Math help: 401k vs debt payoff formula

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ray.james
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Math help: 401k vs debt payoff formula

Post by ray.james » Sat Jul 14, 2018 3:53 pm

I often run into threads, where I was unable to qualitatively put the yield on debt payoff vs 401k saving. The below math is what I struggle to understand which might help explain my point to new members well.

Lets take an example:
1) Debt is at 6%. so the yield in this case is 6%
2) For 401k at 35% tax rate and 25 years compounding at 7% and coming at 20% tax rate. what is the yield on the current dollar?
3) muni yield is 3%.

I know how to compare 1 vs 3 based on tax rates. 6% * 0.65(post tax deduction) = 3.9%. So yield is better than muni bond. What is the same math for 401k?

a) 7%
b)35-20% = 15% saving; so (7 * 1.15*) * (1-20%Tax) = 6.44%
c) 7% - 20% tax = 5.6%

These question especially arise or mortgage/student loan vs savings. Granted there are several other factors like age, income to debt etc., what is the mathematical answer to above question? I know 401k is way ahead but what is the correct answer.
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delamer
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Re: Math help: 401k vs debt payoff formula

Post by delamer » Sat Jul 14, 2018 6:29 pm

Are you trying to decide whether to use a current dollar to 1) payoff debt with post-tax dollars or 2) invest in your pre-tax 401(k) or 3) invest in munis with post-tax dollars?

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Re: Math help: 401k vs debt payoff formula

Post by ray.james » Sat Jul 14, 2018 10:08 pm

delamer wrote:
Sat Jul 14, 2018 6:29 pm
Are you trying to decide whether to use a current dollar to 1) payoff debt with post-tax dollars or 2) invest in your pre-tax 401(k) or 3) invest in munis with post-tax dollars?
Yes. Thank you for putting it much easier.

I know 401k comes ahead probably but I want to know - by how much.
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Re: Math help: 401k vs debt payoff formula

Post by jimb_fromATL » Sat Jul 14, 2018 10:53 pm

ray.james wrote:
Sat Jul 14, 2018 10:08 pm
delamer wrote:
Sat Jul 14, 2018 6:29 pm
Are you trying to decide whether to use a current dollar to 1) payoff debt with post-tax dollars or 2) invest in your pre-tax 401(k) or 3) invest in munis with post-tax dollars?
Yes. Thank you for putting it much easier.

I know 401k comes ahead probably but I want to know - by how much.
Time is an exponential factor in earning compound interest. You'll be earning compound interest for the rest of your life in your 401(k) but even student loans and mortgages are much shorter by comparison -- with any luck at all. There are also yearly limits for 401(k)s that can prevent you from being able to catch up by reinvesting the freed-up payments when you pay off a debt faster.

So for most folks who are paying any significant income taxes, it makes more financial sense to invest as much as possible in tax-advantaged retirement plans as soon as possible, rather than paying down manageable debts too fast. Your 401(k) lets you defer taxes in your case the 35% federal tax bracket (and maybe state tax too). If you reduce your 401(k) contributions, then the money that will be going to pay taxes will not be buying necessities, paying bills, paying down debt, or earning compound interest for your benefit for the rest of your life either.

Here are some links to several threads where my posts show examples of how delaying your tax-advantaged retirement investing and paying taxes prematurely in order to pay down manageable debts too fast can --depending on your age, income and tax brackets -- literally cost anywhere from tens to hundreds of thousands to sometimes millions of dollars out of your future retirement income in exchange for saving only a tiny fraction as much interest on the relatively short term debts. Given more specific information, we can work up a closer estimate for your own situation.

How much are you contributing to the 401(k) now?
Do you get any employer matching payments?
How much are you considering reducing the 401(k) contributions to pay toward the debt?
What is your state income tax rate -- if any ?
What is the current balance, rate, and minimum payment on the debt?
How much extra can you spare to pay on the debt if you are also contributing the yearly max to your 401(k)?

jimb

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danielc
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Re: Math help: 401k vs debt payoff formula

Post by danielc » Sun Jul 15, 2018 8:11 am

ray.james wrote:
Sat Jul 14, 2018 3:53 pm
I often run into threads, where I was unable to qualitatively put the yield on debt payoff vs 401k saving. The below math is what I struggle to understand which might help explain my point to new members well.

Lets take an example:
1) Debt is at 6%. so the yield in this case is 6%
2) For 401k at 35% tax rate and 25 years compounding at 7% and coming at 20% tax rate. what is the yield on the current dollar?
3) muni yield is 3%.

I know how to compare 1 vs 3 based on tax rates. 6% * 0.65(post tax deduction) = 3.9%. So yield is better than muni bond. What is the same math for 401k?
That calculation doesn't make any sense. You don't pay taxes on "not spending money", unless you are specifically referring to some kind of deductible debt. Is the debt tax deductible? If it isn't, then paying debt with 6% interest is a zero-risk tax-free return of 6% and easily beats anything else you might consider.

Next, 7% is not realistic for your 401k. But to answer your question, here is the calculation:

Consider $1 of post-tax money. What return would you get if you decide to forgo this dollar today and leave it in the 401k at 7% for 25 years and then have it taxed at 20%? Well, first of all, $1 post-tax is $1/0.65 = $1.54 pre-tax. Invest this at 7% for 25 years and it becomes (1/0.65) * 1.07^25 = 8.35. Now withdraw at 20% and you get (1/0.65) * 1.07^25 * 0.8 = 6.68. Now compute the equivalent amortized return rate: (1 + r)^25 = 6.68 => r = 6.68^(1/25) - 1 = 0.079. In other words, the equivalent rate of return is 7.9% on an equivalent post-tax basis.

ray.james wrote:
Sat Jul 14, 2018 3:53 pm
a) 7%
b)35-20% = 15% saving; so (7 * 1.15*) * (1-20%Tax) = 6.44%
c) 7% - 20% tax = 5.6%
None of the above.
ray.james wrote:
Sat Jul 14, 2018 3:53 pm
These question especially arise or mortgage/student loan vs savings. Granted there are several other factors like age, income to debt etc., what is the mathematical answer to above question? I know 401k is way ahead but what is the correct answer.
The only reason the 401k is way head is because your inputs were wrong. Not only is 7% unrealistic, but you also ignored the risk from investing in stocks. Paying debt is a risk-free investment.

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Re: Math help: 401k vs debt payoff formula

Post by grabiner » Sun Jul 15, 2018 8:53 am

ray.james wrote:
Sat Jul 14, 2018 3:53 pm
I often run into threads, where I was unable to qualitatively put the yield on debt payoff vs 401k saving. The below math is what I struggle to understand which might help explain my point to new members well.

Lets take an example:
1) Debt is at 6%. so the yield in this case is 6%
2) For 401k at 35% tax rate and 25 years compounding at 7% and coming at 20% tax rate. what is the yield on the current dollar?
3) muni yield is 3%.
If you contribute to the 401(k) in a 35% tax bracket and withdraw in a 20% tax bracket, then $65 contributed is equivalent to $80 tax-free, which is an immediate 23% return. Spread this over the time between contribution and withdrawal. For 25 years, take (1.23)^{1/25}=1.0091, so this adds 0.91% to the return of a 401(k) contribution.

However, the 7% return on the 401(k) is the wrong comparison, because it is a risky return. Paying off debt is a risk-free return, and buying munis is a low-risk return. If you aren't maxing out your 401(k), the fair comparison to use there is the return of a low-risk bond fund in the 401(k) )probably 4% in your example) with duration similar to the loan payoff. Once you have decided whether to pay off the loan, you can then decide how much risk to take. See Paying down loans versus investing on the wiki.
Wiki David Grabiner

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Re: Math help: 401k vs debt payoff formula

Post by jimb_fromATL » Sun Jul 15, 2018 7:12 pm

danielc wrote:
Sun Jul 15, 2018 8:11 am
Next, 7% is not realistic for your 401k.
grabiner wrote:
Sun Jul 15, 2018 8:53 am
However, the 7% return on the 401(k) is the wrong comparison, because it is a risky return. Paying off debt is a risk-free return, and buying munis is a low-risk return.
I think it's reasonable to compare after-tax investments to risk-free returns like munis or other bond funds for paying off debt.

But most people do not invest in stable value funds alone in their 401(k) and other retirement plans. So when it comes to deciding to reduce, delay, or stop contributions to a 401(k), IMO the question should be whether you'd prefer to guarantee to pay taxes in your highest bracket up front or to have more money at risk -- including taxes that you did not pay up front -- in exchange for the likelihood of ending up with possibly a lot more compound interest earned for retirement than the after-tax money would have saved on the debt.

It is highly likely that we will still have a standard or itemized deduction and graduated steps in lower rate tax brackets; and tht those steps will continue to up with inflation as they do now. For 401(k) contributions you get to defer taxes in your highest brackets for fed (and state if applicable) now. But unless you have a HUGE pension and other income in retirement which is higher than your earnings in your working years, you'll probably pay a lower percentage of tax on your retirement income than you got to defer and invest during your working years.

Plus, depending on which state you live in now and after retirement, you may be able to defer state taxes and invest that money in your 401(k) now and never pay state income tax on the withdrawals in retirement later.

In the unlikely event that your total tax percentage were exactly the same in retirement, then your net income after your tax liability would be exactly the same. If your income in retirement is higher in retirement than when you were working, you probably will pay more tax. But you'll still have more income after tax. IMO that would be a lot better than deliberately planning to have less income in retirement by voluntarily paying taxes in your highest brackets several decades sooner than required.

As for the return on your investment in a 401(k) or any other investment, IMO 7% is probably not at all an unreasonable estimate.

Let's look at the 25 year CAGR (Compound Annual Growth Rate) for some samples of popular funds, several of which have been around a long time. This shows the rolling 25 year averages for periodic investments each year. IMO this is more meaningful than the growth of lump sum summaries on a lot of websites, since I don't know a single person who invested a single lump sum at the beginning of their career and never invested anything else, and the results can vary widely if the lump sum happens to be invested just before or after a major peak or valley over the years.
  • S&P500 before expenses:
    In 50 rolling 25 year periods from 1930 through 2017 Dollar-Cost-Averaging with yearly contributions in S&P500 has averaged an APY of 10.87%. with a best of 17.59% for the period 1975-1999 and a worst of 6.94% for the period of 1957-1981. The latest period of 1993-2017 has averaged 9.01%.

    Vanguard S&P 500 index fund:
    In 17 rolling 25 year periods from 1977 through 2017 DCA with yearly contributions in VFINX has averaged an APY of 9.97%. with a best of 14.21% for the period 1979-2003 and a worst of 7.57% for the period of 1992-2016. The latest period of 1993-2017 has averaged 8.91%.

    VG WELLINGTON:
    In 50 rolling 25 year periods from 1930 through 2017 DCA with yearly contributions in VWELX has averaged an APY of 9.51%. with a best of 14.35% for the period 1975-1999 and a worst of 3.97% for the period of 1955-1979. The latest period of 1993-2017 has averaged 8.92%. Notice in the table further down that the worst 25 year period for VWELX ended 39 years ago, and that the last 25 year period under 7% was in 1983.

    VG WINDSOR:
    In 35 rolling 25 year periods from 1959 through 2017 DCA with yearly contributions in VWNDX has averaged an APY of 12.87%. with a best of 17.35% for the period 1975-1999 and a worst of 7.33% for the period of 1987-2011. The latest period of 1993-2017 has averaged 8.89%. Remember, the barely over 7% period ending in 2011 included the second worst market crash in history.

    AMERICAN FUNDS GROWTH FUND OF AMERICA: (This is widely believed to be the fund that Dave Ramsey says has always averaged 12 percent for him)
    In 20 rolling 25 year periods from 1974 through 2017 DCA with yearly contributions in AGTHX has averaged an APY of 13.03%. with a best of 19.75% for the period 1975-1999 and a worst of 9.44% for the period of 1992-2016. The latest period of 1993-2017 has averaged 10.46%.

    VG STAR FUND:
    In 8 rolling 25 year periods from 1986 through 2017 DCA with yearly contributions in VGSTX has averaged an APY of 8.22%. with a best of 8.71% for the period 1986-2010 and a worst of 7.59% for the period of 1992-2016. The latest period of 1993-2017 has averaged 8.07%.

    VG WELLESLEY:
    In 23 rolling 25 year periods from 1971 through 2017 DCA with yearly contributions in VWINX has averaged an APY of 10.35%. with a best of 13.2% for the period 1975-1999 and a worst of 7.7% for the period of 1992-2016. The latest period of 1993-2017 has averaged 7.76%.

    DODGE&COX STOCK:
    In 28 rolling 25 year periods from 1966 through 2017 DCA with yearly contributions in DODGX has averaged an APY of 13.36%. with a best of 16.68% for the period 1975-1999 and a worst of 9.55% for the period of 1966-1990. The latest period of 1993-2017 has averaged 10.74%.

    FIDELITY PURITAN (FPURX):
    In 46 rolling 25 year periods from 1948 through 2017 DCA with yearly contributions in FPURX has averaged an APY of 11.31%. with a best of 15.48% for the period 1975-1999 and a worst of 7.66% for the period of 1992-2016. The latest period of 1993-2017 has averaged 8.11%.

    FIDELITY Index fund (FFIDX):
    In 50 rolling 25 year periods from 1934 through 2017 DCA with yearly contributions in FFIDX has averaged an APY of 11.1%. with a best of 17.47% for the period 1975-1999 and a worst of 7.44% for the period of 1957-1981. The latest period of 1993-2017 has averaged 8.47%.



More about Wellington:

Code: Select all

VWELX	yearly 25yr DCA rolling rate
2017	14.72%	8.922%
2016	11.01%	8.682%
2015	0.06%	8.732%
2014	9.82%	9.349%
2013	19.66%	9.443%
2012	12.57%	9.019%
2011	3.85%	8.916%
2010	10.94%	9.376%
2009	22.20%	9.527%
2008	-22.30%	9.040%
2007	8.34%	11.484%
2006	14.97%	11.917%
2005	6.82%	11.880%
2004	11.17%	12.355%
2003	20.75%	12.573%
2002	-6.90%	12.210%
2001	4.19%	13.317%
2000	10.40%	13.806%
1999	4.41%	14.022%
1998	12.06%	14.351%
1997	23.23%	14.133%
1996	16.19%	13.347%
1995	32.92%	12.917%
1994	-0.49%	11.643%
1993	13.52%	12.074%
1992	7.93%	11.698%
1991	23.65%	11.638%
1990	-2.81%	10.672%
1989	21.60%	11.201%
1988	16.11%	10.349%
1987	2.28%	9.798%
1986	18.40%	9.997%
1985	28.53%	9.318%
1984	10.70%	8.088%
1983	23.57%	7.816%
1982	24.55%	6.909%
1981	2.90%	5.857%
1980	22.58%	6.064%
1979	13.54%	5.125%
jimb

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danielc
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Re: Math help: 401k vs debt payoff formula

Post by danielc » Sun Jul 15, 2018 7:30 pm

jimb_fromATL wrote:
Sun Jul 15, 2018 7:12 pm
danielc wrote:
Sun Jul 15, 2018 8:11 am
Next, 7% is not realistic for your 401k.
grabiner wrote:
Sun Jul 15, 2018 8:53 am
However, the 7% return on the 401(k) is the wrong comparison, because it is a risky return. Paying off debt is a risk-free return, and buying munis is a low-risk return.
I think it's reasonable to compare after-tax investments to risk-free returns like munis or other bond funds for paying off debt.
That has nothing to do with anything. A 7% return is likely fantasy, and risk is not irrelevant.
jimb_fromATL wrote:
Sun Jul 15, 2018 7:12 pm
S&P500 before expenses:
In 50 rolling 25 year periods from 1930 through 2017 Dollar-Cost-Averaging with yearly contributions in S&P500 has averaged an APY of 10.87%. with a best of 17.59% for the period 1975-1999 and a worst of 6.94% for the period of 1957-1981. The latest period of 1993-2017 has averaged 9.01%.
Current yields suggest a future return of 3% real, or around 5% nominal depending on inflation. It would be negligent to expect 9% for no good reason. You have ignored the effects of inflationary periods, you have ignored current yields, and you have ignored trends in GDP growth. Long term equity returns necessarily track GDP growth. GDP growth is slowing and HAS to continue to slow purely for demographic reasons.

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Re: Math help: 401k vs debt payoff formula

Post by ThriftyPhD » Sun Jul 15, 2018 7:42 pm

danielc wrote:
Sun Jul 15, 2018 7:30 pm
Current yields suggest a future return of 3% real, or around 5% nominal depending on inflation. It would be negligent to expect 9% for no good reason. You have ignored the effects of inflationary periods, you have ignored current yields, and you have ignored trends in GDP growth. Long term equity returns necessarily track GDP growth. GDP growth is slowing and HAS to continue to slow purely for demographic reasons.
The current SEC yield on Vanguard High-Yield Corporate Fund Investor Shares (VWEHX) is 5.75%. This is higher than your expected 5% nominal for stocks. Are you moving from equities to high yield bonds? Yes there is a default risk, but if there is a default or bankruptcy, bonds would be paid before stocks. So less risk for high yield bonds than stocks, and a higher return than what you expect.

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Re: Math help: 401k vs debt payoff formula

Post by danielc » Sun Jul 15, 2018 7:54 pm

ThriftyPhD wrote:
Sun Jul 15, 2018 7:42 pm
The current SEC yield on Vanguard High-Yield Corporate Fund Investor Shares (VWEHX) is 5.75%. This is higher than your expected 5% nominal for stocks. Are you moving from equities to high yield bonds?
Nope. I don't invest in non-investment-grade products.
ThriftyPhD wrote:
Sun Jul 15, 2018 7:42 pm
Yes there is a default risk, but if there is a default or bankruptcy, bonds would be paid before stocks. So less risk for high yield bonds than stocks, and a higher return than what you expect.
That statement is both naive and false. First of all, companies that issue junk bonds are not a random sample of the universe of companies. They are companies in financial distress. Second, the risks of junk bonds extend well beyond bankruptcy. For example, their price fluctuations are highly correlated with equities and a lot of those bonds have call options.

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Re: Math help: 401k vs debt payoff formula

Post by grabiner » Sun Jul 15, 2018 8:16 pm

jimb_fromATL wrote:
Sun Jul 15, 2018 7:12 pm
danielc wrote:
Sun Jul 15, 2018 8:11 am
Next, 7% is not realistic for your 401k.
grabiner wrote:
Sun Jul 15, 2018 8:53 am
However, the 7% return on the 401(k) is the wrong comparison, because it is a risky return. Paying off debt is a risk-free return, and buying munis is a low-risk return.
I think it's reasonable to compare after-tax investments to risk-free returns like munis or other bond funds for paying off debt.

But most people do not invest in stable value funds alone in their 401(k) and other retirement plans. So when it comes to deciding to reduce, delay, or stop contributions to a 401(k), IMO the question should be whether you'd prefer to guarantee to pay taxes in your highest bracket up front or to have more money at risk -- including taxes that you did not pay up front -- in exchange for the likelihood of ending up with possibly a lot more compound interest earned for retirement than the after-tax money would have saved on the debt.
You can still compare the two choices independently, whether to pay down the loan, and what to invest in, and that is why the potential returns of stocks are not relevant. Consider these four options for using $6500 in cash:

A. Contribute $10,000 ($6500 after tax in the example 35% bracket) to your 401(k), in your current allocation.
B. Contribute $10,000 to your 401(k), and invest it in bonds.
C. Pay $6500 against your loan, and move $10,000 in your 401(k) from bonds to your current allocation.
D. Pay $6500 against your loan, and leave your 401(k) unchanged.

B and D have the same amount of stock, and thus the same risk. B may be better than D even if the 401(k) bond yield is lower than the loan rate, because of the tax benefit of the 401(k); you will probably withdraw the money at a lower tax rate. (And B is much better than D if you need the money to get an employer match on the 401(k).) Likewise, A and C have the same amount of stock, and thus A is better than C if B is better than D.

For A to be right (add more stock to your 401(k)), it has to be better than C, and that does not depend on stock returns. If the loan rate is high enough that you prefer C to A, and D to B, then you should pay down the loan, and then, if you do want the prospect of higher returns and higher risk, choose C over D. Conversely, if you have a low-rate loan, you prefer A to C, and B to D, so you can choose between A and B.

One exception applies if C is not available to you. If your investments are already 100% stock, then A can be right even if C would be better in theory. However, few investors are 100% stock, particularly if they also have debt.
Wiki David Grabiner

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Re: Math help: 401k vs debt payoff formula

Post by ThriftyPhD » Sun Jul 15, 2018 8:18 pm

danielc wrote:
Sun Jul 15, 2018 7:54 pm
ThriftyPhD wrote:
Sun Jul 15, 2018 7:42 pm
The current SEC yield on Vanguard High-Yield Corporate Fund Investor Shares (VWEHX) is 5.75%. This is higher than your expected 5% nominal for stocks. Are you moving from equities to high yield bonds?
Nope. I don't invest in non-investment-grade products.
ThriftyPhD wrote:
Sun Jul 15, 2018 7:42 pm
Yes there is a default risk, but if there is a default or bankruptcy, bonds would be paid before stocks. So less risk for high yield bonds than stocks, and a higher return than what you expect.
That statement is both naive and false. First of all, companies that issue junk bonds are not a random sample of the universe of companies. They are companies in financial distress. Second, the risks of junk bonds extend well beyond bankruptcy. For example, their price fluctuations are highly correlated with equities and a lot of those bonds have call options.
I wouldn't recommend it either; I follow the 'take your risk on equity side' rule of advice. But I also expect equities out outperform bonds long term. If I didn't, I would buy bonds; they're less risk.

I wouldn't say my statement is naive or false. Bonds get paid before stocks. That's why equities are considered a higher risk and demand a risk premium. And price fluctuations in high yield bonds may be highly correlated with equities, but if the expected growth is higher than your expected equity growth, then why go with equities over bonds?

There are also many types of junk bonds. VWEHX is fairly high grade for junk bonds, mostly B and Ba with very little C or lower. Generally considered to have the financial capacity to meet their commitments, and with a bond fund individual company risk is mitigated by the diversity.

Again, I wouldn't recommend a high yield as the main bond fund; the high correlation to equities makes it a poor choice as an uncorrelated asset alternative. But I think it serves as a good reality check to expected equity return. It's easy to get overly pessimistic with future returns. If people really feel that equities are going to perform so badly that they underperform bonds, then why buy the equities?

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Re: Math help: 401k vs debt payoff formula

Post by danielc » Sun Jul 15, 2018 10:19 pm

ThriftyPhD wrote:
Sun Jul 15, 2018 8:18 pm
I wouldn't say my statement is naive or false. Bonds get paid before stocks.
That was not the only thing that you said. You said "so less risk for high yield bonds than stocks". The jump from your premise to your conclusion was faulty logic, and I explained why. For example, companies that issue junk bonds not a random sample of all companies; they are companies in financial distress. It might be true that "junk bonds" are safer than "junk stocks", and that "good bonds" are safer than "good stocks", but it does not follow that junk bonds are safer than "good stocks".

Consider the similar statement: Countries are usually more credit worthy than companies, therefore Greece is more credit worthy than Microsoft.

ThriftyPhD wrote:
Sun Jul 15, 2018 8:18 pm
That's why equities are considered a higher risk and demand a risk premium.
I strongly disagree. The fact that bonds get paid first does not in any way capture the risk story behind equities relative to bonds. A bond is a contract to pay certain amounts of money on certain dates. It has a specific list of promised cashflows that you can write down and put on a spreadsheet. A stock is nothing of the sort. That fact alone creates a significant difference, and it changes the valuation calculation. The cashflows arising from stocks are tied to future unknown earnings, and they will swing back and forth with the business cycle and external events. The business cycle does not affect the value of the coupons paid by a bond. This is a very salient difference, and I'm pretty sure it has more to do with the lower volatility of bonds than the thing you suggested. The biggest risk of bonds is not companies dying, and the biggest risk of stocks is not companies dying. Those things can happen, but they are not the most important scenario.
ThriftyPhD wrote:
Sun Jul 15, 2018 8:18 pm
And price fluctuations in high yield bonds may be highly correlated with equities, but if the expected growth is higher than your expected equity growth, then why go with equities over bonds?
Because I think you have incorrectly estimated both the risk and the return of junk bonds. Btw, right now Vanguard's VWEAX (junk bonds) has an SEC yield of 5.85% and VTSAX (US stocks) has an SEC yield of 1.83%. Go check for yourself. If you really believe in the line of reasning that you offered, then YOU should be buying VWEAX and selling VTSAX. On the other hand, I do not believe for a second that junk bonds will return 5.85% going forward, or that their risk is as low as you imagine.

ThriftyPhD wrote:
Sun Jul 15, 2018 8:18 pm
It's easy to get overly pessimistic with future returns.
I am not being pessimistic, I am being realistic. Planning on a 7% return is highly irresponsible and it ignores every fact about how the economy works. Stocks cannot grow much faster than GDP. In turn, GDP growth is the sum of producitivty growth and population growth. Historically both have contributed more or less equally to real GDP growth. Going forward, population growth will continue to slow down. In the shorter term, the CAPE is high, and dividend yields are low. A dividend yield of ~ 1.5% combined with a historical ~ 1.5% dividend growth rate gives a ~ 3% expected real return rate. This is just the reality. In addition, it is not possible for bonds to return more than stocks for very long periods of time. Therefore, regardless of whatever yield you are looking at right now for junk bonds, their long term return cannot be higher than the long term return of equities. This is just how math works. It is not possible for the debt obligations of companies to grow faster over the long term than the earnings of said companies.
ThriftyPhD wrote:
Sun Jul 15, 2018 8:18 pm
If people really feel that equities are going to perform so badly that they underperform bonds, then why buy the equities?
Because there is no doubt in my mind that equities will significantly outperform bonds over the course of my (long) investment horizon.

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Re: Math help: 401k vs debt payoff formula

Post by ThriftyPhD » Mon Jul 16, 2018 6:56 am

danielc wrote:
Sun Jul 15, 2018 10:19 pm
Because I think you have incorrectly estimated both the risk and the return of junk bonds. Btw, right now Vanguard's VWEAX (junk bonds) has an SEC yield of 5.85% and VTSAX (US stocks) has an SEC yield of 1.83%. Go check for yourself. If you really believe in the line of reasning that you offered, then YOU should be buying VWEAX and selling VTSAX. On the other hand, I do not believe for a second that junk bonds will return 5.85% going forward, or that their risk is as low as you imagine.
SEC yield on a stock fund is an estimate of dividend yield. It doesn't include price growth, which is a main driver of equity returns. The SEC yield on a bond fund is the dividend yield, which is the main driver of price growth on a bond fund (and long term, averaging out rate increases and decreases, the only growth).

I'm not sure why you're trying to compare SEC yield on an equity fund vs bond fund to compare expected growth.

If you want to assume 5% nominal long term growth on US stocks, by all means go ahead. But with that level of pessimism, you may want to look to safer investment choices that offer a similar yield, or at least a much better risk adjusted yield. If you feel that demographics in the US mean little to no growth going forward, you may want to look into Ex-US funds.

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danielc
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Re: Math help: 401k vs debt payoff formula

Post by danielc » Mon Jul 16, 2018 9:23 am

ThriftyPhD wrote:
Mon Jul 16, 2018 6:56 am
SEC yield on a stock fund is an estimate of dividend yield. It doesn't include price growth, which is a main driver of equity returns.
I showed you a calculation that included dividend growth, which parallels price growth. You just deleted it.
ThriftyPhD wrote:
Mon Jul 16, 2018 6:56 am
If you want to assume 5% nominal long term growth on US stocks, by all means go ahead. But with that level of pessimism,
Not pessimism. Realism. I showed you the math. I am hardly the first person even in this forum to point this out.

ThriftyPhD wrote:
Mon Jul 16, 2018 6:56 am
you may want to look to safer investment choices that offer a similar yield, or at least a much better risk adjusted yield.
I told you. There aren't any.
ThriftyPhD wrote:
Mon Jul 16, 2018 6:56 am
If you feel that demographics in the US mean little to no growth going forward, you may want to look into Ex-US funds.
Other developed countries have an an even slower population growth than the US. That just leaves emerging markets. They make up only 10% of the world market cap and they are a lot more risky. I do overweigh in EM, but they cannot be the core part of your portfolio unless you are into gambling.

KlangFool
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Re: Math help: 401k vs debt payoff formula

Post by KlangFool » Mon Jul 16, 2018 9:33 am

OP,

1) You could contribute to your 401K and put the money into the money market fund aka 0% return. But, save 35% tax.

2) Take a 401K loan and use the money to pay off the debt.

They are 2 separate independent decisions.

For example, you could do this.

<<A. Contribute $10,000 ($6500 after tax in the example 35% bracket) to your 401(k).
B. Take a $10,000 401(k) loan to pay your 6% debt.>>

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Last edited by KlangFool on Mon Jul 16, 2018 10:03 am, edited 1 time in total.

Dottie57
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Re: Math help: 401k vs debt payoff formula

Post by Dottie57 » Mon Jul 16, 2018 10:00 am

Also, paying off debt vs contibuting tp 401k is not a binary situation. You can do 50/50 or 60/40 or some other ratio.

I would not concentrate on mortgage payment in lieu of 401k contributions. But would suggest really trying to pay more on student loans.

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ray.james
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Re: Math help: 401k vs debt payoff formula

Post by ray.james » Tue Jul 17, 2018 4:33 pm

Thank you all for the responses. Based on the math from grabiner, jimb_fromATL ,danielC I was able to understand calculate the return correctly. I also do realize a stock return cannot be used for equivalent yield measure but one might do so in their own personal circumstances like debt payoff finishes soon due to very high income/loss of 401k space.
When in doubt, http://www.bogleheads.org/forum/viewtopic.php?f=1&t=79939

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