What is Adjusted Present Value (APV)?
The Adjusted Present Value (APV) is defined as the sum of the present value of a project assuming solely equity financing and the PV of all financing-related benefits.
Table of Contents
- How to Calculate Adjusted Present Value (APV)
- Adjusted Present Value Formula (APV)
- APV vs. WACC: What is the Difference?
- Adjusted Present Value Calculator (APV)
- 1. Corporate Finance Project Assumptions
- 2. Present Value of Free Cash Flow Calculation (PV)
- 3. Interest Tax Shield Calculation Analysis
- 4. Adjusted Present Value Calculation Example (APV)
How to Calculate Adjusted Present Value (APV)
Since the additional financing benefits are taken into account, the primary benefit of the adjusted present value (APV) approach is that the economic benefits stemming from financing and tax-deductible interest expense payments are broken out.
The formula used to calculate the adjusted present value (APV) consists of two components:
- Present Value (PV) of Unlevered Firm → 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.
- Present Value (PV) of Financing Net Effects → 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, i.e. the interest “tax shield”.
The interest tax shield can be calculated by multiplying the interest amount by the 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.
Adjusted Present Value Formula (APV)
The formula to calculate the adjusted present value (APV) is as follows.
APV vs. WACC: What is the Difference?
The APV method shares many similarities to a DCF analysis. However, one 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 the components for individual analysis to view them as independent factors.
- WACC → The WACC of a company is approximated by blending the cost of equity and after-tax cost of debt
- Adjusted Present Value (APV) → In contrast, the 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.
Adjusted Present Value Calculator (APV)
We’ll now move to a modeling exercise, which you can access by filling out the form below.
1. Corporate Finance Project Assumptions
Suppose a company is considering undertaking a project that is expected to generate the following cash flows.
- Year 0, Cash Flow = -$25m
- Years 1 to 5, Cash Flow = $200m
As for the tax rate, discount rate, and terminal value, we’ll assume the following in our exercise:
- Cost of Equity = 12%
- Cost of Debt = 10%
- Tax Rate = 30%
- Terminal Growth Rate = 2.5%
2. Present Value of Free Cash Flow Calculation (PV)
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 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%) = $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 = $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
3. Interest Tax Shield Calculation Analysis
In the next part of our APV calculation, the following interest expense values are going to be assumed to estimate the interest tax shield, i.e. the tax savings from interest expense.
- Year 0, Interest Expense = $40m
- Year 1, Interest Expense = $32m
- Year 2, Interest Expense = $24m
- Year 3, Interest Expense = $16m
- Year 4, Interest Expense = $8m
- Year 5, Interest Expense = $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:
- Tax Shield: Multiply the interest expense by the tax rate assumptions to calculate the tax shield
- 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.
4. Adjusted Present Value Calculation Example (APV)
In the final section of our exercise, we will utilize the two inputs from the prior steps to calculate the adjusted present value (APV) of the project.
- The PV of the Stage 1 FCFs and Terminal Value (TV)
- The PV of the Interest Tax Shield Values
In conclusion, we compute the adjusted present value (APV) as $1.95bn by adding the two together. The finished output sheet has been posted below for reference.
