What Is the Altman Z-Score?

The Altman Z-score is the output of a credit-strength test that gauges a publicly traded manufacturing company’s likelihood of bankruptcy.

Understanding the Altman Z-Score

The Altman Z-score, a variation of the traditional z-score in statistics, is based on five financial ratios that can be calculated from data found on a company’s annual 10-K report. It uses profitability, leverage, liquidity, solvency, and activity to predict whether a company has a high probability of becoming insolvent.

NYU Stern Finance Professor Edward Altman developed the Altman Z-score formula in 1967, and it was published in 1968. Over the years, Altman has continued to reevaluate his Z-score. From 1969 until 1975, Altman looked at 86 companies in distress, then 110 from 1976 to 1995, and finally 120 from 1996 to 1999, finding that the Z-score had an accuracy of between 82% and 94%.

In 2012, he released an updated version called the Altman Z-score Plus that one can use to evaluate public and private companies, manufacturing and non-manufacturing companies, and U.S. and non-U.S. companies. One can use Altman Z-score Plus to evaluate corporate credit risk. The Altman Z-score has become a reliable measure of calculating credit risk.

How to Calculate the Altman Z-Score

One can calculate the Altman Z-score as follows:

Altman Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E

Where:

• A = working capital / total assets
• B = retained earnings / total assets
• C = earnings before interest and tax / total assets
• D = market value of equity / total liabilities
• E = sales / total assets

A score below 1.8 means it’s likely the company is headed for bankruptcy, while companies with scores above 3 are not likely to go bankrupt. Investors can use Altman Z-scores to determine whether they should buy or sell a stock if they’re concerned about the company’s underlying financial strength. Investors may consider purchasing a stock if its Altman Z-Score value is closer to 3 and selling or shorting a stock if the value is closer to 1.8.

In more recent years, however, a Z-Score closer to 0 indicates a company may be in financial trouble. In a lecture given in 2019 titled “50 Years of the Altman Score,” Professor Altman himself noted that recent data has shown that 0—not 1.8—is the figure at which investors should worry about a company’s financial strength. The two-hour lecture is available to view for free on YouTube.

2008 Financial Crisis

In 2007, the credit ratings of specific asset-related securities had been rated higher than they should have been. The Altman Z-score indicated that the companies’ risks were increasing significantly and may have been heading for bankruptcy.

Altman calculated that the median Altman Z-score of companies in 2007 was 1.81. These companies’ credit ratings were equivalent to a B. This indicated that 50% of the firms should have had lower ratings, were highly distressed and had a high probability of becoming bankrupt.

Altman’s calculations led him to believe a crisis would occur and there would be a meltdown in the credit market. He believed the crisis would stem from corporate defaults, but the meltdown, which brought about the 2008 financial crisis, began with mortgage-backed securities (MBS). However, corporations soon defaulted in 2009 at the second-highest rate in history.

What Is the Alternative Minimum Tax?

An alternative minimum tax (AMT) places a floor on the percentage of taxes that a filer must pay to the government, no matter how many deductions or credits the filer may claim.

The United States currently has an alternative minimum tax for taxpayers who earn above certain income thresholds.

The AMT recalculates income tax after adding certain tax preference items back into adjusted gross income. It uses a separate set of rules to calculate taxable income after allowed deductions. Preferential deductions are added back into the taxpayer’s income to calculate their alternative minimum taxable income (AMTI), and then the AMT exemption is subtracted to determine the final taxable figure.

How the Alternative Minimum Tax Works

The difference between a taxpayer’s alternative minimum taxable income and his AMT exemption is taxed using the relevant rate schedule. This yields the tentative minimum tax (TMT).

If the tentative minimum tax is higher than the taxpayer’s regular tax liability for the year, then they pay the regular tax and the amount by which the tentative minimum tax exceeds the regular tax. In other words, the taxpayer pays the full tentative minimum tax.

There are two alternative minimum tax rates, 26% and 28%. For 2022, the 28% rate applies to excess alternative minimum taxable income of $206,100 or more for all taxpayers ($103,050 for married couples filing separate returns). For 2023, the 28% rate applies to excess alternative minimum taxable income of $220,700 or more for all taxpayers ($110,350 for married couples filing separate returns). The 26% rate applies to incomes up to those levels.

A taxpayer who has a high income and uses large tax breaks may owe a smaller percentage under the standard rules. If so, the taxpayer is obliged to recalculate the taxes owed under the alternative minimum tax system, which eliminates some of those tax breaks.

The taxpayer will owe whichever amount is higher.

AMT Exemption Amounts

For tax year 2022, the AMT exemption for single filers is $75,900. For married joint filers, the figure is $118,100. For tax year 2023, the figures are $81,300 for single filers and $126,500 for married joint filers.

Taxpayers have to complete Form 6251 to see whether they might owe AMT. First, they subtract the exemption amount from their income. If their AMT is less than the exemption, they do not have to pay AMT.

It’s important to note, though, that taxpayers with AMTI over a certain threshold do not qualify for the AMT exemption. For tax year 2022, the phase-out begins at $539,900 for single filers and $1,079,800 for couples filing jointly. For tax year 2023, the phase-out begins at $578,150 for single filers and $1,156,300.

Purpose of AMT

AMT is designed to prevent taxpayers from escaping their fair share of tax liability through tax breaks. However, in the past, the structure was not indexed to inflation or tax cuts. This can cause bracket creep, a condition in which middle-income taxpayers could be subject to this tax instead of just the wealthy taxpayers for whom AMT was invented. In 2012, however, Congress passed a law indexing the AMT exemption amount to inflation.

Calculating AMT

To determine if they owe AMT, individuals can use tax software that automatically does the calculation, or they can fill out IRS Form 6251. This form takes medical expenses, home mortgage interest, and several other miscellaneous deductions into account to help tax filers determine if their deductions are beyond an overall limit set by the IRS.

The form also requests information on certain types of income such as tax refunds, investment interest, and interest from private activity bonds, as well as numbers corresponding with capital gains or losses related to the disposition of property.

The IRS has specific formulas in place to determine which portion of this income and deductions the tax filers need to note on Form 6251. It uses another set of formulas to determine how these numbers lead to AMTI.

The Bottom Line

The Alternative Minimum Tax is an additional or parallel tax system in the U.S. that is designed to ensure that high-income individuals pay their fair share of taxes. Prior to the AMT, certain taxpayers paid little in the way of taxes, due to preferential treatment of certain income and expenses, or tax breaks.

What Is Alpha?

Alpha (α) is a term used in investing to describe an investment strategy’s ability to beat the market, or its “edge.” Alpha is thus also often referred to as “excess return” or “abnormal rate of return,” which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Alpha is often used in conjunction with beta (the Greek letter β), which measures the broad market’s overall volatility or risk, known as systematic market risk.

Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.

Understanding Alpha

Alpha is one of five popular technical investment risk ratios. The others are beta, standard deviation, R-squared, and the Sharpe ratio. These are all statistical measurements used in modern portfolio theory (MPT). All of these indicators are intended to help investors determine the risk-return profile of an investment.

Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

In other words, alpha is the return on an investment that is not a result of a general movement in the greater market. As such, an alpha of zero would indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any additional value compared to the broad market.

The concept of alpha became more popular with the advent of smart beta index funds tied to indexes like the Standard & Poor’s 500 index and the Wilshire 5000 Total Market Index. These funds attempt to enhance the performance of a portfolio that tracks a targeted subset of the market.

Despite the considerable desirability of alpha in a portfolio, many index benchmarks manage to beat asset managers the vast majority of the time. Due in part to a growing lack of faith in traditional financial advising brought about by this trend, more and more investors are switching to low-cost, passive online advisors (often called roboadvisors​) who exclusively or almost exclusively invest clients’ capital into index-tracking funds, the rationale being that if they cannot beat the market they may as well join it.

Moreover, because most “traditional” financial advisors charge a fee, when one manages a portfolio and nets an alpha of zero, it actually represents a slight net loss for the investor. For example, suppose that Jim, a financial advisor, charges 1% of a portfolio’s value for his services and that during a 12-month period Jim managed to produce an alpha of 0.75 for the portfolio of one of his clients, Frank. While Jim has indeed helped the performance of Frank’s portfolio, the fee that Jim charges is in excess of the alpha he has generated, so Frank’s portfolio has experienced a net loss. For investors, the example highlights the importance of considering fees in conjunction with performance returns and alpha.

The Efficient Market Hypothesis (EMH) postulates that market prices incorporate all available information at all times, and so securities are always properly priced (the market is efficient.) Therefore, according to the EMH, there is no way to systematically identify and take advantage of mispricings in the market because they do not exist.

If mispricings are identified, they are quickly arbitraged away and so persistent patterns of market anomalies that can be taken advantage of tend to be few and far between.

Empirical evidence comparing historical returns of active mutual funds relative to their passive benchmarks indicates that fewer than 10% of all active funds are able to earn a positive alpha over a 10-plus year time period, and this percentage falls once taxes and fees are taken into consideration. In other words, alpha is hard to come by, especially after taxes and fees.

Because beta risk can be isolated by diversifying and hedging various risks (which comes with various transaction costs), some have proposed that alpha does not really exist, but that it simply represents the compensation for taking some un-hedged risk that hadn’t been identified or was overlooked.

Seeking Investment Alpha

Alpha is commonly used to rank active mutual funds as well as all other types of investments. It is often represented as a single number (like +3.0 or -5.0), and this typically refers to a percentage measuring how the portfolio or fund performed compared to the referenced benchmark index (i.e., 3% better or 5% worse).

Deeper analysis of alpha may also include “Jensen’s alpha.” Jensen’s alpha takes into consideration the capital asset pricing model (CAPM) market theory and includes a risk-adjusted component in its calculation. Beta (or the beta coefficient) is used in the CAPM, which calculates the expected return of an asset based on its own particular beta and the expected market returns. Alpha and beta are used together by investment managers to calculate, compare, and analyze returns.

The entire investing universe offers a broad range of securities, investment products, and advisory options for investors to consider. Different market cycles also have an influence on the alpha of investments across different asset classes. This is why risk-return metrics are important to consider in conjunction with alpha.

Examples

This is illustrated in the following two historical examples for a fixed income ETF and an equity ETF:

The iShares Convertible Bond ETF (ICVT) is a fixed income investment with low risk. It tracks a customized index called the Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index. The 3-year standard deviation was 18.94%, as of Feb. 28, 2022. The year-to-date return, as of Feb. 28, 2022, was -6.67%. The Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index had a return of -13.17% over the same period. Therefore, the alpha for ICVT was -0 12% in comparison to the Bloomberg U.S. Aggregate Index and a 3-year standard deviation of 18.97%.

However, since the aggregate bond index is not the proper benchmark for ICVT (it should be the Bloomberg Convertible index), this alpha may not be as large as initially thought; and in fact, may be misattributed since convertible bonds have far riskier profiles than plain vanilla bonds.

The WisdomTree U.S. Quality Dividend Growth Fund (DGRW) is an equity investment with higher market risk that seeks to invest in dividend growth equities. Its holdings track a customized index called the WisdomTree U.S. Quality Dividend Growth Index. It had a three-year annualized standard deviation of 10.58%, higher than ICVT.

As of Feb. 28, 2022, DGRW annualized return was 18.1%, which was also higher than the S&P 500 at 16.4%, so it had an alpha of 1.7% in comparison to the S&P 500. But again, the S&P 500 may not be the correct benchmark for this ETF, since dividend-paying growth stocks are a very particular subset of the overall stock market, and may not even be inclusive of the 500 most valuable stocks in America.

Alpha Considerations

While alpha has been called the “holy grail” of investing, and as such, receives a lot of attention from investors and advisors alike, there are a couple of important considerations that one should take into account when using alpha.

1. A basic calculation of alpha subtracts the total return of an investment from a comparable benchmark in its asset category. This alpha calculation is primarily only used against a comparable asset category benchmark, as noted in the examples above. Therefore, it does not measure the outperformance of an equity ETF versus a fixed income benchmark. This alpha is also best used when comparing the performance of similar asset investments. Thus, the alpha of the equity ETF, DGRW, is not relatively comparable to the alpha of the fixed income ETF, ICVT.
2. Some references to alpha may refer to a more advanced technique. Jensen’s alpha takes into consideration CAPM theory and risk-adjusted measures by utilizing the risk-free rate and beta.

When using a generated alpha calculation it is important to understand the calculations involved. Alpha can be calculated using various different index benchmarks within an asset class. In some cases, there might not be a suitable pre-existing index, in which case advisors may use algorithms and other models to simulate an index for comparative alpha calculation purposes.

Alpha can also refer to the abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like CAPM. In this instance, a CAPM model might aim to estimate returns for investors at various points along an efficient frontier. The CAPM analysis might estimate that a portfolio should earn 10% based on the portfolio’s risk profile. If the portfolio actually earns 15%, the portfolio’s alpha would be 5.0, or +5% over what was predicted in the CAPM model.

What Is an Allowance for Doubtful Accounts?

An allowance for doubtful accounts is a contra account that nets against the total receivables presented on the balance sheet to reflect only the amounts expected to be paid. The allowance for doubtful accounts estimates the percentage of accounts receivable that are expected to be uncollectible. However, the actual payment behavior of customers may differ substantially from the estimate.

Understanding the Allowance for Doubtful Accounts

Regardless of company policies and procedures for credit collections, the risk of the failure to receive payment is always present in a transaction utilizing credit. Thus, a company is required to realize this risk through the establishment of the allowance for doubtful accounts and offsetting bad debt expense. In accordance with the matching principle of accounting, this ensures that expenses related to the sale are recorded in the same accounting period as the revenue is earned. The allowance for doubtful accounts also helps companies more accurately estimate the actual value of their account receivables.

Because the allowance for doubtful accounts is established in the same accounting period as the original sale, an entity does not know for certain which exact receivables will be paid and which will default. Therefore, generally accepted accounting principles (GAAP) dictate that the allowance must be established in the same accounting period as the sale, but can be based on an anticipated or estimated figure. The allowance can accumulate across accounting periods and may be adjusted based on the balance in the account.

How to Estimate the Allowance for Doubtful Accounts

Two primary methods exist for estimating the dollar amount of accounts receivables not expected to be collected.

Percentage of Sales Method

The sales method applies a flat percentage to the total dollar amount of sales for the period. For example, based on previous experience, a company may expect that 3% of net sales are not collectible. If the total net sales for the period is $100,000, the company establishes an allowance for doubtful accounts for $3,000 while simultaneously reporting $3,000 in bad debt expense.

If the following accounting period results in net sales of $80,000, an additional $2,400 is reported in the allowance for doubtful accounts, and $2,400 is recorded in the second period in bad debt expense. The aggregate balance in the allowance for doubtful accounts after these two periods is $5,400.

Accounts Receivable Aging Method

The second method of estimating the allowance for doubtful accounts is the aging method. All outstanding accounts receivable are grouped by age, and specific percentages are applied to each group. The aggregate of all group results is the estimated uncollectible amount.

For example, a company has $70,000 of accounts receivable less than 30 days outstanding and $30,000 of accounts receivable more than 30 days outstanding. Based on previous experience, 1% of accounts receivable less than 30 days old will be uncollectible, and 4% of those accounts receivable at least 30 days old will be uncollectible.

Therefore, the company will report an allowance of $1,900 (($70,000 * 1%) + ($30,000 * 4%)). If the next accounting period results in an estimated allowance of $2,500 based on outstanding accounts receivable, only $600 ($2,500 – $1,900) will be the adjusting entry amount.

Risk Classification Method

Some companies may classify different types of debt or different types of vendors using risk classifications. For example, a start-up customer may be considered a high risk, while an established, long-tenured customer may be a low risk. In this example, the company often assigns a percentage to each classification of debt. Then, it aggregates all receivables in each grouping, calculates each group by the percentage, and records an allowance equal to the aggregate of all products.

Historical Percentage Method

If a company has a history of recording or tracking bad debt, it can use the historical percentage of bad debt if it feels that historical measurement relates to its current debt. For example, a company may know that its 10-year average of bad debt is 2.4%. Therefore, it can assign this fixed percentage to its total accounts receivable balance since more often than not, it will approximately be close to this amount. The company must be aware of outliers or special circumstances that may have unfairly impacted that 2.4% calculation.

Pareto Analysis Method

A Pareto analysis is a risk measurement approach that states that a majority of activity is often concentrated among a small amount of accounts. In many different aspects of business, a rough estimation is that 80% of account receivable balances are made up of a small concentration (i.e. 20%) of vendors. This 80%/20% ratio is used throughout business.

Though the Pareto Analysis can not be used on its own, it can be used to weigh accounts receivable estimates differently. For example, a company may assign a heavier weight to the clients that make up a larger balance of accounts receivable due to conservatism.

Specific Identification Method

Assume a company has 100 clients and believes there are 11 accounts that may go uncollected. Instead of applying percentages or weights, it may simply aggregate the account balance for all 11 customers and use that figure as the allowance amount. Companies often have a specific method of identifying the companies that it wants to include and the companies it wants to exclude.

How to Account for the Allowance for Doubtful Accounts

Establishing the Allowance

The first step in accounting for the allowance for doubtful accounts is to establish the allowance. This is done by using one of the estimation methods above to predict what proportion of accounts receivable will go uncollected. For this example, let’s say a company predicts it will incur $500,000 of uncollected accounts receivable.

To create the allowance, the company must debit a loss. Most often, companies use an account called ‘Bad Debt Expense’. Then, the company establishes the allowance by crediting an allowance account often called ‘Allowance for Doubtful Accounts’. Though this allowance for doubtful accounts is presented on the balance sheet with other assets, it is a contra asset that reduces the balance of total assets.

• DR Bad Debt Expense $500,000
• CR Allowance for Doubtful Accounts $500,000

Adjusting the Allowance

Let’s say six months passes. The company now has a better idea of which account receivables will be collected and which will be lost. For example, say the company now thinks that a total of $600,000 of receivables will be lost. This means its allowance of $500,000 is $100,000 short. The company must record an additional expense for this amount to also increase the allowance’s credit balance.

• DR Bad Debt Expense $100,000
• CR Allowance for Doubtful Accounts $100,000

Writing Off Account

Now, let’s say a specific customer that owes a company $50,000 officially files for bankruptcy. This client’s account had previously been included in the estimate for the allowance. Because the company has a very low priority claim without collateral to the debt, the company decides it is unlikely it will every receive any of this $50,000. To properly reflect this change, the company must reduce its accounts receivable balance by this amount. On the other hand, once the receivable is removed from the books, there is no need to record an associated allowance for this account.

• DR Allowance for Doubtful Accounts $50,000
• CR Accounts Receivable $50,000

Note that the debit to the allowance for doubtful accounts reduces the balance in this account because contra assets have a natural credit balance. Also, note that when writing off the specific account, no income statement accounts are used. This is because the expense was already taken when creating or adjusting the allowance.

Recovering an Account

By miracle, it turns out the company ended up being rewarded a portion of their outstanding receivable balance they’d written off as part of the bankruptcy proceedings. Of the $50,000 balance that was written off, the company is notified that they will receive $35,000.

The company can recover the account by reversing the entry above to reinstate the accounts receivable balance and the corresponding allowance for doubtful account balance. Then, the company will record a debit to cash and credit to accounts receivable when the payment is collected. You’ll notice that because of this, the allowance for doubtful accounts increases. A company can further adjust the balance by following the entry under the “Adjusting the Allowance” section above.

• DR Accounts Receivable $35,000
• CR Allowance for Doubtful Accounts $35,000
• DR Cash $35,000
• CR Accounts Receivable $35,000

The Bottom Line

The allowance for doubtful accounts is a general ledger account that is used to estimate the amount of accounts receivable that will not be collected. A company uses this account to record how many accounts receivable it thinks will be lost. The balance may be estimated using several different methods, and management should periodically evaluate the balance of the allowance account to ensure the appropriate bad debt expense and net accounts receivables are being recorded.