It is a valuation method used commonly on highly levered companies.

Adjusted Present Value (APV) is commonly used in highly levered companies. The idea behind it is to value the firm as if it has no debt and then add the Present Value (PV) of the net effect of debt.

It was first introduced in 1974 by Steward Myers as a way to analyze the interactions between corporate finance and investment decisions, to make it a general pattern of including debt in valuation models.

Most scholars consider methods like Weighted Average Cost of Capital (WACC) in exceptional cases; on the other hand, APV is a general approach. Therefore, WACC and APV should give the same result in a stable capital structure.

The PV of the net effect of debt is all the benefits received from issuing debt discounted to its present value. Net impacts of debt include debt issuance costs, tax shields, financial distress costs, financial subsidies, etc.

This is commonly used to value companies and projects, especially ones with significant debt, like leveraged buyouts (LBO).

It is helpful because, unlike the Discounted cash flow model (DCF), Adjusted Present Value analyzes the equity side of a company and the debt side separately and sums them at the end.

Therefore, We use the following formula to calculate APV:

Adjusted Present Value = PV of Unlevered Firm + Net effect of debt

## How to calculate Adjusted Present Value?

Calculating APV can be very involved since we are valuing many components (tax shields, cost of debt issuance, cost of financial distress, financial subsidies) separately. In addition, each part can have restrictions that we need to consider.

Take debt issuance cost, for example, we need to calculate legal fees, underwriting fees, and registration fees all into account and each price will vary based on the type of debt we're issuing. Likewise, tax shields and financial subsidies can vary based on the tax laws of the region.

The value of the unleveraged firm can also come with complications as the discount rate depends on many factors. Predicting cash flows can be very involved in some companies, especially ones with a limited track record.

This method calculates the financing effect and equity effect separately. The steps to calculate APV:

1. Calculate the Present Value of the unlevered firm by discounting cashflows by the cost of capital (rU).
2. Calculate the Present Value of the net effect of debt, which can include tax shield, debt issuance cost, financial subsidies, and financial distress.
3. Sum up the results from Step 1 and Step 2 to get the Adjusted Present Value.

## What is APV used for?

APV is commonly used in Leveraged Buyouts since these transactions are heavily financed by debt, and the tax shields are a significant part of the value. It is also useful when trying to understand the effect of debt on a company or a project.

It is commonly known among academics that Adjusted Present Value gives a more accurate and reliable valuation than the DCF most of the time.

Example 1:

To illustrate the use of Adjusted Present Value, let's assume we are assessing an investment in a construction company with a tax rate of 25%.

After discounting projected future cashflows, we valued the unlevered firm at $500,000, and we plan to use a$100,000 loan to finance the purchase with a cost of debt of 10% for 5 years.

You are assuming a risk-free rate of 2%.

Tax shield = Taxable expense * tax rate

= (100,000 * 10%) * 25% / 1.002^1 = $2495.01 ( PV of first-year tax shield) = (100,000 * 10%) * 25% / 1.002^2 =$2490.03 ( PV of second year tax shield)

= (100,000 * 10%) * 25% / 1.002^3 = $2485.06 ( PV of third year tax shield) Net effect of debt =$2495.01 + $2490.03 +$2485.06 = 7470.1

APV = $500,000 +$7470.1 = $507470.1 While the above example is simplified, The main thing you need to take out is how APV separates the cost of equity and debt to estimate a value for the company. ## What is the difference between Adjusted Present Value (APV) and Discounted Cash flow (DCF)? APV and DCF are similar valuation models, except that the Weighted Average Cost of Capital (WACC) in DCF does not capture the financing effects like in APV, where we value the cost of equity and debt separately. WACC vs. APV Weighted Average Cost of Capital (WACC) and Adjusted Present Value (APV) are two approaches to incorporating tax shields into valuation models. We discount Free Cash Flow (FCF) in WACC using the weighted average of after-tax debt costs and equity costs. In contrast, in the APV approach, we value the company as if it were all-equity financed and add the PV of the tax shield of debt and other side effects. As illustrated in this Harvard Business Review piece, APV is considered a more reliable valuation method than WACC because of "less restrictive assumptions" with the former. Think of a blender with many ingredients, and we turn it on; this is the WACC method. On the other hand, with the APV method, we have a recipe, grab the ingredients one by one and then put everything into the blender at the end. The problem with WACC is if we have one rotten ingredient in the blender, then the smoothie is undrinkable, but with APV, we can inspect each element before putting it in the blender. APV gives the investor more to work with because it analyzes equity capital and debt capital separately, allowing the investor to change the assumptions on each side of the capital structure. Another advantage is that it can be information-rich because it breaks down the company's value into components which is especially useful in acquisition scenarios. APV tells the buyer how much of the value of their target company comes from tax shields, streamlining operations, etc. And how much weight the buyer will retain. ## Tax Shields and Adjusted Present Value (APV) Tax Shields are the most important and frequently used component of the "net effect of debt" in the APV equation. They come from the tax deductions accrued from interest expenses. There are several ways to calculate tax shields depending on the region's tax laws and the transaction's nature. The most straightforward situation is when interest expense is deducted from taxable income, calculated as such: Tax shield = Tax-deductible expense* Tax rate Tax shield example In a scenario where a company has$1,000,000 in debt with a 10% cost of debt and is taxed at 40%, we will calculate the tax shield as such:

Interest paid= $1,000,000 * 10% =$100,000

Tax shield = $100,000 * 40% =$40,000

Because the company has $100,000 less in its taxable income that was paid as interest, they have to pay$40,000 less in taxes.

A typical example of a tax shield we see daily is the use of mortgages, where many individuals are eligible to deduct the interest portion of their mortgage, reducing their taxable income.

One must be very careful with the use of tax shields. Although they can add value, they can also destroy it if it increases the risk of financial distress.

## Usability

While Adjusted Present Value is considered a more accurate and reliable valuation method, WACC and DCF are much more prevalent in finance. The reason for that is Calculating APV is a more involved process that costs more time and resources.

In a world where spreadsheets can make all the calculations momentarily, the calculation inconvenience has disappeared, so it is becoming more popular nowadays. Further, the relatively recent popularity has made APV more of an appropriate valuation method today.

## Key Takeaways

• Adjusted Present value is an alternative valuation method where we calculate the cost of capital and cost of debt separately and then get the sum of the two.
• APV is less popular than WACC within the investment business, but it is considered a more reliable method within the academic community.
• Taking tax shields into account is the most common reason for APV to be used, especially in leveraged buyout transactions.

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