What Is the Accounting Rate of Return (ARR)?

The accounting rate of return (ARR) is a formula that reflects the percentage rate of return expected on an investment or asset, compared to the initial investment’s cost. The ARR formula divides an asset’s average revenue by the company’s initial investment to derive the ratio or return that one may expect over the lifetime of an asset or project. ARR does not consider the time value of money or cash flows, which can be an integral part of maintaining a business.

Understanding the Accounting Rate of Return (ARR)

The accounting rate of return is a capital budgeting metric that’s useful if you want to calculate an investment’s profitability quickly. Businesses use ARR primarily to compare multiple projects to determine the expected rate of return of each project, or to help decide on an investment or an acquisition.

ARR factors in any possible annual expenses, including depreciation, associated with the project. Depreciation is a helpful accounting convention whereby the cost of a fixed asset is spread out, or expensed, annually during the useful life of the asset. This lets the company earn a profit from the asset right away, even in its first year of service.

The Formula for ARR

The formula for the accounting rate of return is as follows:

$ARR = \frac{Average\, Annual\, Profit}{Initial\, Investment}$ARR=InitialInvestmentAverageAnnualProfit​

How to Calculate the Accounting Rate of Return (ARR)

1. Calculate the annual net profit from the investment, which could include revenue minus any annual costs or expenses of implementing the project or investment.
2. If the investment is a fixed asset such as property, plant, and equipment (PP&E), subtract any depreciation expense from the annual revenue to achieve the annual net profit.
3. Divide the annual net profit by the initial cost of the asset or investment. The result of the calculation will yield a decimal. Multiply the result by 100 to show the percentage return as a whole number.

Example of the Accounting Rate of Return (ARR)

As an example, a business is considering a project that has an initial investment of $250,000 and forecasts that it would generate revenue for the next five years. Here’s how the company could calculate the ARR:

• Initial investment: $250,000
• Expected revenue per year: $70,000
• Time frame: 5 years
• ARR calculation: $70,000 (annual revenue) / $250,000 (initial cost)
• ARR = 0.28 or 28%

Accounting Rate of Return vs. Required Rate of Return

The ARR is the annual percentage return from an investment based on its initial outlay of cash. Another accounting tool, the required rate of return (RRR), also known as the hurdle rate, is the minimum return an investor would accept for an investment or project that compensates them for a given level of risk.

The RRR can vary between investors as they each have a different tolerance for risk. For example, a risk-averse investor likely would require a higher rate of return to compensate for any risk from the investment. It’s important to utilize multiple financial metrics including ARR and RRR to determine if an investment would be worthwhile based on your level of risk tolerance.

Advantages and Disadvantages of the Accounting Rate of Return (ARR)

Advantages

The accounting rate of return is a simple calculation that does not require complex math and is helpful in determining a project’s annual percentage rate of return. Through this, it allows managers to easily compare ARR to the minimum required return. For example, if the minimum required return of a project is 12% and ARR is 9%, a manager will know not to proceed with the project.

ARR comes in handy when investors or managers need to quickly compare the return of a project without needing to consider the time frame or payment schedule but rather just the profitability or lack thereof.

Disadvantages

Despite its advantages, ARR has its limitations. It doesn’t consider the time value of money. The time value of money is the concept that money available at the present time is worth more than an identical sum in the future because of its potential earning capacity.

In other words, two investments might yield uneven annual revenue streams. If one project returns more revenue in the early years and the other project returns revenue in the later years, ARR does not assign a higher value to the project that returns profits sooner, which could be reinvested to earn more money.

The accounting rate of return does not consider the increased risk of long-term projects and the increased uncertainty associated with long periods.

Also, ARR does not take into account the impact of cash flow timing. Let’s say an investor is considering a five-year investment with an initial cash outlay of $50,000, but the investment doesn’t yield any revenue until the fourth and fifth years.

In this case, the ARR calculation would not factor in the lack of cash flow in the first three years, while in reality, the investor would need to be able to withstand the first three years without any positive cash flow from the project.

The Bottom Line

The accounting rate of return (ARR) is a simple formula that allows investors and managers to determine the profitability of an asset or project. Because of its ease of use and determination of profitability, it is a handy tool in making decisions. However, the formula does not take into consideration the cash flows of an investment or project, the overall timeline of return, and other costs, which help determine the true value of an investment or project.

What Is an Auditor’s Report?

An auditor’s report is a written letter from the auditor containing their opinion on whether a company’s financial statements comply with generally accepted accounting principles (GAAP) and are free from material misstatement.

The independent and external audit report is typically published with the company’s annual report. The auditor’s report is important because banks and creditors require an audit of a company’s financial statements before lending to them.

How an Auditor’s Report Works

An auditor’s report is a written letter attached to a company’s financial statements that expresses its opinion on a company’s compliance with standard accounting practices. The auditor’s report is required to be filed with a public company’s financial statements when reporting earnings to the Securities and Exchange Commission (SEC).

However, an auditor’s report is not an evaluation of whether a company is a good investment. Also, the audit report is not an analysis of the company’s earnings performance for the period. Instead, the report is merely a measure of the reliability of the financial statements.

The Components of an Auditor’s Report

The auditor’s letter follows a standard format, as established by generally accepted auditing standards (GAAS). A report usually consists of three paragraphs.

• The first paragraph states the responsibilities of the auditor and directors.
• The second paragraph contains the scope, stating that a set of standard accounting practices was the guide.
• The third paragraph contains the auditor’s opinion.

An additional paragraph may inform the investor of the results of a separate audit on another function of the entity. The investor will key in on the third paragraph, where the opinion is stated.

The type of report issued will be dependent on the findings by the auditor. Below are the most common types of reports issued for companies.

Clean or Unqualified Report

A clean report means that the company’s financial records are free from material misstatement and conform to the guidelines set by GAAP. A majority of audits end in unqualified, or clean, opinions.

Qualified Opinion

A qualified opinion may be issued in one of two situations: first, if the financial statements contain material misstatements that are not pervasive; or second, if the auditor is unable to obtain sufficient appropriate audit evidence on which to base an opinion, but the possible effects of any material misstatements are not pervasive. For example, a mistake might have been made in calculating operating expenses or profit. Auditors typically state the specific reasons and areas where the issues are present so that the company can fix them.

Adverse Opinion

An adverse opinion means that the auditor has obtained sufficient audit evidence and concludes that misstatements in the financial statements are both material and pervasive. An adverse opinion is the worst possible outcome for a company and can have a lasting impact and legal ramifications if not corrected.

Disclaimer of Opinion

A disclaimer of opinion means that, for some reason, the auditor is unable to obtain sufficient audit evidence on which to base the opinion, and the possible effects on the financial statements of undetected misstatements, if any, could be both material and pervasive. Examples can include when an auditor can’t be impartial or wasn’t allowed access to certain financial information.

Example of an Auditor’s Report

Excerpts from the audit report by Deloitte & Touche LLP for Starbucks Corporation, dated Nov. 15, 2019, follow.

Paragraph 1: Opinion on the Financial Statements

“We have audited the accompanying consolidated balance sheets of Starbucks Corporation and subsidiaries (the ‘Company’) as of September 29, 2019, and September 30, 2018, the related consolidated statements of earnings, comprehensive income, equity, and cash flows, for each of the three years in the period ended September 29, 2019, and the related notes (collectively referred to as the ‘financial statements’).

In our opinion, the financial statements present fairly, in all material respects, the financial position of the Company as of September 29, 2019, and September 30, 2018, and the results of its operations and its cash flows for each of the three years in the period ended September 29, 2019, in conformity with accounting principles generally accepted in the United States of America.”

Paragraph 2: Basis for Opinion

“We conducted our audits in accordance with the standards of the Public Company Accounting Oversight Board (PCAOB). Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements are free of material misstatement, whether due to error or fraud. Our audits included performing procedures to assess the risks of material misstatement of the financial statements, whether due to error or fraud, and performing procedures that respond to those risks.

Such procedures included examining, on a test basis, evidence regarding the amounts and disclosures in the financial statements. Our audits also included evaluating the accounting principles used and significant estimates made by management, as well as evaluating the overall presentation of the financial statements. We believe that our audits provide a reasonable basis for our opinion.”

What Is Annual Percentage Rate (APR)?

Annual percentage rate (APR) refers to the yearly interest generated by a sum that’s charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment. This includes any fees or additional costs associated with the transaction but does not take compounding into account. The APR provides consumers with a bottom-line number they can compare among lenders, credit cards, or investment products.

How the Annual Percentage Rate (APR) Works

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you’ll pay each year by taking things such as monthly payments and fees into account. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.

The Truth in Lending Act (TILA) of 1968 mandates that lenders disclose the APR they charge to borrowers. Credit card companies are allowed to advertise interest rates on a monthly basis, but they must clearly report the APR to customers before they sign an agreement.

How Is APR Calculated?

APR is calculated by multiplying the periodic interest rate by the number of periods in a year in which it was applied. It does not indicate how many times the rate is actually applied to the balance.

$\begin{aligned} &\text{APR} = \left ( \left ( \frac{ \frac{ \text{Fees} + \text{Interest} }{ \text {Principal} } }{ n } \right ) \times 365 \right ) \times 100 \\ &\textbf{where:} \\ &\text{Interest} = \text{Total interest paid over life of the loan} \\ &\text{Principal} = \text{Loan amount} \\ &n = \text{Number of days in loan term} \\ \end{aligned}$​APR=((nPrincipalFees+Interest​​)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term​

Types of APRs

Credit card APRs vary based on the type of charge. The credit card issuer may charge one APR for purchases, another for cash advances, and yet another for balance transfers from another card. Issuers also charge high-rate penalty APRs to customers for late payments or violating other terms of the cardholder agreement. There’s also the introductory APR—a low or 0% rate—with which many credit card companies try to entice new customers to sign up for a card.

Bank loans generally come with either fixed or variable APRs. A fixed APR loan has an interest rate that is guaranteed not to change during the life of the loan or credit facility. A variable APR loan has an interest rate that may change at any time.

The APR borrowers are charged also depends on their credit. The rates offered to those with excellent credit are significantly lower than those offered to those with bad credit.

APR vs. Annual Percentage Yield (APY)

Though an APR only accounts for simple interest, the annual percentage yield (APY) takes compound interest into account. As a result, a loan’s APY is higher than its APR. The higher the interest rate—and to a lesser extent, the smaller the compounding periods—the greater the difference between the APR and APY.

Imagine that a loan’s APR is 12%, and the loan compounds once a month. If an individual borrows $10,000, their interest for one month is 1% of the balance, or $100. That effectively increases the balance to $10,100. The following month, 1% interest is assessed on this amount, and the interest payment is $101, slightly higher than it was the previous month. If you carry that balance for the year, your effective interest rate becomes 12.68%. APY includes these small shifts in interest expenses due to compounding, while APR does not.

Here’s another way to look at it. Say you compare an investment that pays 5% per year with one that pays 5% monthly. For the first month, the APY equals 5%, the same as the APR. But for the second, the APY is 5.12%, reflecting the monthly compounding.

Given that an APR and a different APY can represent the same interest rate on a loan or financial product, lenders often emphasize the more flattering number, which is why the Truth in Savings Act of 1991 mandated both APR and APY disclosure in ads, contracts, and agreements. A bank will advertise a savings account’s APY in a large font and its corresponding APR in a smaller one, given that the former features a superficially larger number. The opposite happens when the bank acts as the lender and tries to convince its borrowers that it’s charging a low rate. A great resource for comparing both APR and APY rates on a mortgage is a mortgage calculator.

APR vs. APY Example

Let’s say that XYZ Corp. offers a credit card that levies interest of 0.06273% daily. Multiply that by 365, and that’s 22.9% per year, which is the advertised APR. Now, if you were to charge a different $1,000 item to your card every day and waited until the day after the due date (when the issuer started levying interest) to start making payments, you’d owe $1,000.6273 for each thing you bought.

To calculate the APY or effective annual interest rate—the more typical term for credit cards—add one (that represents the principal) and take that number to the power of the number of compounding periods in a year; subtract one from the result to get the percentage:

$\begin{aligned} &\text{APY} = (1 + \text{Periodic Rate} ) ^ n – 1 \\ &\textbf{where:} \\ &n = \text{Number of compounding periods per year} \\ \end{aligned}$​APY=(1+Periodic Rate)n−1where:n=Number of compounding periods per year​

In this case your APY or EAR would be 25.7%:

$\begin{aligned} &( ( 1 + .0006273 ) ^ {365} ) – 1 = .257 \\ \end{aligned}$​((1+.0006273)365)−1=.257​

If you only carry a balance on your credit card for one month’s period, you will be charged the equivalent yearly rate of 22.9%. However, if you carry that balance for the year, your effective interest rate becomes 25.7% as a result of compounding each day.

APR vs. Nominal Interest Rate vs. Daily Periodic Rate

An APR tends to be higher than a loan’s nominal interest rate. That’s because the nominal interest rate doesn’t account for any other expense accrued by the borrower. The nominal rate may be lower on your mortgage if you don’t account for closing costs, insurance, and origination fees. If you end up rolling these into your mortgage, your mortgage balance increases, as does your APR.

The daily periodic rate, on the other hand, is the interest charged on a loan’s balance on a daily basis—the APR divided by 365. Lenders and credit card providers are allowed to represent APR on a monthly basis, though, as long as the full 12-month APR is listed somewhere before the agreement is signed.

Disadvantages of Annual Percentage Rate (APR)

The APR isn’t always an accurate reflection of the total cost of borrowing. In fact, it may understate the actual cost of a loan. That’s because the calculations assume long-term repayment schedules. The costs and fees are spread too thin with APR calculations for loans that are repaid faster or have shorter repayment periods. For instance, the average annual impact of mortgage closing costs is much smaller when those costs are assumed to have been spread over 30 years instead of seven to 10 years.

APR also runs into some trouble with adjustable-rate mortgages (ARMs). Estimates always assume a constant rate of interest, and even though APR takes rate caps into consideration, the final number is still based on fixed rates. Because the interest rate on an ARM will change when the fixed-rate period is over, APR estimates can severely understate the actual borrowing costs if mortgage rates rise in the future.

Mortgage APRs may or may not include other charges, such as appraisals, titles, credit reports, applications, life insurance, attorneys and notaries, and document preparation. There are other fees that are deliberately excluded, including late fees and other one-time fees.

All this may make it difficult to compare similar products because the fees included or excluded differ from institution to institution. In order to accurately compare multiple offers, a potential borrower must determine which of these fees are included and, to be thorough, calculate APR using the nominal interest rate and other cost information.

The Bottom Line

The APR is the basic theoretical cost or benefit of money loaned or borrowed. By calculating only the simple interest without periodic compounding, the APR gives borrowers and lenders a snapshot of how much interest they are earning or paying within a certain period of time. If someone is borrowing money, such as by using a credit card or applying for a mortgage, the APR can be misleading because it only presents the base number of what they are paying without taking time into the equation. Conversely, if someone is looking at the APR on a savings account, it doesn’t illustrate the full impact of interest earned over time.

APRs are often a selling point for different financial instruments, such as mortgages or credit cards. When choosing a tool with an APR, be careful to also take into account the APY because it will prove a more accurate number for what you will pay or earn over time. Though the formula for your APR may stay the same, different financial institutions will include different fees in the principal balance. Be aware of what is included in your APR when signing any agreement.

What Is an Anti-Dilution Provision?

Anti-dilution provisions are clauses built into convertible preferred stocks and some options to help shield investors from their investment potentially losing value. When new issues of a stock hit the market at a cheaper price than that paid by earlier investors in the same stock, then equity dilution can occur. Anti-dilution provisions are also referred to as anti-dilution clauses, subscription rights, subscription privileges, or preemptive rights.

Understanding Anti-Dilution Provisions

Anti-dilution provisions act as a buffer to protect investors against their equity ownership positions becoming diluted or less valuable. This can happen when the percentage of an owner’s stake in a company decreases because of an increase in the total number of shares outstanding. Total shares outstanding may increase because of new share issuance based on a round of equity financing. Dilution can also occur when holders of stock options, such as company employees, or holders of other optionable securities exercise their options.

Sometimes the company receives enough cash in exchange for the shares that the increase in the value of the shares offsets the effects of dilution; but often this is not the case.

Anti-Dilution Provisions at Work

Dilution can be particularly vexing to preferred shareholders of venture capital deals, whose stock ownership may become diluted when later issues of the same stock hit the market at a cheaper price. Anti-dilution provisions can discourage this from happening by tweaking the conversion price between convertible securities, such as corporate bonds or preferred shares, and common stocks. In this way, anti-dilution clauses can keep an investor’s original ownership percentage intact.

Dilution in Action

• As a simple example of dilution, assume that an investor owns 200,000 shares of a company that has 1,000,000 shares outstanding. The price per share is $5, meaning that the investor has a $1,000,000 stake in a company valued at $5,000,000. The investor owns 20% of the company.
• Next, assume that the company enters a new round of financing and issues 1,000,000 more shares, bringing the total shares outstanding to 2,000,000. Now, at that same $5 per share price, the investor owns a $1,000,000 stake in a $10,000,000 company. Instantly, the investors’ ownership has been diluted to 10%.

Types of Anti-Dilution Provisions

The two common types of anti-dilution clauses are known as “full ratchet” and “weighted average.”

With a full ratchet provision, the conversion price of the existing preferred shares is adjusted downward to the price at which new shares are issued in later rounds. Very simply, if the original conversion price was $5 and in a later round the conversion price is $2.50, the investor’s original conversion price would adjust to $2.50.

The weighted average provision uses the following formula to determine new conversion prices:

• C2 = C1 x (A + B) / (A + C)

Where:

• C2 = new conversion price
• C1 = old conversion price
• A = number of outstanding shares before a new issue
• B = total consideration received by the company for the new issue
• C = number of new shares issued