Financial advisors are asked to assist their clients in

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Financial advisors are asked to assist their clients in achieving personal financial goals involving a variety of areas such as investment, insurance, retirement, and debt planning. Two of the most important steps in achieving financial independence involve funding a 401(k) or other retirement plan and repaying consumer debt. (Individuals typically pursue these goals after they establish an adequate emergency fund.)

Ideally, an individual would eliminate his or her outstanding consumer debt immediately while simultaneously contributing the maximum allowed amount into a retirement account. But what happens when people must choose between one of these two objectives because of budgetary constraints?

After all, it is not atypical to have insufficient funds to pay off consumer debt and maximize retirement contributions at the same time. Should one goal be pursued to the exclusion of another, or should both be partially pursued to the extent allowed by available resources and contractual constraints?

An article in the April 2006 issue of Money magazine ad- dressed this question.¹While it provided good advice, it did not attempt to create a general methodology to identify optimal courses of action given a particular individual’s situation.

It did, however, cause us to come up with our own method.

In this article we attempt to provide specific guidance to financial planners and their clients that will help them optimize

Which Would You Choose:

Funding Retirement or

Paying Off Consumer Debt?

EXECUTIVE SUMMARY

Paying off consumer debt and funding a retirement plan are high-priority goals, but individuals with binding budgetary constraints are unable to do both simultaneously. The preferred strategy—to either focus on paying off the consumer debt or on funding retirement—varies according to interest rates, assumed investment returns, and employer matching rules.

By James M. Grayson, Ph.D.; Peter M. Basciano, Ph.D.; and Christopher L. Cain, J.D., Ph.D., CFA

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the allocation of limited financial resources between retirement savings and consumer debt repayment.

Methodology

At its core, the decision rule governing the allocation of an individual’s funds between these objectives is relatively simple. To identify the optimal course of action, we make a basic assumption concerning individual behavior: We assume that consumers are motivated to pay off their existing debt and that they will not incur any additional debt during the planning period. This assumption allows the identification of an optimal solution without complicating the analysis by requiring additional constraints. Obviously, deviations from this behavioral assumption, which is not atypical, will lead to suboptimal results. Nonetheless, there is still value in identifying the optimal solution, even with the tenuous assumption of rational human behavior, in order to make fully informed decisions and to identify the cost associated with less-than-optimal courses of action and human behaviors.

Given the specified behavioral assumption, the optimal decision rule reduces to a net present value (NPV) or terminal wealth analysis. Under these decision crite- ria, an individual should choose the alternative resulting in the highest NPV or terminal wealth. The NPV and terminal wealth analysis methodologies will result in the same decision—as long as the discount rate used is held constant across the various alternatives under consideration. Utilizing a terminal wealth methodology, however, simplifies the analysis by avoiding the need to determine the appropriate discount rate to use in identifying the present value of the relevant cash flows over the relevant time horizon. Given this consideration, the simpler criterion of maximizing terminal wealth over the planning period is utilized to identify the optimal strategy.

There are four possible allocation strategies:

1. Individuals can use all of their available funds to repay their debt.

2. They can use all of their available funds in excess of their required minimum payments on their debt to accumulate retirement savings.

3. They can split their available funds to simultaneously pay more than the required minimum pay-

ment on their outstanding debt and accumulate retirement savings.

4. They can switch between the three strategies over the planning period.

The terminal wealth analysis takes the form of an optimization problem in which our decision variables are the amount to allocate each month to repay credit card debt and/or invest for retirement. Although the analysis focuses specifically on credit card debt, the methodology is applicable for consumer debt in general.

The objective is to maximize ending wealth, specified as:

EW = RB – CC

Where:

EW = Ending wealth

RB = The terminal balance in the retirement account at the end of the period

CC = The credit card balance remaining at the end of the period

As with most optimization problems, the decision variables are subject to constraints, which include:

1. An individual is required to make a contractually specified minimum payment on his or her credit card. While this can vary from card to card, a re- cent survey by CreditCard.com says most compa- nies require a minimum payment of 1% of the full balance plus any interest accrued in the billing cy- cle, plus any fees incurred.²But many card issuers impose a more stringent requirement that the minimum payment be at least 3%-4% of the outstanding balance.³Consequently, we impose the most financially conservative constraint—requiring that the individual must always make a minimum payment of 4% of the outstanding credit card balance per month.

2. At any point in time, an individual faces a budgetary constraint limiting the amount of funds available to meet the minimum required payment and the amount of additional funds available to either accelerate the repayment of debt or fund retirement. A monthly budgetary constraint of $500

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is assumed. (This assumption was made for consis- tency with the earlier referenced article appearing in Money.)

We assume an initial outstanding balance on credit card debt of $7,800. This amount corresponds to the ap- proximate average balance for individuals who normally carry credit card balances between billing cycles. Other starting debt balances or monthly budgetary constraints do not change the results qualitatively.

We also analyze a five-year time period on a monthly basis. The monthly time intervals correspond to typical credit card payment terms. Five years represents a rea- sonable length of time for consumers to pursue the goal of eliminating their credit card debt. It also provides sufficient time to evaluate the relative effectiveness of the four allocation strategies.⁴

A complicating factor concerns the tax consequences associated with each alternative. Most retirement plans allow for the contribution of pre-tax earnings and the deferred taxation of plan earnings. The credit card is paid with after-tax earnings. Additionally, workplace retirement plans often involve matching pre-tax contributions by the employer that also grow on a tax-deferred basis. To incorporate the differential tax treatments into this analysis, we convert the retirement plan contributions to equivalent after-tax dollars by utilizing this formula:

TAC = C ^✕(1 + M) (1 – t) Where:

TAC = Tax-Adjusted Contribution C = Employee Contribution M = Employer Match Rate t = Applicable Marginal Tax Rate

Although the matching provisions take various forms in practice, they operate the same way. For example, if an employer offers a 100% match, for every dollar the employee contributes to the retirement account the employer will match the contribution with an additional dollar. Consequently, every $1 the employee contributes would result in a $2 increase in the balance of the retirement account. Obviously, the existence and

specific terms of any matching provisions are important factors to consider when deciding whether to invest in retirement accounts or, alternatively, to accelerate the repayment of credit card debt. (See Table 1.)

Preferred Strategy

A review of the results reveals that there is an optimal strategy.⁵Depending on a particular set of factors, the best strategy is either to invest in the retirement plan while making the required minimum payment on the credit card debt or to eliminate the credit card debt before contributing to the retirement account. In no case is it optimal to simultaneously contribute to the retirement account and pay in excess of the minimum required payment on the credit card debt.

Yet sometimes it is optimal to begin sending money in excess of the required minimum payment to the credit card company and then to later switch strategies and begin contributing to the retirement plan at a particular point. For this reason, the results initially are reported using a switching regime. The default strategy is to use all available cash to repay the credit card. If this strategy is not optimal, the individual “switches” to use all of the available funds in excess of the minimum payment on the credit card to fund retirement savings. The numbers reported are the months in which switching from making exclusive payments on the credit card to begin making contributions to the retirement account becomes optimal. For instance, if a switch occurs in the first month, the best strategy is to start out investing as much as possible in retirement savings instead of accel- erating the repayment of credit card debt.

We now examine the results associated with a variety of different credit card rates, assumed investment returns, and employer match rates given the assumed initial $7,800 credit card balance and $500 monthly cash flow constraint. The results are calculated assuming a marginal tax rate of 25%.⁶(See Table 2.)

Not surprisingly, the relative rates of return play a large role in determining the dominant strategy. In the cases of high credit card rates and low investment rates of return, it is better to pay off the credit card first.

Alternatively, for scenarios involving low credit card rates and high investment rates of return, it is better to invest in retirement accounts. Under the established

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parameters, the credit card debt is paid off after the 17th or 18th month if all of the free cash flow is chan- neled to paying off the credit card. Consequently, there is always a crossover in the 17th or 18th month, even for the highest interest rates.

The results indicate that the employer match is also important for determining the optimal strategy. As the

employer match increases from 20% to 100%, contributing to the retirement plan becomes relatively more at- tractive. Scenarios involving switching as an optimal strategy begin to appear at a 20% match. In scenarios involving switching, paying off the credit card debt is the most beneficial strategy initially, but at some subse- quent point it becomes advantageous to switch strate-

Table 1: Explanation of Spreadsheet Model

Period Cell Explanation Period Cell Explanation

1 C9 Credit card beginning 2 C10 Credit card beginning balance for

balance for period period 2

= Prior Period Ending Balance

D9 Required Minimum Payment I10 Beginning Period Balance for

= Minimum Payment Percent ^✕ Investment

Beginning Balance for Period = Prior Period Ending Balance

E9 Payment M10 Return for Current Period

Optimized Payment Amount = Beginning Balance ^✕Investment

Return Percent / 12 F9 Interest Charged

= Beginning Balance ^✕Credit Card Annual Interest Rate / 12

G9 Ending Balance for Credit Card Terminal Wealth K72 Ending Wealth

= Beginning Balance – Payment = Investment Ending Balance

+ Interest Charged (period 60) ^✕(1 – Tax Rate) – Credit

Card Ending Balance (period 60) I9 Beginning Balance for Investment

J9 Investment Amount

= Available Cash – Credit Card Payment

K9 Match Amount

= Match Percent ^✕Investment Amount L9 Tax Adjustment

= (Investment Amount + Match Amount) / (1 – Tax Rate)

M9 Return

N9 Ending Investment Balance

= Beginning Balance + Tax Adjustment + Return

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Table 2: Optimal Month to Begin Sending Available Free Cash Flow to Retirement Fund, Given Various Levels of Employer Matching,

Credit Card Rates, and Investment Rates of Return

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gies and use the available funds in excess of the minimum required payment. Switching occurs before the balance is fully repaid and at a time corresponding to the crossover point between incremental accrued interest on the credit card and the incremental earnings associated with the retirement plan. Although the employer match is important, it is a relatively less important consideration than the relationship between rates of return and interest rates.

Initially it appears that if the interest rate on the credit card is equal to or greater than the expected rate of return on the retirement plan, the investor should dedicate all of his or her free cash flow to the debt payment. Yet this simple strategy fails to take the employer match into account. The results indicate that it may lead to suboptimal allocations to the credit card or retirement plan. For example, with a 100% employer match, a 10% investment return, and a 12% credit card rate, the individual actually should use all available funds in excess of the required minimum payment to fund retirement savings, which is contrary to the simple interest rate differential rule.

An alternate decision strategy is the Match-Based Allocation Rule (MBAR) shown in Table 3. The MBAR is based on the Minimum Rate Spread (MRS), which is the amount by which the credit card rate must exceed the assumed investment return, taking into account the employer match percentage, in order to justify using all of the excess funds to accelerate the repayment of the

debt. The results indicate that the required rate spread varies directly with the amount of the employer match.

For example, at a 0% employer match, a 0.5% difference would justify using all excess money to repay the credit card. Alternatively, when the employer offers a 100% match, the credit card rate should exceed the assumed investment rate of return by 4% before the ac- celeration of credit card repayment is pursued. In summary, any free cash flow in excess of the required minimum payment on the credit card should be in- vested in retirement savings as long as the rate spread is less than the indicated MRS.

The MBAR would identify the optimal strategy in a vast majority of the scenarios. For example, given a match of 100%, an investment rate of return of 12%, and a credit card rate of 10%, the resultant MRS is -2%.

Given this MRS value, which is less than the 4% specified in Table 3, the MBAR recommends using all available free cash in excess of the required minimum payment on the credit card to fund retirement savings.

Alternatively, if the credit card rate is 18%, the resultant MRS is 6%. Given that this value exceeds the 4%

threshold, the MBAR recommends using all available free cash flow to repay the credit card. These results are consistent with the strategy specified previously.

Despite its advantages, the MBAR is not a perfect decision rule. We now examine the optimal strategy for a wide variety of credit card rates and assumed investment rates of return for scenarios involving a 100% employer

Table 3: Match-Based Allocation Rule (MBAR):

The Combined Minimum Rate Spreads and Various Company Match Percentages Needed to Send All Free Cash to Credit Card

Company Match Minimum Rate Spread

(Debt% – Return%)

0% 0.5%

10 1.0

20 1.5

30 2.0

40 2.5

50 2.5

100 4.0

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match. (See Table 4.) Comparing this more detailed analysis with the decisions reached by applying the specified MBAR in Table 3, it is apparent that the MBAR captures all of the situations in which it is ideal to begin using all available cash flow to fund retirement savings immediately. It also captures all of the situations where it is optimal to pay off the credit card debt before funding the retirement plan (represented by the value of 10 in Table 4). Yet the MBAR fails to recommend the ideal course of action when money should be applied to the credit card first and then switched to the retirement account (in months 4, 10, or 14, for example.)

Economic Significance

Although the results indicate that there is a preferred strategy for allocating excess cash, the economic significance is not readily apparent. For instance, if the preferred strategy is to use all excess cash flow beyond the required minimum payment on the credit card to fund retirement savings, but pursuing a suboptimal strategy results only in a minor reduction in terminal wealth, it may be argued that this is just an academic exercise. To investigate this possibility, we compare the results associated with the optimal outcome to the results associated with two popular decision rules and the MBAR.

A common recommendation suggests always paying

off your debt, regardless of any opportunity costs. This advice has the advantages of being simple and easy to apply in any situation and instilling in the individual the importance of controlling consumer debt and living within one’s budget. We compare this simple decision rule to the more detailed approach.

The calculations are based on the same parameters of a $7,800 credit card balance, a five-year planning horizon, and $500 monthly free cash flow. We also assume a 100% employer match. The base case is the terminal wealth at the end of 60 months when paying off the credit card before contributing to a retirement account.

Reported in the text and accompanying tables is the difference in terminal wealth at the end of 60 months of a particular alternative strategy minus the terminal wealth at the end of 60 months of the strategy of paying off the credit card first. We will call this difference the terminal wealth difference. (See Table 5.)

For the scenarios where the detailed analysis recommends paying off the credit card first, there obviously is no advantage over the simple strategy because the two recommendations are identical. In several other situations, however, the difference in terminal wealth exceeds $1,000, and in some scenarios the difference ap- proaches $2,000 or more. It is important to recognize that the credit card balance of $7,800 is at the outset,

Table 4: Optimal Month to Begin Sending Available Free Cash Flow to Retirement Fund, Given Various Levels of Employer Matching

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and the reported terminal wealth numbers are at the end of five years. Relative to the starting balance, however, the calculated terminal wealth differences are not

inconsequential. These results indicate that the analysis is more than an academic exercise.

It also is important to observe that several of the sce-

Table 5: Terminal Wealth Difference

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narios that result in large differences in the observed terminal wealth correspond to realistic scenarios. For example, someone who faces a 10% credit card rate, has a 100% employer match, and expects a market return of 11% may expect $1,442.61 in additional terminal wealth if he or she follows the recommendation associated with the more detailed analysis instead of merely paying off the debt first. Obviously, this is not universally applicable because it would correspond to an individual fortunate enough to have a 100% employer match, strong credit, and a risk tolerance consistent with an investment allocation resulting in an 11% return over the planning horizon.

A second common decision rule recommends paying off the credit card if the contracted interest rate is greater than the expected return on the retirement savings. Alternatively, if retirement savings are expected to yield a higher return, invest all of the free cash flow in excess of the minimum required payment in retirement savings. This rule is actually just an erroneous applica- tion of the NPV rule; it neglects to include the effects of an employer match in the decision process.

Unfortunately, this rule may still lead to suboptimal decisions when the employer match is factored into the equation. For example, when there is a 100% employer match, the credit card rate is 12%, and the investment return is assumed to be 11%, paying off the credit card

debt first will result in terminal wealth difference of

$930.30. Even if the assumed investment return is 10%, there is still terminal wealth difference of $623.32.

Recall that the indicated differences in terminal wealth relate to the initial balance of $7,800 and would be even larger given higher initial levels of debt.

The third decision rule, the MBAR, represents a slightly more sophisticated strategy, yet it is still easy to apply. To review, the MBAR indicates the required spread between the credit card rate and assumed rate of return on the retirement account for various levels of employer matching before an individual should make above-minimum debt payments. The use of the MBAR would result in an economically optimal decision in the majority of scenarios—including those reported previously where the other two decision rules failed. But the MBAR does not always choose the best solution when it is optimal to switch strategies.

Now we review the economic benefits of following the optimal strategy rather than funding retirement first. This is the reverse of the perspective to correspond to the MBAR default strategy of using the monthly free cash flow in excess of the minimum required credit card payment to fund retirement savings unless the difference in rates exceeds the indicated MRS. (See Table 6.)

Table 6: Terminal Wealth Difference Obtained by Utilizing Optimal Solution Instead of Funding Retirement First

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In summary, if the MBAR fails to recommend the optimal course of action, individuals will use their free cash flow to fund retirement savings instead of the optimal action of repaying their credit card.

We can see that the MBAR will fail to choose the optimal strategy only when there is a switch midway through the planning period (corresponding to a reported value of four, 10, 14, or 15 months). The worst occurs when investment returns are assumed to be 13%

and the credit card rate is 17%. This costs $210.03 in terminal wealth. Overall, these results indicate that in the scenarios where the MBAR results in a less-than- optimal decision, the economic impact is relatively small given the 60-month period of analysis.

Considering the economic benefits, the MBAR appears to offer practical advantages when compared to alternative decision rules. It also is significantly easier to employ than a full optimization and will result in an optimal economic decision in the vast majority of situations. Further, in the limited cases where the MBAR fails to identify the optimal decision, the economic consequences appear minimal. In general, the MBAR will lead to better decisions than the other “simple” allocation rules and yield recommendations consistent with a more complex optimization.

One Optimal Strategy

The question about whether to use free cash flow in excess of the required minimum credit card payments to fund retirement savings or to accelerate the repayment of credit card debt is a common one. Obviously, either course of action is better than the alternative of increasing consumption, but the alternatives are not of equal value to all individuals.

The economically optimal alternative for an individual is dependent on such factors as credit card rates, assumed investment returns, and employer matches, but there is only one optimal strategy for each combination of factors. To say that individuals are equally well off with either strategy would be incorrect. Furthermore, the optimal strategy may result in significant economic benefit as compared to the alternatives. The MBAR can help individuals identify their optimal strategy. ^■

James M. Grayson, Ph.D., is a professor at James M. Hull College of Business, Georgia Regents University, Augusta, Ga. He can be reached at jgrayson@gru.edu.

Peter M. Basciano, Ph.D., is a professor at James M. Hull College of Business, Georgia Regents University. You can contact him at pbasciano@gru.edu.

Christopher L. Cain, J.D., Ph.D., CFA, is a visiting assis- tant professor with the School of Business of the College of Charleston in Charleston, S.C. You can reach him at caincl@cofc.edu.

Endnotes

1 Ryan D’Agostino, “Which ‘Top Priority’ Is Really No. 1?”

Money, April 2006.

2 Karen Haywood Queen, “Survey: Minimum Card Payments Rising,” CreditCards.com, June 2014, www.creditcards.com/

credit-card-news/minimum- credit_card-payments-survey- 1276.php#minimum.

3 Bankrate: Credit Card Minimum Payments Rising, May 3, 2005, and July 21, 2007, www.bankrate.com.

4 We also investigated a 10-year time horizon. Although we did not provide them, the results and implications were consistent with the five-year time horizon reported in this article.

5 When we refer to “optimal,” we are indicating the solution obtained using Excel Solver to solve an optimization problem in which the objective function is the ending wealth, the decision variables are the amount to allocate to the credit card and the amount to allocate to the retirement fund, and the constraints are meeting minimum credit card payments and not exceeding the free cash flow amount.

6 A 25% marginal tax rate was assumed in this analysis, but the results are insensitive to the utilization of other marginal rates.

This result follows from the assumption that the tax rate re- mains constant from the point of credit card payments or retirement contributions, during the planning period, and at the point of the terminal wealth calculation. The model presented in Table 1 is easily adaptable to evaluate scenarios involving deviations from this assumption.