Skip to main content
diversification.com
← Back to A Definitions

Adjusted gross present value

What Is Adjusted Gross Present Value?

Adjusted Gross Present Value (AGPV), more commonly known as Adjusted Present Value (APV), is a corporate finance valuation method that determines the value of a project or firm by first calculating its value assuming it is entirely equity-financed, and then adding or subtracting the present value of various "financing side effects." This approach is particularly useful in situations where a company's capital structure is expected to change significantly over time, or when specific financing arrangements create unique benefits or costs. The core idea behind Adjusted Gross Present Value is to separate the operating value of a business or project from the value contributed by its financing decisions, offering a clear, segmented view of value drivers.

History and Origin

The Adjusted Present Value (APV) method was primarily developed by Stewart C. Myers in 1974, emerging as a response to situations where traditional valuation methods, such as the Weighted Average Cost of Capital (WACC), proved less suitable due to complexities in a firm's financial structure. Myers conceptualized APV as a tool to value investments by first calculating the net present value of a project as if it were financed entirely by equity, and then explicitly adding the present value of the benefits from debt financing, notably the tax shield on interest expense. This method gained prominence, especially in the analysis of leveraged buyouts (LBOs), where the target company's debt levels and, consequently, its capital structure, undergo significant and often predictable changes over the investment horizon. Stewart Myers himself has continued to refine and discuss the applications of APV, particularly concerning real options and the tax implications of financial leverage.3

Key Takeaways

  • Adjusted Gross Present Value (AGPV), or Adjusted Present Value (APV), values a project or firm by summing its unlevered value and the present value of financing side effects.
  • It is particularly effective when a company's capital structure is not constant or predictable, unlike methods that rely on a stable Weighted Average Cost of Capital.
  • The primary financing side effect typically accounted for in APV is the tax shield provided by debt.
  • APV separates investment decisions from financing decisions, allowing for a clearer analysis of each component's contribution to value.
  • This method is widely used in project finance, leveraged buyouts, and complex valuation scenarios.

Formula and Calculation

The Adjusted Gross Present Value (APV) formula is structured into two main components: the present value of the unlevered project (or firm) and the present value of various financing side effects.

The general formula for Adjusted Gross Present Value (APV) is:

APV=NPVunlevered+NPVfinancing_side_effectsAPV = NPV_{unlevered} + NPV_{financing\_side\_effects}

Where:

  • ( NPV_{unlevered} ) = Net Present Value of the project or firm as if it were all-equity financed. This is calculated by discounting the project's Free Cash Flow by the unlevered cost of capital, which reflects the business risk of the project without any financial leverage.
  • ( NPV_{financing_side_effects} ) = Net Present Value of the benefits or costs arising from the financing structure. The most common and significant side effect is the present value of the tax shield from debt. Other potential side effects could include the costs of financial distress, subsidies from debt, or flotation costs of issuing new securities.

The present value of the tax shield from debt is typically calculated as:

PVTaxShield=∑t=1nInterest_Expenset×Corporate_Tax_Ratet(1+rf)tPV_{TaxShield} = \sum_{t=1}^{n} \frac{Interest\_Expense_t \times Corporate\_Tax\_Rate_t}{(1 + r_f)^t}

Where:

  • ( Interest_Expense_t ) = Interest expense in period t.
  • ( Corporate_Tax_Rate_t ) = The corporate tax rate in period t.
  • ( r_f ) = The risk-free rate or the cost of debt, depending on the assumption about the riskiness of the tax shields.
  • ( n ) = The number of periods.

The unlevered Net Present Value ( NPV_{unlevered} ) is calculated by:

NPVunlevered=∑t=1nFCFt(1+r0)t−Initial_InvestmentNPV_{unlevered} = \sum_{t=1}^{n} \frac{FCF_t}{(1 + r_0)^t} - Initial\_Investment

Where:

  • ( FCF_t ) = Free Cash Flow in period t, generated by the project or firm as if it were unlevered.
  • ( r_0 ) = The unlevered cost of capital, which is the discount rate appropriate for an all-equity firm with the same business risk.
  • ( Initial_Investment ) = The initial outlay required for the project.

Interpreting the Adjusted Gross Present Value

Interpreting the Adjusted Gross Present Value (APV) involves understanding its components and what the final value signifies. A positive APV indicates that the project or firm, when considering both its operational profitability and the benefits of its financing structure, is expected to create value for shareholders. Conversely, a negative APV suggests that the project or firm is expected to destroy value.

The strength of APV lies in its ability to isolate the value contributed by financing. By starting with the unlevered value, decision-makers can first assess the fundamental attractiveness of a project based purely on its operational cash flow generation and inherent business risk. The subsequent addition of financing side effects, particularly the tax shield from debt, quantifies the incremental value or cost associated with how the project is funded. This clear separation allows for a more granular understanding of value drivers compared to methods that embed financing effects into the discount rate, such as the Weighted Average Cost of Capital.

Hypothetical Example

Consider a new project that requires an initial investment of $1,000,000. It is expected to generate unlevered Free Cash Flow of $300,000 per year for 5 years. The unlevered cost of capital for this type of project is 10%. The company plans to finance part of the project with a $500,000 loan at an annual interest rate of 6%. The corporate tax rate is 25%.

Step 1: Calculate the Unlevered Present Value

First, calculate the present value of the unlevered free cash flows:

PVunlevered=$300,000(1+0.10)1+$300,000(1+0.10)2+$300,000(1+0.10)3+$300,000(1+0.10)4+$300,000(1+0.10)5PV_{unlevered} = \frac{\$300,000}{(1+0.10)^1} + \frac{\$300,000}{(1+0.10)^2} + \frac{\$300,000}{(1+0.10)^3} + \frac{\$300,000}{(1+0.10)^4} + \frac{\$300,000}{(1+0.10)^5}

Using a present value annuity factor for 5 years at 10% (3.7908):

(PV_{unlevered} = $300,000 \times 3.7908 = $1,137,240 )

Now, calculate the unlevered Net Present Value:

( NPV_{unlevered} = $1,137,240 - $1,000,000 = $137,240 )

Step 2: Calculate the Present Value of the Tax Shield

The annual interest expense on the $500,000 loan at 6% is $30,000 ($500,000 * 0.06).
The annual tax shield is $30,000 * 0.25 = $7,500.
Assuming the tax shield is discounted at the cost of debt (6%), which is a common approach due to its relatively certain nature:

PVTaxShield=$7,500(1+0.06)1+$7,500(1+0.06)2+$7,500(1+0.06)3+$7,500(1+0.06)4+$7,500(1+0.06)5PV_{TaxShield} = \frac{\$7,500}{(1+0.06)^1} + \frac{\$7,500}{(1+0.06)^2} + \frac{\$7,500}{(1+0.06)^3} + \frac{\$7,500}{(1+0.06)^4} + \frac{\$7,500}{(1+0.06)^5}

Using a present value annuity factor for 5 years at 6% (4.2124):

( PV_{TaxShield} = $7,500 \times 4.2124 = $31,593 )

Step 3: Calculate the Adjusted Gross Present Value

APV=NPVunlevered+PVTaxShieldAPV = NPV_{unlevered} + PV_{TaxShield}

( APV = $137,240 + $31,593 = $168,833 )

In this example, the Adjusted Gross Present Value of $168,833 indicates that the project, considering its operational value and the tax benefits from its debt financing, is12