Adjusted Present Value (APV): Overview, Formula, and Example

Adjusted present value (APV) is a sophisticated method for assessing a company or project's worth compared with traditional techniques. APV separates the valuation process into two components: the first treats the company as if it were financed wholly by equity, and the second takes account of its debt financing.

Suppose you're thinking about buying a house. The basic value of the house comes from its location, size, condition, and so on. That's like the core value of a business: what it's worth based on its operations alone. But when you buy a house, you usually take out a mortgage, right? That mortgage changes things since you can deduct the interest from your taxes, which saves you money. Meanwhile, if you borrow too much, you might struggle with payments and risk foreclosure. These financial effects change the overall value of your house-buying decision.

APV is a way for businesses to look at their value in a similar way. It starts by figuring out what a company is worth just based on its business operations—as if it had no debt at all. Then, it adds or subtracts value based on how the company is financed.

This is important for a few reasons:

1. It helps businesses make smarter decisions about how much debt to take on. They can see clearly how different levels of borrowing will affect the company's value.
2. For investors, it gives a fuller picture of what a company is worth. They can understand how well the business is doing and how its financial choices affect its value.
3. In big financial deals, such as when one company buys another, it helps everyone involved understand the value being exchanged, especially if the agreement changes how much debt the company has.

To get the APV, you first calculate the base case value, which is the NPV of the company or project as if it were financed entirely with equity. This is the fundamental value of the business operations without considering any effects of debt financing. The second part of APV accounts for the PV of all financial side effects resulting from the company or project's debt. These effects primarily include tax shields, which are the tax savings generated by the tax deductibility of interest payments on debt.

However, it also considers the potential costs of financial distress that might arise from high levels of debt, as well as other financing-related impacts like subsidies or hedging.

This allows you to better understand how different capital structure choices affect the company's value. It's particularly useful when a company's debt-to-equity ratio is expected to change significantly over time or when complex financing is involved.

APV can provide a more nuanced approach to valuation than methods like discounted cash flow (DCF) analysis. APV is particularly valuable in situations where a company's capital structure is expected to change significantly, such as in leveraged buyouts (LBOs), projects that are financed, or when evaluating companies with complex debt structures. Its main advantage is separating out the value created by decisions for funding, primarily through tax shields resulting from interest payments on debt.

How To Calculate Adjusted Present Value (APV)

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

The net effect of debt includes tax benefits 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 only applies to one year of interest and tax. The PV of the interest tax shield is thus calculated as follows:

• (Tax Rate × Debt Load × Interest Rate) / Interest Rate.

Here are the steps to determine APV:

1. Calculate the firm's value without debt: Start by valuing the company as if it were financed entirely by equity. This involves projecting future cash flows and discounting them back to their PV using the cost of equity. This step gives you the core operational value of the business.
2. Determine the effects of debt financing: Begin by calculating the PV of tax shields by estimating the future interest tax deductions from debt and discounting them to PV value. Then estimate the costs of financial distress by assessing the potential negative impacts of having debt, such as bankruptcy costs or lost business prospects. Calculate their PV. Combine these to get the net value of debt financing.
3. Sum up the components: Add the value from step 1 (the all-equity firm value) to the net value of debt financing from step 2. This gives you the APV.

For more detailed analyses, you can use Excel, Google Sheets, or similar software to perform these calculations, especially when dealing with several years of projections or complex debt structures.

What Does Adjusted Present Value Tell You?

APV highlights the financial benefits of debt financing, primarily through tax shields from interest payment deductions and potentially from subsidized loans at below-market rates. APV is particularly useful for analyzing leveraged transactions such as LBOs.

A debt-financed project can have a higher value than an all-equity-financed project because debt typically lowers the overall cost of capital. In some cases, debt can transform a project with a negative NPV into one with a positive NPV.

It's important to note the difference in discount rates used by these methods:

• NPV calculations typically use the weighted average cost of capital (WACC) as the discount rate.
• APV, meanwhile, uses the cost of equity as the discount rate for the base case (all-equity) valuation and then separately accounts for debt effects.

This separation allows APV to give a clearer picture of how financing decisions impact overall project or company value, making it especially valuable in situations with changing capital structures or complex financing arrangements.

Example: Finding the Adjusted Present Value (APV)

In a financial projection where a base-case NPV is calculated, the sum of the PV of the interest tax shield is added to obtain the APV. Let's consider the following example:

• Project cost: $1,000,000
• Expected annual free cash flow (FCF): $200,000 for 10 years
• Unlevered (without debt) cost of equity: 12%
• Corporate tax rate: 30%
• Debt financing available: $400,000 at 8% interest rate

Step 1: Calculate the Base Case NPV (Assuming All-Equity Financing)

First, we calculate the PV of the expected FCFs using the unlevered cost of equity as the discount rate:

PV of FCF = $200,000 × (1 - 1 / (1 + 0.12)¹⁰) / 0.12 = $1,130,144

PV of FCF - Initial Investment = Base Case NPV
$1,130,144 - $1,000,000 = $130,144

Step 2: Calculate the Present Value (PV) of the Tax Shield

The annual interest payment on the debt is as follows:


• Annual Interest = $400,000 × 8% = $32,000

The annual tax shield is as follows:

• Annual Tax Shield = $32,000 × 30% = $9,600

To find the PV of the tax shield, we discount this annual benefit using the cost of debt (since the tax shield is as risky as the debt itself):

• PV of Tax Shield = $9,600 × (1 - 1 / (1 + 0.08)¹⁰) / 0.08 = $64,165

Step 3: Calculate the APV

APV = Base Case NPV + PV of Tax Shield
$130,144 + $64,165 = $194,309

The positive APV of $194,309 suggests that the project is valuable and should be undertaken. It's worth more than its cost, even accounting for financing. The example also shows how debt financing can increase a project's value. The tax shield from debt adds significant value ($64,165) to the project.

Managers could use this model to evaluate different financing structures. For example, they could recalculate the APV with different debt levels to find an optimal capital structure for the project While not calculated in this example, a comprehensive APV might also subtract the PV of expected financial distress costs associated with taking on debt.

APV vs. Discounted Cash Flow (DCF)

While the APV is similar to the DCF method, adjusted present cash flow doesn't capture taxes or other financing effects in a weighted average cost of capital (WACC) or other adjusted discount rates.

DCF is a valuation method used to estimate the value of an investment based on its expected future cash flows. It involves projecting future cash flows and discounting them back to their PV using an appropriate discount rate, typically the WACC. The sum of these discounted cash flows represents the estimated value of the investment.

Unlike WACC used in discounted cash flow, the APV seeks to value the effects of the cost of equity and cost of debt separately.

The APV is not used as much in practice as DCF. It's used more by academics, though it's often regarded as giving better, more accurate valuations.

Net Present Value vs. Adjusted Present Value

NPV and APV are both valuation methods used to determine the value of projects or companies. Still, they differ in their approach and application, particularly in handling the effects of debt financing.

In the APV framework, the effects of debt (primarily as a tax shield) are explicitly calculated and added to the base case equity-only valuation. Any adverse effects, such as an increased probability of financial distress, can also be estimated and subtracted.

By separating these effects, APV clarifies how financing decisions impact value, allowing for more informed decisions about capital and financing strategies. This is particularly valuable when financing plays a crucial role in the overall value-creation process, such as in LBOs or projects that are financed.

NPV

• Uses WACC, which blends the cost of equity and cost of debt

• Assumes a constant capital structure over time

• The effects of financing are embedded in the WACC and not easily isolated

APV

• Uses the unlevered cost of equity for the base case valuation, then separately considers debt effects

• Can more easily accommodate changing capital structures and complex financing arrangements

• Clearly shows the value added (or subtracted) by financing decisions

When to Use NPV vs. APV

In general, here's when to use NPV:

• The company or project has a stable capital structure.
• You want a straightforward calculation that's widely understood and accepted.
• The financing effects are expected to be relatively simple or consistent over time.

In general, here's when to use APV:

• The capital structure is expected to change significantly over time.
• There are complex financing arrangements (e.g., subsidized loans financed projects).
• You want to clearly see the value impact of different financing strategies.
• LBOs or other highly leveraged transactions
• Cross-border valuations where tax effects may vary

Is APV More Accurate than NPV?

APV isn't necessarily more accurate than NPV, but it can provide more detailed insights in certain situations. If all the assumptions are correct and consistent, both methods should give similar results. APV's strength is in its transparency, as it clearly shows how much value comes from operations and how much comes from financing decisions. This can make it more useful for decisions, especially when financing plays a big role in the project or company's value. However, APV requires more inputs and calculations, which can introduce more room for error if not done carefully.

Why Is APV Useful in Cross-Border Transactions?

Different countries have varying tax rates and structures, which can significantly impact the value of tax shields from debt. APV allows for these differences to be explicitly modeled. For instance, if a company operates in several countries with different tax rates, the tax shield for each country's operations can be calculated separately using the appropriate tax rate.

This makes APV very useful for multinational corporations or for comparing investments across tax jurisdictions.

How Can APV Be Used by Corporate Managers for Capital Budgeting?

APV can be very helpful in these decisions. By separating the effects of debt financing, APV allows managers to see clearly how different levels of debt affect the company's value. It shows the benefits of debt (like tax savings) as well as potential costs (like increased risk of financial trouble). This clear breakdown can help in finding a balance between too little debt (missing out on tax benefits) and too much debt (increasing financial risk).

Why Use APV Instead of WACC?

APV and the WACC are both methods used in capital budgeting and valuation, but they have distinct characteristics that make them more suitable in different scenarios. While WACC remains a standard in many valuation scenarios, APV offers distinct advantages in situations with changing or complex capital structures, international investments, or when a more detailed understanding of value sources is required. The choice between APV and WACC should be based on the specific characteristics of the company or project being valued and the level of detail needed in the analysis.

The Bottom Line

APV is a variation of NPV that separates a project or company's value into two components: its value if financed entirely by equity and the value added by debt financing, primarily through tax shields. This approach is handy for scenarios with changing capital structures, LBOs, or other complex financing arrangements. While APV requires more detailed calculations than traditional NPV methods, it provides greater transparency in understanding the sources of value creation,