafter regardless of whether the account size reaches zero. This fixed payment got hammered by high inflation over that period losing 80% of it's purchasing power.

Alternatively, the investor could have withdrawn 4% of a 70/30 portfolio account value in year one and increased this withdrawal by inflation for 30 years.

If I'm trying to total the amount of real payments made from each program is it correct to simply add all the deflated annuity payments and multiply the first years 4% withdrawal from the 70/30 portfolio by 30? If I did it correctly the 70/30 portfolio delivered 70% more real payments.

Kelly
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Kosmo
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Re: What is the present value of future payments?

Post by Kosmo »

Kelly wrote:I'm trying to simulate how an annuity with a guarantee withdrawal benefit would have performed during period 1968 to 1997. This was the worst retirement period according to the 1992 Bengen study that gave us the 4% withdrawal rate.
Unrelated to the OP...how can a study done in 1992 use data from 1993-1997?
123
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Re: What is the present value of future payments?

Post by 123 »

Wouldn't it be more accurate if you used the appropriate treasury risk-free rate separately for each individual payment date? Payments for the first few years would be low but they would gradually increase to the 30 year rate.
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dbr
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Re: What is the present value of future payments?

Post by dbr »

Kelly wrote: If I'm trying to total the amount of real payments made from each program is it correct to simply add all the deflated annuity payments and multiply the first years 4% withdrawal from the 70/30 portfolio by 30? If I did it correctly the 70/30 portfolio delivered 70% more real payments.

Kelly
That sounds right to me.
dbr
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Re: What is the present value of future payments?

Post by dbr »

123 wrote:Wouldn't it be more accurate if you used the appropriate treasury risk-free rate separately for each individual payment date? Payments for the first few years would be low but they would gradually increase to the 30 year rate.
I think what he is doing is not a present value calculation, but something simpler as described above.
dbr
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Re: What is the present value of future payments?

Post by dbr »

Kosmo wrote:
Kelly wrote:I'm trying to simulate how an annuity with a guarantee withdrawal benefit would have performed during period 1968 to 1997. This was the worst retirement period according to the 1992 Bengen study that gave us the 4% withdrawal rate.
Unrelated to the OP...how can a study done in 1992 use data from 1993-1997?
Bengen wouoldn't have data all the way to 1997, but the result would already be evident in the data he does have. It is true that the worst 30 year retirement year in other studies is 1966 or right along in there. Observing that one reason for that was the high inflation in late seventies/early eighties might be valid, and it isn't until 1982 that stocks take off, which is too late for that investor.
Topic Author
Kelly
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Re: What is the present value of future payments?

Post by Kelly »

Kosmo wrote:
Kelly wrote:I'm trying to simulate how an annuity with a guarantee withdrawal benefit would have performed during period 1968 to 1997. This was the worst retirement period according to the 1992 Bengen study that gave us the 4% withdrawal rate.
Unrelated to the OP...how can a study done in 1992 use data from 1993-1997?
Ha! Good point. The study has been updated.

Kelly
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