 The investment amount is deductible in the contribution year,
 Returns grow taxdeferred usually until retirement, and
 Withdrawals are fully taxable at ordinary income tax rates.
 First, when the tax rate in the contribution year equals the tax rate in the withdrawal year, the aftertax value of funds in qualified retirement accounts grows effectively taxexempt. The $250 tax savings grows to $500, which pays the tax liability on the $2,000 withdrawal. From Table 1, it is clear that, when the tax rate in the contribution year equals the tax rate in the withdrawal year, the initial tax savings will always grow to pay the full tax liability. Thus the aftertax value of funds in qualified retirement accounts effectively grows taxexempt.
 Second, when calculating the couples asset allocation, the $2,000 in Rays 401(k) should be considered equivalent to the $1,500 in Jessicas Roth IRA, since they both finance $1,500 of spending. Because goods and services are purchased with aftertax funds, their asset allocation should, in my way of looking at things, be based on aftertax funds [and Ill address this issue in more detail in the next section]. The traditional approach, in contrast, views $1 of pretax funds in a 401(k) as equivalent to $1 of aftertax funds in a Roth IRA or taxable account.
 Third, you can convert pretax funds in qualified retirement accounts to aftertax funds by multiplying the pretax funds by the value (1 tax rate), where the tax rate is the expected tax rate during retirement, in decimal form. The $2,000 in Rays 401(k) is worth $1,500 [$2,000(1 0.25)] after taxes, assuming a 25% tax rate during retirement. The aftertax approach to calculating asset allocation says that Rays account is worth $1,500 after taxes, the same as Jessicas.
 The first choice should be the 401(k) with matching contribution. If the company provides a 100% matching contribution then the beginning balance and ending aftertax balance are twice as large as the corresponding balances for the 401(k) without the match. Even if the company match is only 50%, the ending wealth per original aftertax dollar of contribution is larger from this 401(k) than from the Roth IRA. If you are in this situation, as long as you will be around long enough to retain the companys matching contribution, you should contribute enough to get the match.
 The next choices depend upon the relationship between the tax rate in the contribution year and the tax rate in the withdrawal year. If the withdrawalyear tax rate is less than the contributionyear tax rate, then the 401(k) without matching contribution or similar retirement plan should be preferred to an equal aftertax contribution to the Roth IRA. For example, in Table 2 the $1,000 contribution to the 401(k) is better than the $750 contribution to the Roth IRA.
 If the withdrawal tax rate is greater than or equal to the contribution tax rate then the Roth IRA should be the second choice. When the two tax rates are equal, as in Table 1, the ending aftertax wealth values are equal, but the Roth gets the advantage since it has no minimum withdrawal requirements. However, if the expected tax rate during retirement exceeds the tax rate before retirement, then the Roth IRA should be preferred to the qualified retirement account.
 It may seem that someone who expects to be in a higher tax bracket during retirement should save in a taxable account rather than a qualified retirement account. But this is not usually the case. Suppose Joe is in a 25% tax bracket before retirement but expects to be in a 30% bracket during retirement. Assume the funds will earn 8% per year before being withdrawn in nine years, so the investment would double if it grows taxfree. A $1,000 contribution to a 401(k) represents a $750 aftertax investment. At withdrawal, it represents $2,000 of pretax funds or $1,400 after taxes. This represents a 7.18% aftertax return. This investor receives about 90% of the pretax return, [7.18% ÷ 8%], for an effective tax rate of about 10%. In contrast, the taxable investor pays taxes at 25% on interest income and shortterm capital gains and 15% on dividends and longterm capital gains. As this example shows, Joe should save in the qualified retirement account instead of the taxable account even though he will be in a higher tax bracket during retirement.
TaxEfficient Investing and What It Means to Your Portfolio
by William Reichenstein
Is it possible to be a taxefficient investor in an everchanging tax environment?
Provisions of the current tax code are scheduled to sunset each year for the remainder of this decade, and new tax legislation is passed every few years. In this state of flux it may seem like a waste of time to focus on taxefficiency.
However, the keys to taxefficient investing are provided in a relatively small number of tax provisions, and it is unlikely that these will be eliminated in the near future.
This article is the first of a twopart series that will focus on taxefficient investing and the role it plays in the asset allocation decision.
The first article examines the tax benefits of qualified retirement plans such as 401(k)s, and why individuals should continue to use these accounts as much as possible. In addition, I will present a new way of thinking about your asset allocation that considers the aftertax values when determining your mix. Be forewarned—this is not the traditional approach to calculating asset allocation, and it is also more cumbersome. However, I believe it is a useful alternative.
The second article, which will be published in the July 2005 AAII Journal, builds on the first, and will focus on taxefficient stock management (harvesting capital losses) and the assetlocation decision (which of your assets should be placed in taxable accounts and which should be placed in retirement accounts).
Tax Implications of Retirement Accounts
Most people understand that qualified retirement accounts provide good tax benefits. Qualified retirement accounts include any retirement account where:
Table 1 compares the Roth IRA and qualified accounts for a married couple, Jessica and Ray. They are in the 25% ordinary income tax bracket before retirement, and expect to remain in this bracket during retirement. Jessica invests $750 in a Roth IRA, while Ray invests $1,000 in a 401(k). Contributions to a Roth IRA are not deductible in the contribution year. So, Jessicas $750 contribution reduces that years spending by $750. Rays $1,000 contribution to the 401(k) also reduces that years spending by $750; the contribution reduces taxable income by $1,000, which reduces taxes by $250. So, we can think of this $1,000 pretax contribution as consisting of $250 of tax savings plus $750 of Rays aftertax funds. Both Jessicas $750 contribution to the Roth IRA and Rays $1,000 contribution to the 401(k) are essentially the same, since they both represent contributions of $750 after taxes and they both reduce contributionyear spending by $750.
TABLE 1. Roth IRA vs. Qualified Retirement Plan Tax Benefits: Tax Rates Same Before and After Retirement  
Savings Vehicle  Original Investment  Ending Wealth  
Jessica:  
Roth IRA  $750 aftertax contribution  $1,500 (no tax due)  
Ray:  
401(k) 



Assumptions: Both investments grow at exactly the same rate and double through time; income tax rate in both contribution year and retirement year is 25%. 
Both Jessica and Ray invest in the same mutual fund for the same length of time. For simplicity, the table assumes the funds are withdrawn during retirement after the account values have doubled. Jessicas Roth IRA is worth $1,500; since it is a Roth IRA, this is an aftertax value—there are no taxes due upon withdrawal. Ray withdraws $2,000 of funds from his 401(k), but he must pay taxes on the withdrawal—at a 25% tax rate, this translates to $1,500 after taxes [$2,000 ($2,000 × 25%)]. In short, both Ray and Jessica invested $750 of aftertax funds and both accounts were worth $1,500 after taxes at withdrawal.
This example illustrates three points:
TABLE 2. Roth IRA and Qualified Retirement Plan Tax Benefits: Tax Rates Lower After Retirement 

Savings Vehicle  Original Investment  Ending Wealth  
Jessica:  
Roth IRA  $750 aftertax contribution  $1,500 (no tax due)  
Ray:  
401(k) 



Assumptions: Both investments grow at exactly the same rate and double through time; income tax rate in contribution year is 25% and in withdrawal year it is 15%. 
This example illustrates two points.
First, when the tax rate in retirement is below the tax rate in the contribution year, the effective tax rate on a qualified account is negative. Rays $1,000 contribution of pretax funds to the 401(k) reduced that years spending by $750. However, after adjusting for the 15% expected tax rate, Rays pretax contribution is worth $1,700 after taxes in retirement. Its aftertax value more than doubled, meaning its effective tax rate is negative. The $250 of tax savings in the contribution year grew to $500 at withdrawal. Since taxes at withdrawal were only $300, Ray retained the other $200, which explains why his aftertax ending wealth is $200 higher than Jessicas ending wealth.
Second, as before, you should convert pretax funds in qualified retirement accounts to aftertax funds by multiplying the pretax value by (1 retirement tax rate). In Table 2, Rays $1,000 contribution only reduces that years spending by $750, but for asset allocation purposes, after the contribution he should view its aftertax value as $850 [$1,000(1 0.15)]. The aftertax value grows from $850 today to $1,700 at withdrawal; that is, the aftertax value of qualified retirement accounts grows effectively taxexempt. We will return to this point in the second article in this series.
Calculating the Aftertax Asset Allocation
I am suggesting here that individuals may want to consider using an aftertax approach to calculating their asset allocation. This approach is not (yet) part of standard financial planning—I present it here because I think it is right, and I want you to see some of its implications. Perhaps as important, to properly address taxefficiency and assetlocation issues examined in the second article in this series, it is necessary to demonstrate that the aftertax value of funds in qualified retirement accounts grows effectively taxexempt. In a nutshell, the traditional approach to calculating asset allocation compares apples to oranges—that is, it compares pretax funds in qualified accounts to aftertax funds. I advocate calculating the asset allocation using an aftertax approach because it compares oranges to oranges, that is, aftertax values to aftertax values.
The Calculation
The first step when calculating an aftertax asset allocation is to convert all account values to aftertax values; you then calculate the asset allocation in the usual manner. Table 3 presents a simple example that calculates someones aftertax asset allocation.
TABLE 3. Calculating the Aftertax Asset Allocation: Example 1  
Savings Vehicle  Market Value  Aftertax Value  Asset Class 
401(k)  $1,333  $1,000  Stocks 
Taxable Account  $1,000  $1,000  Bonds 
Total  $2,333  $2,000  
Assumes expected tax bracket in retirement of 25%. Cost basis equals market value for asset in taxable account. 

Traditional allocation:
57% stocks and 43% bonds [$1,333 ÷ $2333 in stocks and $1,000 ÷ $2,333 in bonds]
Aftertax Value Allocation:

This individual has $1,333 market value in a 401(k) or other qualified account, and $1,000 in a taxable account. The cost basis and market value of the bonds held in the taxable account are $1,000. The first step is to convert market values to aftertax values. The $1,333 in the 401(k) converts to $1,000 if the expected tax rate during retirement is 25%. The aftertax asset allocation is 50% stocks and 50% bonds. The conventional approach to calculating the asset allocation says it is 57% stocks, [$1,333 ÷ $2,300], and 43% bonds. The traditional approach tends to exaggerate the individuals exposure to the dominant asset held in the qualified retirement account. In this example, that means that the individual in reality has less allocated to stocks than he thinks he has.
Problems With the Approach
One concern with the aftertax asset allocation is that it requires an estimate of the expected tax rate during retirement, and some people may say they have no idea what that tax rate will be.
However, from Table 3, it is clear that, since the traditional approach treats $1 of pretax funds in a qualified account as worth as much as $1 of aftertax funds, it implicitly assumes a 0% tax rate during retirement. So even though the tax rate during retirement is uncertain, it is easy to improve upon the traditional approachs implicit assumption of 0%.
Table 4 presents a more typical portfolio. Janice has stocks and bonds in both the 401(k) and taxable accounts. Also, she has unrealized gains in taxable accounts. [To calculate her aftertax asset allocation, we must first convert market values to aftertax value for assets held in taxable accounts. The box at the end of this article discusses this issue.]
TABLE 4. Calculating the Aftertax Asset Allocation: Example 2  
Savings Vehicle  Market Value  Aftertax Value  Asset Class 
401(k) Plan  $1,000 333 
$750 250 
Stocks Bonds 
Total  $1,333  $1,000  
Taxable Account  $300 700 
$285 700 
Stocks Bonds 
Total  $1,000  $985  
Total Portfolio  $2,333  $1,985  
Assumes expected tax bracket in retirement of 25% and capital gains tax rate of 15%. Cost bases are $200 for stocks and $700 for bonds held in taxable account.  
Traditional allocation:
56% stocks and 44% bonds [$1,300 ÷ $2,333 in stocks and $1,033 ÷ $2,333 in bonds]
Aftertax Value Allocation:

If she is like most investors and will realize capital gains within a few years, then she can approximate an appreciated assets market value by assuming that she sells it today and pays taxes at capital gains preferential tax rates. From Table 4, the stock with a market value of $300, cost basis of $200, and $100 of unrealized capital gains has an aftertax value of about $285, [$300 less taxes on the $100 gain at 15%]. The $1,000 in stocks and $333 in bonds in the 401(k) convert to $750 and $250 after taxes.
Her aftertax asset allocation is 52% stocks and 48% bonds. The conventional approach says she has 56% stocks and 44% bonds. Remember, the traditional approach tends to overweight the individuals exposure to the dominant asset held in the qualified retirement account—in other words, you have less invested in that dominate asset than is indicated by the traditional allocation approach. You can see that the exaggeration is not necessarily a large amount, but enough (over 5%) that investors may want to take this into consideration in their allocations.
When converting market values to aftertax values, the most important adjustment is usually the conversion of pretax funds in qualified retirement accounts to aftertax funds. If you are like Janice and primarily have stocks in qualified accounts, the traditional approach to calculating an asset allocation tends to overestimate your stock exposure when measured using an aftertax approach.
Portfolio Implications
There are a number of lessons you can draw from these examples. First, when saving for retirement, you should save all you are allowed to save or all you can afford to save in Roth IRA and qualified retirement accounts. Since tax rates in retirement are generally expected to be less than or at least equal to tax rates before retirement, contributions to these accounts usually grow taxexempt or better. Investments in these most taxfavored savings vehicles are the ultimate in tax efficiency.
Second, qualified retirement accounts contain pretax funds, while taxable accounts usually contain aftertax funds. The traditional approach to calculating someones asset allocation treats $1 of pretax funds in a qualified retirement account as equivalent to $1 of aftertax funds in a taxable account. In reality, $1 of pretax funds in a qualified account is worth less than $1 of aftertax funds in a taxable account. Thus, the traditional approach to calculating the asset allocation tends to exaggerate the allocation to the dominant asset held in qualified retirement accounts.
Third, an individuals asset allocation should be based on aftertax dollars because goods and services are purchased with aftertax dollars. The first step in calculating an aftertax asset allocation is to convert each assets market value to aftertax value. To convert funds in qualified retirement accounts to aftertax funds, you should multiply the pretax value by (1 tax rate), where the tax rate is your expected tax rate on ordinary income during retirement in decimal form. The appropriate treatment of unrealized capital gains in taxable accounts depends upon when the individual expects to realize the gains. For investors who expect to realize gains within a few years, the assets aftertax value can be estimated by assuming that the gain or loss is realized today.
Fourth, the framework presented here can help someone determine a preference order for saving in a Roth IRA, a 401(k) or any other qualified retirement account without a matching contribution, and a 401(k) or similar retirement account with matching contributions:
Determining the Aftertax Value for Assets in Taxable Accounts 
If you adopt my approach of determining your asset allocation based on aftertax values, how do you determine the aftertax market values for assets held in taxable accounts?
Unfortunately, there is not one method that is always right.
Consider a capital asset with a market value of $1,000, but a cost basis of $600. If the asset will be sold today and the holding period is one year or less, then the gain will be short term and taxed at ordinary income tax rates. If we assume a 25% ordinary income tax rate then the aftertax value would be $900 [$1,000 0.25 ($1,000 $600)]. If the asset will be sold today and the holding period exceeds one year, then the gain will be long term and taxed at the preferential capital gains tax rate. If we assume a 15% capital gains tax rate, then the aftertax value is $940. If the gain will be realized years later (when the preferential tax rate is still 15%) then the effective tax rate will be less than 15%. However, the effective tax rate would be only slightly lower than 15% if the gains will be realized in five years. Thus, for investors who will realize the gain within a few years—and this probably includes most investors—the assets aftertax value is approximately $940. In two situations, the unrealized gain would be taxfree: First, if the appreciated asset is given to charity then the individual can deduct the $1,000 market value. The charity would sell the asset, but it would not owe capital gains taxes because of its taxexempt status. Second, the capital gain would be taxexempt if the asset is held until after death. For example, suppose a husband dies when the asset has a book value of $600 and a market value of $2,000. In a community property state, the surviving wifes basis is steppedup to $2,000, so she could sell it after his death for $2,000 and owe no capital gains taxes. In a common law state, the basis would be steppedup to $1,300 or by half the unrealized gain. Sometimes capital assets have unrealized capital losses. These losses have value in that they can be used to offset gains or, if there are net losses up to $3,000 can be written off against taxable income. Assuming the loss is used to offset longterm gains, an asset with a cost basis of $600 and market value of $400 has an aftertax value of $430, [$400 + 0.15($600 $400)]. Again, the right way to treat unrealized gains depends upon each taxpayers circumstances. But knowing the tax implications of the available options should help individuals make informed decisions. 
William Reichenstein, CFA, holds the Pat and Thomas R. Powers Chair in Investment Management at Baylor University, Waco, Texas. He may be reached at Bill_Reichenstein@baylor.edu.