What Is an Auditor’s Opinion?

An auditor’s opinion is a certification that accompanies financial statements. It is based on an audit of the procedures and records used to produce the statements and delivers an opinion as to whether material misstatements exist in the financial statements. An auditor’s opinion may also be called an accountant’s opinion.

Understanding Auditor’s Opinions

An auditor’s opinion is presented in an auditor’s report. The audit report begins with an introductory section outlining the responsibility of management and the responsibility of the audit firm. The second section identifies the financial statements on which the auditor’s opinion is given. A third section outlines the auditor’s opinion on the financial statements. Although it is not found in all audit reports, a fourth section may be presented as a further explanation regarding a qualified opinion or an adverse opinion.

For audits of companies in the United States, the opinion may be an unqualified opinion in accordance with generally accepted accounting principles (GAAP), a qualified opinion, or an adverse opinion. The audit is performed by an accountant who is independent of the company being audited.

Unqualified Opinion Audit

An unqualified opinion is also known as a clean opinion. The auditor reports an unqualified opinion if the financial statements are presumed to be free from material misstatements. In addition, an unqualified opinion is given over the internal controls of an entity if management has claimed responsibility for its establishment and maintenance, and the auditor has performed fieldwork to test its effectiveness.

Qualified Audit

A qualified opinion is given when a company’s financial records have not followed GAAP in all financial transactions. Although the wording of a qualified opinion is very similar to an unqualified opinion, the auditor provides an additional paragraph including deviations from GAAP in the financial statements and points out why the auditor report is not unqualified.

A qualified opinion may be given due to either a limitation in the scope of the audit or an accounting method that did not follow GAAP. However, the deviation from GAAP is not pervasive and does not misstate the financial position of the company as a whole.

Adverse Opinion

The most unfavorable opinion a business may receive is an adverse opinion. An adverse opinion indicates financial records are not in accordance with GAAP and contain grossly material and pervasive misstatements. An adverse opinion may be an indicator of fraud. Investors, lenders, and other financial institutions do not typically accept financial statements with adverse opinions as part of their debt covenants.

Disclaimer of Opinion

In the event that the auditor is unable to complete the audit report due to the absence of financial records or insufficient cooperation from management, the auditor issues a disclaimer of opinion. This is referred to as a scope limitation and is an indication that no opinion over the financial statements was able to be determined. A disclaimer of opinion is not an opinion itself.

What Is an Annual Return?

The annual return is the return that an investment provides over a period of time, expressed as a time-weighted annual percentage. Sources of returns can include dividends, returns of capital and capital appreciation. The rate of annual return is measured against the initial amount of the investment and represents a geometric mean rather than a simple arithmetic mean.

Understanding Annual Return

The de facto method for comparing the performance of investments with liquidity, an annual return can be calculated for various assets, which include stocks, bonds, funds, commodities and some types of derivatives. This process is a preferred method, considered to be more accurate than a simple return, as it includes adjustments for compounding interest. Different asset classes are considered to have different strata of annual returns.

Annual Returns on Stocks

Also known as an annualized return, the annual return expresses the stock’s increase in value over a designated period of time. In order to calculate an annual return, information regarding the current price of the stock and the price at which it was purchased are required. If any splits have occurred, the purchase price needs to be adjusted accordingly. Once the prices are determined, the simple return percentage is calculated first, with that figure ultimately being annualized. The simple return is just the current price minus the purchase price, divided by the purchase price.

Example Annual Return Calculation


$\begin{aligned} &\text{CAGR} = \left ( \left ( \frac{ \text{Ending Value} }{ \text{Beginning Value } } \right ) ^ \frac{ 1 }{ \text{Years} } \right ) – 1 \\ &\textbf{where:} \\ &\text{CAGR} = \text{compound annual growth rate} \\ &\text{Years} = \text{holding period, in years} \\ \end{aligned}$​CAGR=((Beginning Value Ending Value​)Years1​)−1where:CAGR=compound annual growth rateYears=holding period, in years​

Consider an investor that purchases a stock on Jan. 1, 2000, for $20. The investor then sells it on Jan. 1, 2005, for $35 – a $15 profit. The investor also receives a total of $2 in dividends over the five-year holding period. In this example, the investor’s total return over five years is $17, or (17/20) 85% of the initial investment. The annual return required to achieve 85% over five years follows the formula for the compound annual growth rate (CAGR):


$\begin{aligned} &\left ( \left ( \frac { 37 }{ 20 } \right ) ^ \frac{ 1 }{ 5 } \right ) – 1 = 13.1\% \text{ annual return} \\ \end{aligned}$​((2037​)51​)−1=13.1% annual return​

The annualized return varies from the typical average and shows the real gain or loss on an investment, as well as the difficulty in recouping losses. For instance, losing 50% on an initial investment requires a 100% gain the next year in order to make up the difference. Because of the sizable difference in gains and losses that can occur, annualized returns help even out investment results for better comparison. 

Annual Returns on a 401K

The calculation differs when determining the annual return of a 401K during a specified year. First, the total return must be calculated. The starting value for the time period being examined is needed, along with the final value. Before performing the calculations, any contributions to the account during the time period in question must be subtracted from the final value.

Once the adjusted final value is determined, it is divided by the starting balance. Finally, subtract 1 from the result and multiply that amount by 100 to determine the percentage total return.

What Is Accretion of Discount?

Accretion of discount is the increase in the value of a discounted instrument as time passes and the maturity date looms closer. The value of the instrument will accrete (grow) at the interest rate implied by the discounted issuance price, the value at maturity, and the term to maturity.

How Accretion of Discount Works

A bond can be purchased at par, at a premium, or at a discount. Regardless of the purchase price of the bond, however, all bonds mature at par value. The par value is the amount of money that a bond investor will be repaid at maturity. A bond that is purchased at a premium has a value above par. As the bond gets closer to maturity, the value of the bond declines until it is at par on the maturity date. The decrease in value over time is referred to as the amortization of premium.

A bond that is issued at a discount has a value that is less than the par value. As the bond approaches its redemption date, it will increase in value until it converges with the par value at maturity. This increase in value over time is referred to as an accretion of discount. For example, a three-year bond with a face value of $1,000 is issued at $975. Between issuance and maturity, the value of the bond will increase until it reaches its full par value of $1,000, which is the amount that will be paid to the bondholder at maturity.

Special Considerations

Accretion can be accounted for using a straight-line method, whereby the increase is evenly spread throughout the term. Using this method of portfolio accounting, accretion of discount can be said to be a straight-line accumulation of capital gains on a discount bond in anticipation of receipt of par at maturity.

Accretion can also be accounted for using a constant yield, whereby the increase is closest to maturity. The constant yield method is the method required by the Internal Revenue Service (IRS) for calculating the adjusted cost basis from the purchase amount to the expected redemption amount. This method spreads out the gain over the remaining life of the bond, instead of recognizing the gain in the year of the bond’s redemption.

Calculating Accretion

To calculate the amount of accretion, use the formula:

Accretion Amount = Purchase Basis x (YTM / Accrual periods per year) – Coupon Interest

The first step in the constant yield method is determining the yield to maturity (YTM) which is the yield that will be earned on a bond held until it matures. The yield to maturity depends on how frequently the yield is compounded. The IRS allows the taxpayer some flexibility in determining which accrual period to use for computing yield. For example, a bond with a $100 par value and a coupon rate of 2% is issued for $75 with a 10-year maturity date. Let’s assume it is compounded annually for the sake of simplicity. The YTM can, therefore, be calculated as:

• $100 par value = $75 x (1 + r)¹⁰
• $100/$75 = (1 + r)¹⁰
• 1.3333 = (1 + r)¹⁰
• r = 2.92%

Coupon interest on the bond is 2% x $100 par value = $2. Therefore,

• Accretion_period1 = ($75 x 2.92%) – Coupon interest
• Accretion _period1 = $2.19 – $2
• Accretion_period1 = $0.19

The purchase price of $75 represents the bond’s basis at issuance. However, in subsequent periods, the basis becomes the purchase price plus accrued interest. For example, after year 2, the accrual can be calculated as:

• Accretion_period2 = [($75 + $0.19) x 2.92%] – $2
• Accretion_period2 = $0.20

Using this example, one can see that a discount bond has a positive accrual; in other words, the basis accretes, increasing over time from $0.19, $0.20, and so on. Periods 3 to 10 can be calculated in a similar manner, using the former period’s accrual to calculate the current period’s basis.

What Is an Account Statement?

An account statement is a periodic summary of account activity with a beginning date and an ending date. The most commonly known are checking account statements, usually provided monthly, and brokerage account statements, which are provided monthly or quarterly. Monthly credit card bills are also considered account statements.

Understanding Account Statements

Account statements refer to almost any official summary of an account, wherever the account is held. Insurance companies may provide account statements summarizing paid-in cash values, for example. Statements can be generated for almost any type of accounts that represent ongoing transactions where funds are repeatedly exchanged. This can include online payment accounts such as PayPal, credit card accounts, brokerage accounts, and savings accounts.

Utility companies, as well as telephone and subscription television service providers, usually generate account statements for their customers detailing their usage and any overages during the payment cycle. Such statements typically list debits paid, incoming funds or credits received by the account holder, and fees associated with maintaining the account. For example, certain types of savings accounts might incur regular maintenance fees unless a certain minimum balance of funds is maintained in the account. Cable television subscriptions may include state taxes and other surcharges that are included in providing regular service.

How Account Statements Are Used

Account statements should be scrutinized for accuracy, and historical statements are critical for budgeting. A credit or loan account statement, for example, may show not only the outstanding balance due but the interest rate charged on that debt and any fees that have been added during the payment cycle. This can include late charges for payments not received by their due date as well as overdraft fees when bank account holders overspend. Your account statements are a window into your finances.

The statement may also list financial information that relates to the account holder such as their credit score, or the estimated time it will take to completely pay off a debt via installment payments. Alerts and notices to the account holder may also appear on these statements, calling attention to matters with the account that need to be addressed, such unusual charges that should be reviewed and verified.

Red Flags on Account Statements

Anomalous items on an account statement may be a sign the account has been compromised, perhaps through a stolen credit or debit card or through identity thieves who gained access to account information. For example, an account holder or the financial institution might spot a charge for concert tickets or a luxury item that seems out of the ordinary. Account-holders may be able to dispute such out-of-place charges and file a claim that they did not make the purchase themselves. Reviewing your account statements as they come in is a good financial habit that can catch these red flags before they become a financial disaster.