# Adjusted Present Value

Adjusted present value is a valuation method which segregates the impact of financing cash flows such as debt tax shield on a project’s net present value by discounting non-financing cash flows and financing cash flows separately.

The principal difference between equity and debt lies in their tax treatment. Tax laws allow deduction of interest expense in computation of taxable income, but no such advantage is granted in case of dividends paid to common stockholders. This favorable tax treatment of debt results in debt tax shield.

The traditional approach to accommodate the debt tax shield in capital budgeting and valuation is to multiply the pre-tax cost of debt with (1 – tax rate) and calculate an after-tax weighted-average cost of capital (WACC). Under this method, taxes decrease the WACC and increase the present value of cash flows.

Adjusted present value is an alternative to this approach in that it determines present value of cash flows under the assumption that they are all-equity financed and then adds the present value of tax shield (or any other debt side-effects) to arrive at the total present value of a project or a company’s operations.

## Formula

The adjusted present value is the sum of present value of operating cash flows and present value of debt-related cash flow.

Adjusted Present Value = NPV_{L} + PV_{D}

Where NPV_{L} is the net present value of cash flows calculated using the unlevered cost of equity (also called ungeared cost of equity, unlevered cost of capital or opportunity cost of capital).

Unlevered/ungeared cost of equity is the required rate of return for a firm which is solely financed by equity. It can be calculated using the following formula:

Unlevered Cost of Equity = r_{f} + β_{A} × MRP

Where r_{f} is the risk-free rate, β_{A} is the asset beta (also called unlevered beta) and MRP is the market (equity) risk premium i.e. the difference between expected market return and risk-free rate.

Similarly, PV_{D} is the present value of the tax shield. Tax savings in any one period can be calculated as follows:

Tax Savings = T × r_{d} × D

Where T is the tax rate, r_{d} is the pre-tax cost of debt and D is the total value of debt.

Present value of tax savings can be calculated using risk free interest rate when a company is certain it will not default on the debt and that enough pre-tax profit will be available to avail the debt tax credit. In most cases, companies cannot be sure of this, hence the appropriate discount rate is higher than the risk-free rate but lower than unlevered cost of debt. Many practitioners use the gross cost of debt as the appropriate discount rate.

## Example

A project costing $50 million is expected to generate after-tax cash flows of $10 million a year forever. Risk free rate is 3%, asset beta is 1.5, required return on market is 12%, cost of debt is 8%, annual interest costs related to project are $2 million and tax rate is 40%. Calculate the adjusted present value of the project.

### Solution

We need to find the unlevered cost of equity. The easiest method is to use asset beta and capital asset pricing model:

Unlevered Cost of Equity

= Risk-Free Rate + Asset Beta × (Market Return – Risk Free Rate)

= 3% + 1.5 × ( 12 – 3%)

= 16.5%

At discount rate of 16.5%, the present value of cash flows is $60.61 million

$$ \text{PV of Cash Flows}\ =\ \frac{\text{\$10 million}}{\text{0.165}}=\text{\$60.61 million} $$

Since the initial investment is $50 million, the net present value of future cash flows at ungeared cost of equity is $10.61 million.

NPV = $60.61 million - $50 million = $10.61 million

Present value of tax savings = $2 million × 0.4 / 0.08 = $10 million

$$ {\rm \text{PV}} _ \text{D}\ =\ \frac{\text{\$2 million}\ \times \text{0.4}}{\text{8%}}=\text{\$10 million} $$

Now that we have worked out all the intermediate calculations, we can calculate adjusted present value as follows:
APV

= NPV_{L} + PV_{D}

= $10.61 million + $10 million

= $20.61 million

## Decision rule

The decision rule for adjusted present value is the same as net present value: accept positive APV projects and reject negative APV projects. The project discussed in the example has an APV of $20.61 which is positive hence the company should undertake the project.

## Advantages of APV method

Even though the APV method requires a number of intermediate calculations before we reach the ultimate answer, it is worth it due to the following advantages:

- It allows us to see whether adding any more debt is resulting in any increase in value.
- It does not require a constant proportion of debt in a company’s capital structure like the WACC approach. It enables us to model different levels of debt for different stages of valuation. This makes the APV approach especially useful in analysis of projects where debt is repaid in accordance with a fixed schedule.
- Unlike the WACC approach which incorporates only the debt tax shield, the APV method can be used to account for other financing side effects such as equity issue costs, cost of financial distress, etc.

by Obaidullah Jan, ACA, CFA and last modified on