- September 20, 2020
- Posted by: Ramkumar
- Category: Mergers And Acquisitions

## Valuing a Company by Adjusted Present Value (APV) Method

In the last article, I had presented a step-by-step model for analyzing and valuing a company, including technical details for adequately measuring and evaluating the drivers of value. I concentrated mainly on two: enterprise discounted cash flow (DCF) and discounted economic profit. Both the enterprise DCF and economic-profit models rely on WACC; however, WACC models serve best when a business keeps a comparatively steady debt-to-value ratio. If a company’s debt-to-value ratio shifts, WACC-based models can still produce reliable results but are challenging to execute accurately. In such instances, I suggest an alternative to WACC-based models: adjusted present value (APV). APV discounts the same free cash flows as the enterprise DCF model but employs the unlevered cost of equity as the discount rate (without the tax advantage of debt). It then values the tax benefits associated with debt and sums them to the all-equity value to ascertain the total enterprise value. In this post, i present a step by step approach on valuing a company by Adjusted Present Value (APV) method. When appropriately applied, the APV model results in an identical value as the enterprise DCF value.

### Adjusted Present Value Method

When developing an enterprise DCF or economic-profit valuation, most analysts discount all future flows at a fixed WACC. However, using a regular WACC considers the firm operates its capital structure to a target debt-to-value ratio.

In most conditions, the debt increases with firm value. However, assume the firm intended to adjust its capital structure significantly, as in a leveraged buyout. Admittedly, firms with a large proportion of debt usually pay it down as cash flow improves, reducing their future debt-to-value ratios. In these situations, a valuation based on a constant WACC would exaggerate the tax shield’s value. Although the WACC can be modified annually to control a changing capital structure, the process is complicated. Hence, we use a flexible valuation model: adjusted present value (APV).

The APV model classifies the value of operations into two segments: the value of operations assuming 100% equity-financed and the value of tax shields that emerge from debt financing:

**APV = Enterprise value assuming 100% equity funded + Present Value of Tax Shields**

The APV valuation model develops straight from the pedagogy of economists Franco Modigliani and Merton Miller, who stated that in a market with no taxes (among other things), a firm’s choice of financial structure will not change the value of its financial assets. Only market imperfections, such as taxes and distress costs, impact enterprise value.

When developing a valuation model, it is natural to overlook these teachings. To comprehend this, assume a firm (in a world with no taxes) with a 50/50 mix of debt and equity. If the company’s debt has an expected return of 5%, and the firm’s equity has an expected return of 15%, its WACC would be 10%. Assume the company chooses to issue more debt, employing the proceeds to repurchase shares. Considering the cost of debt is lower than the cost of equity, it would seem that issuing debt to retire equity should reduce the WACC, boosting the enterprise value.

This line of reasoning is flawed, though. In a world without taxes, a shift in capital structure would not improve the cash flow generated by operations, nor the risk of those cash flows. Consequently, neither the firm’s enterprise value nor its WACC would vary. So why would we believe it would? When adding debt, we altered the weights, but we failed to raise the equity cost accurately. Since debt payments have precedence over cash flows to equity, adding leverage raises equity holders’ risk. When leverage increases, the stockholders command a higher return. Modigliani and Miller proposed that this increase would negate the change in weights. In actuality, taxes play a role in deciding capital structure. Since interest is tax-deductible, profitable firms can reduce taxes by increasing debt. However, assume the firm relies a lot on debt. In that event, its customers and suppliers may worry about financial distress and be unwilling to do business with the firm, reducing future cash flow (academics describe this deadweight costs). Rather than model the impact of capital-structure changes in the WACC, APV explicitly measures and evaluates the cash flow effects independently.

To build an APV valuation, value the company as if it is 100% equity by discounting FCF by the unlevered cost of equity. To this value, add any value generated by the firm’s use of debt.

### Valuing FCF at Unlevered Cost of Equity

When valuing a business using the APV, clearly separate the unlevered value of operations (Vo) from any value generated by financing, such as tax shields (Vtax). For a firm with debt (D) and equity (E), this connection is as follows:

**Vo + Vtax = D + E**

The other consequence of Modigliani and Miller’s work is that the absolute risk of the company’s assets, real and financial, must match the entire risk of the financial claims against those assets. Consequently, in equilibrium, the blended cost of capital for operating assets (ko) and financial assets (ktax) must match the blended cost of capital for debt (kd) and equity (ke):

**(Vo/V) Ko + (Vtax/V)Ktax = (D/V)Ko + (E/V)Ke**

In the corporate-finance research, we combine Modigliani and Miller’s two equations to determine the cost of equity (ke) to illustrate the relationship between leverage and equity.

Solving for Ke, we get:

**ke = Ko + (D/E) (Ko-Kd) – (Vtax/E) (Ko-Ktax)**

As the above equation shows, the cost of equity depends on the unlevered cost of equity, or the cost of equity when the company has no debt, plus a premium for leverage, less a tax reduction. See that when a firm has no debt (D = 0) and, consequently, no tax shields (Vtax = 0), ke equals Ko.

If you assume the firm will maintain its debt-to-value ratio to a target level (the firm’s debt will rise with the business), then the value of the tax shields will follow the value of the operating assets. Thus, tax shields’ risk will mirror the risk of operating assets (Ktax = Ko). When ktax = Ko then,

**Ke= Ko + (D/E) (Ko – Kd)**

The unlevered cost of equity can get reverse-engineered by applying the observed cost of equity, debt, and the market debt-to-equity ratio.

### Valuing Tax Shields and Other Capital Structure Effects

To build an APV valuation, forecast, and discount capital structure side effects like tax shields, security issuance costs, and distress costs. A firm with significant leverage may not entirely utilize the tax shields as it may not have adequate profits to shield. If the firm faces a high likelihood of default, you must model expected tax shields, rather than the estimated tax shields based on agreed interest payments. To do this, reduce every guaranteed tax shield by the aggregate probability of default.