Whether you have student loans, practice loans or a mortgage, one of the most common questions asked is whether it makes sense to pay out your loans early.  Opinions always vary.  Some say you should repay your loans quickly.  Others say invest your money in stocks instead.  Does your loan interest rate matter when deciding whether to repay it quickly or not?  What rate of return do you need to get from your investment to justify investing vs. prepaying the loan?  Should the money be invested in the stock market or would a safer investment such as municipal bonds be more appropriate? In this article we’ll discuss the answers to the above questions and come up with general guidelines that can help you develop the best strategy for loan repayment.

Investing vs. prepaying: student loan

Prepaying a loan is a good idea because you end up saving a significant amount of money on interest payments. What is your actual return on loan prepayment? Can investing instead of prepaying be a better idea?

Let’s consider the following question:  assuming the interest is X%, if we could contribute $Y towards our loan vs. investing $Y into a particular investment with a return of Z%, what should Z be to make us decide to invest vs. prepay the loan? Conventional wisdom says that the return on investment has to be higher than the loan interest to make investing worthwhile (Z > X).  To see if this is true, let’s take a 25-year $500k student loan with 6.8% interest and a monthly payment of $3,470 ($41,640 per year), and let’s consider three prepayment scenarios.

Regular Payments Prepayment Scenario #1 Prepayment Scenario #2 Prepayment Scenario #3
Principal $500,000 $500,000 $500,000 $500,000
Interest 6.8% 6.8% 6.8% 6.8%
Monthly payment $3,470 $3,470 $3,470 $3,470
Extra monthly payment $0 $1,000 $3,000 $6,000
Repayment period (years) 25.00 14.82 8.50 5.24
Total interest payment $541,108 $294,749 $159,626 $95,812
Total payment $1,041,108 $794,749 $659,626 $595,812
Interest Savings $0 $246,359 $381,479 $445,296

Table 1. Interest rate savings for prepaying the loan.  It is assumed that interest tax deduction does not apply.

Let’s now consider what happens if instead of prepaying the loan, we’ll invest the money instead.  For each prepayment scenario we’ll compare the remaining principal under the regular payments and the compounded extra payments at the end of the repayment period for each scenario. The compounded monthly extra payments have to be larger than the remaining principal to justify investing vs. prepaying.  The following table shows what happens when extra payments are invested over the repayment period at different rates of return:

Prepayment Scenario #1 Prepayment Scenario #2 Prepayment Scenario #3
Repayment Period:  14.82 Year Repayment Period:  8.50 Years Repayment Period: 5.24 Years
Rate of return Remaining Principal Compounded Payments Remaining Principal Compounded Payments Remaining Principal Compounded Payments
5% $305,432 $262,632 $412,425 $380,088 $452,010 $430,559
6.8% $305,432 $305,432 $412,425 $412,425 $452,010 $452,010
8% $305,432 $338,781 $412,425 $435,927 $452,010 $467,070

Table 2. Extra monthly payment invested at different rates of return over the repayment period of each loan.  No inflation assumed.

Inflation will affect both the investment and prepayment returns equally, so in this analysis inflation is ignored.  Thus, when the rate of return on our investment exceeds the loan interest rate, it makes more sense to invest rather than prepay. If the investment is in an after-tax account, however, we also have to worry about taxes, so even if we only consider the long term capital gains tax, the actual tax rate can be anywhere from 15%-33% of the final amount (depending on which state you live in and your marginal tax bracket).  There are other taxes to worry about, including interest/dividend tax (which can also range from 15%-33% for qualified dividends up to your highest state plus federal bracket for non-qualified dividends such as dividends from REITs and certain foreign stocks and bond interest which is taxed as income), to the 3.8% net investment income tax which applies if your modified AGI is above $250k (if married filing jointly).

Proposition. With all taxes included, the yield (return) on investment has to be higher than the loan interest rate to justify investment vs. prepayment.

Can Stock Market deliver?

Why not just invest in the stock market instead of prepaying a 6.8% student loan – after all, historical return on the S&P500 was 10% over the past 100 years?

Can we expect to get a 10% return if we invest in the stock market? From 2000 to 2010, S&P500 10-year return was 0.4%, and from 2003-2013, the 10-year returns on the S&P500 is 9%.  However, from 2000 to 2013 the return was only 3.5%. Conservative balanced/diversified index portfolios may have gotten around 6.5% return over that time, yet a portfolio with 50% in stocks and 50% in bonds still fell 25% in 2008, and nobody knew how long it would stay there.  In 2010 when the S&P return was 0.4% annualized over 10 years, a CD or money market seemed like a great investment choice.  Much of the stock market returns (both positive and negative) happen in short periods of time, and one or two good years can easily skew the annualized return numbers.  A decade of bad returns can be transformed by a quick rally, or a decade of good returns can be destroyed by an even quicker crash.

Extrapolating historical return into the future can create a false sense of security and may lead us to make a future prediction that all we have to do is wait long enough to get 10% returns from the market. Market statistics (and research) does not support the hypothesis that past average returns can be extended into the future.  This is consistent with the fact that the markets are governed by power laws, not by Normal distribution, so it can be shown that future returns can be anything at all without any regard to past history.  There may be scenarios under which a portfolio can get a return higher than 10%, but it can also experience negative returns and long periods of drawdowns, so it is not advisable to use stock market as a primary investment vehicle to outperform your loan.  The average return might come out to be much lower than 6.8%, so it is always advisable to pay down your high interest loans rather than invest.  Because loan repayment provides a guaranteed return, we may consider loan repayment to be a part of the fixed income portfolio allocation.

Investing vs. prepaying: mortgage

What about repaying a mortgage?  Does it make sense to prepay or invest?  Mortgage interest can be tax deductible, yet for those with high incomes the deduction is gradually phased out.  What are some rules of thumb to determine whether you want to prepay your mortgage or invest?

Here are two scenarios to consider:

1) Full mortgage interest deduction.  In this case, a portion of your mortgage payments is subsidized by the government.  Suppose you are in the 33% federal tax bracket and your mortgage interest rate is 4.5%.  In this case, your actual effective interest rate would be 4.5% x (1 – 0.33) or 3%.  Should you prepay this mortgage or invest?  If you can get an investment that can produce an after-tax yield in excess of 3%, you just might consider investing instead, especially if you have a readily available pool of cash.

2) Standard itemized deduction (effectively phasing out your mortgage interest deduction).  Assuming that you might have $30k in itemized deductions, the phase-out starts affecting you when your AGI is around $1M or so.  As a result, your itemized deductions are decreased by as much as $20k, which essentially makes the standard deduction ($12,400 for 2014) the default choice.  In this case, prepaying the 4.5% mortgage provides a return of 4.5%, so it would make sense to repay it quicker, since there are currently no fixed income investments that can provide a safe 4.5% return.  An alternative is to refinance a 30-year mortgage into a 15-year one – this can be considered to be a form of prepayment.

Investing your prepayment

To make sure that our repayment plan succeeds we need to use an investment that has a fixed rate of return and is relatively safe.  What would be an ideal investment we can use? Of all the choices available right now, municipal bonds will work best.  The return is relatively high and tax advantages are obvious – a 4% tax-free return is equivalent to a 6.7% return from a taxable bond (or other investments taxed as income) if your effective tax rate is 40%.  Another important reason for using municipal bonds is because they beat inflation consistently and comfortably in the past, and even though that’s no guarantee that this will happen in the future, the chances are high that it will, especially if a bond portfolio is designed and managed properly.  As of 2014, the yield on 15-year high quality municipal bonds ranges from 3% to 3.5%, and given the real risk of rising interest rates it is not recommended to invest in long maturity bonds, so any loans with interest higher than 3.5% should be prepaid.  Note that individual bonds will have to be held to maturity, otherwise principal can be lost.

Summary

For any type of loan, your ROI for investing (adjusted for taxes and deductions) vs. prepaying your loan has to be greater than the rate on your loan, so for high interest loans you might want to prepay your loan as quickly as possible.   If you are getting the full mortgage interest deduction, chances are you might consider investing your money instead.  If your AGI is too high and your itemized deductions are phased out, you might want to consider refinancing into a 15-year mortgage.