Guide to Understanding Adjusted Present Value (APV)

## How to Calculate APV (Step-by-Step)

Since the additional financing benefits are taken into account, the primary benefit of the APV approach is that the economic benefits stemming from financing and tax-deductible interest expense payments (e.g. the “interest tax shield”) are broken out.

The formula used to calculate the adjusted present value (APV) consists of two components:

1. Present Value (PV) of Unlevered Firm
2. Present Value (PV) of Financing Net Effects

First, the present value (PV) of an unlevered firm refers to the present value of the firm, under the pretense that the company has zero debt within its capital structure (i.e. is 100% equity-financed).

By discounting the projected free cash flows (FCFs) to the firm at the unlevered cost of capital – i.e. the cost of equity – the value of the unlevered firm can be estimated.

Next, the financing effects are the net benefits related to debt financing, most notably the interest tax shield. The interest tax shield is an important consideration because interest expense on debt (i.e. the cost of borrowing) is tax-deductible, which reduces the taxes due in the current period.

The interest tax shield can be calculated by multiplying the interest amount by the tax rate.

Interest Tax Shield = Interest Expense x Tax Rate

The APV approach allows us to see whether adding more debt results in a tangible increase (or decrease) in value, as well as enables us to quantify the effects of debt.

Note that since the APV is based on the present-day valuation, both the unlevered firm value and the financing effects must be discounted back to the current date.

## APV Formula

The formula for computing the adjusted present value (APV) is as follows.

Adjusted Present Value (APV) = PV of Unlevered Firm + PV of Financing Effects

## APV vs. WACC

The APV approach shares many similarities to the DCF methodology, however, the major difference lies in the discount rate (i.e. the weighted average cost of capital).

Unlike the WACC, which is a blended discount rate that captures the effect of financing and taxes, the APV attempts to unbundle them for individual analysis and view them as independent factors.

The WACC of a company is approximated by blending the cost of equity and after-tax cost of debt, whereas APV values the contribution of these effects separately.

But despite providing a handful of benefits, APV is used far less often than WACC in practice, and it is predominantly used in the academic setting.

## APV Calculator – Excel Model Template

We’ll now move to a modeling exercise, which you can access by filling out the form below.

Submitting ...

## Step 1. Project Cash Flow and Risk Assumptions

First, let’s list out the assumptions we’ll be using in this hypothetical scenario.

For the cash flow assumptions, assume the project generates the following values:

• Year 0: -\$25m
• Years 1 to 5: \$200m

As for the tax rate, discount rate, and terminal value assumptions, the following assumptions are going to be used:

• Cost of Equity: 12%
• Cost of Debt: 10%
• Tax Rate: 30%
• Terminal Growth Rate: 2.5%

## Step 2. Present Value (PV) of Free Cash Flow Calculation

From our financials, we know that in Year 0, the FCF is \$25m while the forecasted years are kept constant at \$200m. To discount each of the FCFs to the present day, we’ll use the following formula:

• PV of FCF = Free Cash Flow / (1 + Cost of Equity) ^ Period Number

For example, the following formula is used for discounting Year 1’s FCF.

• PV of Year 1 FCF: \$200m / (1 + 12%) ^ 1
• PV of Year 1 FCF: \$179m

Once this process is repeated for each period, we can take the sum of all of the PV of FCFs, which comes out to \$696m.

Then, we’ll estimate the terminal value (TV) – the lump sum value of the project at the end of the explicit forecast period – by using the formula below:

• Terminal Value (TV) = Year 5 Free Cash Flow * (1 + Terminal Growth Rate) / (Cost of Equity – Terminal Growth Rate)
• TV = \$200m * (1 + 2.5%) / (12% – 2.5%)
• TV = \$2,158m

But recall that the APV calculation is as of the present date, thus we must discount this TV amount to the present.

• PV of Terminal Value (TV) = Terminal Value / (1 + Cost of Equity) ^ Period Number
• PV of TV = \$2,158m / (1 + 2.5%) ^ 5
• PV of TV = \$1,224m

To wrap up the 1st part of our APV calculation, the only remaining step is to add the PV of Stage 1 FCFs and PV of TV:

• Sum of PV of FCFs + TV = \$696m + \$1,224m = \$1,920m

## Step 3. Interest Tax Shield Calculation

Now, onto the 2nd stage of our APV calculation. The following interest expense values are going to be assumed to estimate the interest tax shield.

• Year 0: \$40m
• Year 1: \$32m
• Year 2: \$24m
• Year 3: \$16m
• Year 4: \$8m
• Year 5: \$0m

From the list above, we can see the interest expense is reducing down by \$8m each year until reaching \$0m in Year 5. As a result, there will be no debt assumed heading into the terminal value period.

To discount each of the interest tax shield amounts, we’ll do the following two steps:

1. Tax Shield: Multiply the interest expense by the tax rate assumptions to calculate the tax shield
2. PV of Tax Shield: Calculate the present value (PV) of each interest tax shield amount by dividing the tax shield value by (1 + cost of debt) ^ period number

The PV of the interest tax shield can be calculated by discounting the annual tax savings at the pre-tax cost of debt, which we are assuming to be 10% in our example.

Upon doing so, we get \$32m as the sum of the PV of the interest tax shield.

For more complex models, we’d recommend using the “MIN” function in Excel to make sure that the interest tax shield value does NOT exceed the value of the taxes paid in the relevant period.

## Step 4. Adjusted Present Value (APV) Calculation Analysis

In conclusion, we have our two inputs for calculating the APV.

1. The PV of the Stage 1 FCFs and Terminal Value (TV)
2. The PV of the Interest Tax Shield Values

By adding the two together, we compute the adjusted present value (APV) as \$1.95bn. The finished output sheet has been posted below for reference.

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