What Is Adjusted Present Value (APV)?

The adjusted present value is the net present value (NPV) of a project or company if financed solely by equity plus the present value (PV) of any financing benefits, which are the additional effects of debt. By taking into account financing benefits, APV includes tax shields such as those provided by deductible interest.

The Formula for APV Is


$\begin{aligned} &\text{Adjusted Present Value = Unlevered Firm Value + NE}\\ &\textbf{where:}\\ &\text{NE = Net effect of debt}\\ \end{aligned}$​Adjusted Present Value = Unlevered Firm Value + NEwhere:NE = Net effect of debt​

The net effect of debt includes tax benefits that are created when the interest on a company’s debt is tax-deductible. This benefit is calculated as the interest expense times the tax rate, and it only applies to one year of interest and tax. The present value of the interest tax shield is therefore calculated as: (tax rate * debt load * interest rate) / interest rate.

How to Calculate Adjusted Present Value (APV)

To determine the adjusted present value:

1. Find the value of the un-levered firm.
2. Calculate the net value of debt financing.
3. Sum the value of the un-levered project or company and the net value of the debt financing.

How to Calculate APV in Excel

An investor can use Excel to build out a model to calculate the net present value of the firm and the present value of the debt.

What Does Adjusted Present Value Tell You?

The adjusted present value helps to show an investor the benefits of tax shields resulting from one or more tax deductions of interest payments or a subsidized loan at below-market rates. For leveraged transactions, APV is preferred. In particular, leveraged buyout situations are the most effective situations in which to use the adjusted present value methodology.

The value of a debt-financed project can be higher than just an equity-financed project, as the cost of capital falls when leverage is used. Using debt can actually turn a negative NPV project into one that’s positive. NPV uses the weighted average cost of capital as the discount rate, while APV uses the cost of equity as the discount rate.

Example of How to Use Adjusted Present Value (APV)

In a financial projection where a base-case NPV is calculated, the sum of the present value of the interest tax shield is added to obtain the adjusted present value.

For example, assume a multi-year projection calculation finds that the present value of Company ABC’s free cash flow (FCF) plus terminal value is $100,000. The tax rate for the company is 30% and the interest rate is 7%. Its $50,000 debt load has an interest tax shield of $15,000, or ($50,000 * 30% * 7%) / 7%. Thus, the adjusted present value is $115,000, or $100,000 + $15,000.

The Difference Between APV and Discounted Cash Flow (DCF)

While the adjusted present value method is similar to the discounted cash flow (DCF) methodology, adjusted present cash flow does not capture taxes or other financing effects in a weighted average cost of capital (WACC) or other adjusted discount rates. Unlike WACC used in discounted cash flow, the adjusted present value seeks to value the effects of the cost of equity and cost of debt separately. The adjusted present value isn’t as prevalent as the discounted cash flow method.

Limitations of Using Adjusted Present Value (APV)

In practice, the adjusted present value is not used as much as the discounted cash flow method. It is more of an academic calculation but is often considered to result in more accurate valuations.

Learn More About Adjusted Present Value (APV)

To dig deeper into calculating the adjusted present value, check out Investopedia’s guide to calculating net present value.

What Is the Arbitrage Pricing Theory (APT)?

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset’s returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced.

The Formula for the Arbitrage Pricing Theory Model Is


$\begin{aligned} &\text{E(R)}_\text{i} = E(R)_z + (E(I) – E(R)_z) \times \beta_n\\ &\textbf{where:}\\ &\text{E(R)}_\text{i} = \text{Expected return on the asset}\\ &R_z = \text{Risk-free rate of return}\\ &\beta_n = \text{Sensitivity of the asset price to macroeconomic} \\ &\text{factor}\textit{ n}\\ &Ei = \text{Risk premium associated with factor}\textit{ i}\\ \end{aligned}$​E(R)i​=E(R)z​+(E(I)−E(R)z​)×βn​where:E(R)i​=Expected return on the assetRz​=Risk-free rate of returnβn​=Sensitivity of the asset price to macroeconomicfactor nEi=Risk premium associated with factor i​

The beta coefficients in the APT model are estimated by using linear regression. In general, historical securities returns are regressed on the factor to estimate its beta.

How the Arbitrage Pricing Theory Works

The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (CAPM). Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.

However, this is not a risk-free operation in the classic sense of arbitrage, because investors are assuming that the model is correct and making directional trades—rather than locking in risk-free profits.

Mathematical Model for the APT

While APT is more flexible than the CAPM, it is more complex. The CAPM only takes into account one factor—market risk—while the APT formula has multiple factors. And it takes a considerable amount of research to determine how sensitive a security is to various macroeconomic risks.

The factors as well as how many of them are used are subjective choices, which means investors will have varying results depending on their choice. However, four or five factors will usually explain most of a security’s return. (For more on the differences between the CAPM and APT, read more about how CAPM and arbitrage pricing theory differ.)

APT factors are the systematic risk that cannot be reduced by the diversification of an investment portfolio. The macroeconomic factors that have proven most reliable as price predictors include unexpected changes in inflation, gross national product (GNP), corporate bond spreads and shifts in the yield curve. Other commonly used factors are gross domestic product (GDP), commodities prices, market indices, and exchange rates.

Example of How Arbitrage Pricing Theory Is Used

For example, the following four factors have been identified as explaining a stock’s return and its sensitivity to each factor and the risk premium associated with each factor have been calculated:

• Gross domestic product (GDP) growth: ß = 0.6, RP = 4%
• Inflation rate: ß = 0.8, RP = 2%
• Gold prices: ß = -0.7, RP = 5%
• Standard and Poor’s 500 index return: ß = 1.3, RP = 9%
• The risk-free rate is 3%

Using the APT formula, the expected return is calculated as:

• Expected return = 3% + (0.6 x 4%) + (0.8 x 2%) + (-0.7 x 5%) + (1.3 x 9%) = 15.2%

What Is Asset/Liability Management?

Asset/liability management is the process of managing the use of assets and cash flows to reduce the firm’s risk of loss from not paying a liability on time. Well-managed assets and liabilities increase business profits. The asset/liability management process is typically applied to bank loan portfolios and pension plans. It also involves the economic value of equity.

Understanding Asset/Liability Management

The concept of asset/liability management focuses on the timing of cash flows because company managers must plan for the payment of liabilities. The process must ensure that assets are available to pay debts as they come due and that assets or earnings can be converted into cash. The asset/liability management process applies to different categories of assets on the balance sheet.

[Important: A company can face a mismatch between assets and liabilities because of illiquidity or changes in interest rates; asset/liability management reduces the likelihood of a mismatch.]

Factoring in Defined Benefit Pension Plans

A defined benefit pension plan provides a fixed, pre-established pension benefit for employees upon retirement, and the employer carries the risk that assets invested in the pension plan may not be sufficient to pay all benefits. Companies must forecast the dollar amount of assets available to pay benefits required by a defined benefit plan.

Assume, for example, that a group of employees must receive a total of $1.5 million in pension payments starting in 10 years. The company must estimate a rate of return on the dollars invested in the pension plan and determine how much the firm must contribute each year before the first payments begin in 10 years.

Examples of Interest Rate Risk

Asset/liability management is also used in banking. A bank must pay interest on deposits and also charge a rate of interest on loans. To manage these two variables, bankers track the net interest margin or the difference between the interest paid on deposits and interest earned on loans.

Assume, for example, that a bank earns an average rate of 6% on three-year loans and pays a 4% rate on three-year certificates of deposit. The interest rate margin the bank generates is 6% – 4% = 2%. Since banks are subject to interest rate risk, or the risk that interest rates increase, clients demand higher interest rates on their deposits to keep assets at the bank.

The Asset Coverage Ratio

An important ratio used in managing assets and liabilities is the asset coverage ratio which computes the value of assets available to pay a firm’s debts. The ratio is calculated as follows:


$\begin{aligned} &\text{Asset Coverage Ratio} = \frac{ ( \text{BVTA} – \text{IA} ) – ( \text{CL} – \text{STDO}) }{ \text{Total Debt Outstanding} } \\ &\textbf{where:} \\ &\text{BVTA} = \text{book value of total assets} \\ &\text{IA} = \text{intangible assets} \\ &\text{CL} = \text{current liabilities} \\ &\text{STDO} = \text{short term debt obligations} \\ \end{aligned}$​Asset Coverage Ratio=Total Debt Outstanding(BVTA−IA)−(CL−STDO)​where:BVTA=book value of total assetsIA=intangible assetsCL=current liabilitiesSTDO=short term debt obligations​

Tangible assets, such as equipment and machinery, are stated at their book value, which is the cost of the asset less accumulated depreciation. Intangible assets, such as patents, are subtracted from the formula because these assets are more difficult to value and sell. Debts payable in less than 12 months are considered short-term debt, and those liabilities are also subtracted from the formula.

The coverage ratio computes the assets available to pay debt obligations, although the liquidation value of some assets, such as real estate, may be difficult to calculate. There is no rule of thumb as to what constitutes a good or poor ratio since calculations vary by industry.

Key Takeaways

• Asset/liability management reduces the risk that a company may not meet its obligations in the future.
• The success of bank loan portfolios and pension plans depend on asset/liability management processes.
• Banks track the difference between the interest paid on deposits and interest earned on loans to ensure that they can pay interest on deposits and to determine what a rate of interest to charge on loans.

[Fast Fact: Asset/liability management is a long-term strategy to manage risks. For example, a home-owner must ensure that they have enough money to pay their mortgage each month by managing their income and expenses for the duration of the loan.]

What Is Antitrust?

Antitrust laws are regulations that encourage competition by limiting the market power of any particular firm. This often involves ensuring that mergers and acquisitions don’t overly concentrate market power or form monopolies, as well as breaking up firms that have become monopolies.

Antitrust laws also prevent multiple firms from colluding or forming a cartel to limit competition through practices such as price fixing. Due to the complexity of deciding what practices will limit competition, antitrust law has become a distinct legal specialization.

Understanding Antitrust

Antitrust laws are the broad group of state and federal laws that are designed to make sure businesses are competing fairly. The “trust” in antitrust refers to a group of businesses that team up or form a monopoly to dictate pricing in a particular market.

Supporters say antitrust laws are necessary and that competition among sellers gives consumers lower prices, higher-quality products and services, more choices, and greater innovation. Most people agree with this concept and the benefits of an open marketplace, although there are some who claim that allowing businesses to compete as they see fit would ultimately give consumers the best prices.

The Antitrust Laws

The Sherman Act, the Federal Trade Commission Act, and the Clayton Act are the key laws that set the groundwork for antitrust regulation. Predating the Sherman Act, the Interstate Commerce Act was also beneficial in establishing antitrust regulations, although it was less influential than some of the others.

Congress passed the Interstate Commerce Act in 1887 in response to growing public demand that railroads be regulated. Among other requirements, the law ordered railroads to charge a fair fee to travelers and post those fees publicly. It was the first example of antitrust law but was less influential than the Sherman Act, passed in 1890.

The Sherman Act outlawed contracts and conspiracies restraining trade and/or monopolizing industries in an attempt to stop competing individuals or businesses fixing prices, dividing markets, or attempting to rig bids. The Sherman Act laid out specific penalties and fines for violating the terms.

In 1914, Congress passed the Federal Trade Commission Act, banning unfair competition methods and deceptive acts or practices. The Clayton Act was also passed in 1914, addressing specific practices that the Sherman Act does not ban. For example, the Clayton Act prohibits appointing the same person to make business decisions for competing corporations.

Special Considerations

The Federal Trade Commission (FTC) and the U.S. Department of Justice (DOJ) are tasked with enforcing federal antitrust laws. In some cases, these two authorities may also work with other regulatory agencies to ensure that certain mergers fit the public interest.

The FTC mainly focuses on segments of the economy where consumer spending is high, including healthcare, drugs, food, energy, technology, and anything related to digital communications. Factors that could spark an FTC investigation include premerger notification filings, certain consumer or business correspondence, congressional inquiries, or articles on consumer or economic subjects.

If the FTC thinks that a law has been violated, the agency will try to stop the questionable practices or find a resolution to the anticompetitive portion of, say, a proposed merger between two competitors. If no resolution is found, the FTC may put out an administrative complaint and/or pursue injunctive relief in federal court.

The FTC might also refer evidence of criminal antitrust violations to the DOJ. The DOJ has the power to impose criminal sanctions and holds sole antitrust jurisdiction in certain sectors, such as telecommunications, banks, railroads, and airlines.

Major Example of Antitrust Law

In January 2023, the DOJ and eight states filed an antitrust lawsuit against Alphabet’s Google, alleging that the search giant has illegal monopolization of the digital advertising business. “Today’s complaint alleges that Google has used anticompetitive, exclusionary, and unlawful conduct to eliminate or severely diminish any threat to its dominance over digital advertising technologies,” the government agency said.

The filing, which seeks to make Google divest parts of its advertising business, alleges that the company has used acquisitions as a strategy for “neutralizing or eliminating” rivals and forces advertisers to use its products by making competitors’ products difficult to use. The complaint claims that the company’s monopolistic practices curtail innovation, raise advertising fees, and prevent small businesses and publishers from growing.

Google’s advertising business has come under fire from critics who argue that the search giant controls both the supply and demand sides of the digital advertising market. The company provides tools that help websites offer ad space and that assist advertisers in placing online ads. The suit alleges that Google’s dominance in the market allows it to pocket 30 cents of each dollar that advertisers spend using its suite of advertising tools.

The lawsuit marks the second federal antitrust complaint against Google in three years. Under the former Trump administration, the DOJ filed a lawsuit in October 2020, accusing the tech giant of using its monopoly to reduce competition through exclusionary agreements. That case is expected to go to trial this fall.

Google responded to the suit, saying the DOJ was attempting to intervene in the free market. “Today’s lawsuit from the Department of Justice attempts to pick winners and losers in the highly competitive advertising technology sector,” Google Global Ads Vice President Dan Taylor said in a statement.

The Bottom Line

Antitrust laws regulate the concentration of economic power to prevent companies from price colluding or creating monopolies. Proponents of antitrust laws argue that they keep consumer prices lower and foster innovation through increased competition. Critics say antitrust regulations intervene in the free market and reduce efficiency.

Antitrust laws are enforced by the FTC and DOJ, with the agencies focusing on areas of the economy that receive significant consumer spending, such as technology, healthcare, pharmaceuticals, and communications. Typically, antitrust investigations arise from premerger notification filings, congressional inquiries, or consumer and business correspondence.