2. Advanced Valuation I Capital Budgeting and Valuation with Leverage

Wacc method

APV method (Adjusted present value)

FTE (Flow-to-equity)

1. The project has average risk

Market risk of the project is equivalent to the average market risk of the firm‘s investment. Project‘s cost of capital can be assessed based on the risk of the firm.

1. The firm‘s debt-equity ratio is constant

Risk of the firm‘s equity and debt, and therefore its weighted average cost of capital, will not fluctuate due to leverage changes.

1. Corporate taxes are the only imperfection

Main effect of leverage on valuation is due to the corporate tax shield. Personal taxes and issuance costs are ignored, other imperfections such as financial distress or agency costs are assumed to be not significant at the level of debt chosen.

For now it is assumed that debt-equity ratio and WACC are constant over time

WACC method takes the interest tax shield into account by using the after tax-cost of capital as discount rate. When the market risk of a project is similar to the average risk of the firm‘s investments, then its cost of capital is equal to WACC.

The WACC incorporates the benefit of the ITS by using the firm’s after-tax cost of capital for debt

Because the WACC incorporates the tax savings from debt, we can compute the levered value of an investment, which is its value including the benefit of interest tax shields given the firm’s leverage policy, by discounting its future free cash flow using the WACC

To summarize, the key steps in the WACC valuation method are as follows:

1. Determine the free cash flow of the investment.

2. Compute the weighted average cost of capital using Eq. 18.1.

3. Compute the value of the investment, including the tax benefit of leverage, by discounting the free cash flow of the investment using the WACC.

In many firms, the corporate treasurer performs the second step, calculating the firm’s WACC. This rate can then be used throughout the firm as the company-wide cost of capital for new investments that are of comparable risk to the rest of the firm and that will not alter the firm’s debt-equity ratio. Employing the WACC method in this way is very simple and straight-forward. As a result, it is the method that is most commonly used in practice for capital budgeting purposes.

The debt capacity Dt is the amount of debt at date t that is required to maintain the firm’s target debt-to-value ration, d

1. Reducing cash

2. Borrowing and increasing debt

Valuation method to determine the levered value of an investment by first calculating its unlevered value and then adding the value of the interest tax shield

The APV method incorporates the value of the interest tax shield directly, rather than by adjusting the discount rate as in the WACC method.

The first step in the APV method is to calculate the value of the FCFs using the project’s cost of capital if it were financed without leverage

The pre-tax WACC represents investors’ required return for holding the entire firm (equity and debt). Thus, it will depend only on the firm’s overall risk. So long as the firm’s leverage choice does not change the overall risk of the firm, the pre-tax WACC must be the same whether the firm is levered or unlevered—recall Figure 15.2 on page 563.

Of course, this argument relies on the assumption that the overall risk of the firm is independent of the choice of leverage. As we showed in Chapter 14, this assumption always holds in a perfect market. It will also hold in a world with taxes whenever the risk of the tax shield is the same as the risk of the firm (so the size of the tax shield will not change the overall riskiness of the firm). This chapter’s appendix shows that the tax shield will have the same risk as the firm if the firm maintains a target leverage ratio. A target leverage ratio means that the firm adjusts its debt proportionally to the project’s value, or its cash flows, so that a constant debt-equity ratio is a special case.

When the firm maintains a target leverage ratio, its future interest tax shields have similar risk to the project’s cash flows, so they should be discounted at the project’s unlevered cost of capital.

To determine the value of a levered investment using the APV method, we proceed as follows:

1. Determine the investment’s value without leverage, V U, by discounting its free cash flows at the unlevered cost of capital, rU. With a constant debt-equity ratio, rU may be estimated using Eq. 18.6.

2. Determine the present value of the interest tax shield.

a. Determine the expected interest tax shield: Given expected debt Dt on date t, the interest tax shield on date t + 1 is tc rD Dt

b. Discount the interest tax shield. If a constant debt-equity ratio is maintained, using rU is appropriate.

3. Add the unlevered value, V U, to the present value of the interest tax shield to determine the value of the investment with leverage, V L.

Despite its complexity, the APV method has some advantages. As we shall see in Section 18.6, it can be easier to apply than the WACC method when the firm does not maintain a constant debt-equity ratio. It also provides managers with an explicit valuation of the tax shield itself. The APV approach also explicitly values market imperfections and therefore allows managers to measure their contribution to value.

In the WACC and APV methods, we value a project based on its free cash flow, which is computed ignoring interest and debt payments. Some students find these methods confusing because, if the goal is to determine the benefit of the project to shareholders, it seems to them that we should focus on the cash flows that shareholders will receive.

In the flow-to-equity (FTE) valuation method, we explicitly calculate the free cash flow available to equity holders after taking into account all payments to and from debt holders. The cash flows to equity holders are then discounted using the equity cost of capital.8 Despite this difference in implementation, the FTE method produces the same assessment of the project’s value as the WACC or APV methods.

The first step in the FTE method is to determine the project’s free cash flow to equity (FCFE). The FCFE is the free cash flow that remains after adjusting for interest payments, debt issuance, and debt repayment.

The project’s free cash flow to equity shows the expected amount of additional cash the firm will have available to pay dividends (or conduct share repurchases) each year. Because these cash flows represent payments to equity holders, they should be discounted at the project’s equity cost of capital.

The value of the project’s FCFE represents the gain to shareholders from the project. It is identical to the NPV we computed using the WACC and APV methods.

The key steps in the flow-to-equity method for valuing a levered investment are as follows:

1. Determine the free cash flow to equity of the investment using Eq. 18.9.

2. Determine the equity cost of capital, rE.

3. Compute the contribution to equity value, E, by discounting the free cash flow to equity using the equity cost of capital.

Applying the FTE method was simplified in our example because the project’s risk and leverage matched the firm’s, and the firm’s equity cost of capital was expected to remain constant. Just as with the WACC, however, this assumption is reasonable only if the firm maintains a constant debt-equity ratio. If the debt-equity ratio changes over time, the risk of equity—and, therefore, its cost of capital—will change as well.

The FTE method can offer an advantage when calculating the value of equity for the entire firm if the firm’s capital structure is complex and the market values of other securities in the firm’s capital structure are not known. In that case, the FTE method allows us to compute the value of equity directly. In contrast, the WACC and APV methods compute the firm’s enterprise value, so that a separate valuation of the other components of the firm’s capital structure is needed to determine the value of equity. Finally, by emphasizing a project’s implications for the firm’s payouts to equity, the FTE method may be viewed as a more transparent method for discussing a project’s benefit to shareholders—a managerial concern.

FTE method offers some advantages:

• May be simpler to use when calculating the value of equity for the entire firm if the firm‘s capital structure is complex and the market values of other securities in the firm‘s capital structure are not known

• May be viewed as a more transparent method for discussing a project‘s benefit to shareholders by emphasizing a project‘s implication for equity

• FTE method has a disadvantage, namely we have to compute the project‘s debt capacity to determine the interest and net borrowing before we can make the capital budgeting decision.

Thus far we have assumed that both the risk and the leverage of the project under consideration matched those characteristics for the firm as a whole. This allowed us to assume that the cost of capital for a project matched the cost of capital of the firm.

• In the real world, a specific project may have different market risk than the average project for the firm.

• In addition, different projects may vary in the amount of leverage they will support.

Incremental leverage refers to the additional debt taken on by a company to finance a specific project or investment. It represents the increase in the company's overall debt level resulting from the funding requirements of the project

To determine the cost of capital for a project, the incremental financing that results if the firm takes on the project needs to be calculated

• In other words, what is the change in the firm‘s total debt (net of cash) with the project versus without the project (Note: The incremental financing of a project doesn‘t necessarily correspond to the financing that is directly tied to the project)

To determine the equity or weighted average cost of capital for a project, we need to know the amount of debt to associate with the project. For capital budgeting purposes, the project’s financing is the incremental financing that results if the firm takes on the project. That is, it is the change in the firm’s total debt (net of cash) with the project versus without the project.

1. Cash is negative debt

2. A fixed equity payout (and issuance) policy implies 100% debt financing of the project

3. Optimal leverage depends on project and firm characteristics

4. Safe cash flows of a project can be 100% debt financed

Up to this point, it has been assumed the firm wishes to maintain a constant debt-equity ratio

• When we relax the assumption of a constant debt-equity ratio, the equity cost of capital and WACC for a project will change over time as the debt-equity ratio changes

• In this situation, WACC and FTE methods are difficult to implement, while the APV method is relatively straightforward to use

Two alternative leverage policies will now be examined:

1. Constant interest coverage (Zinsdeckungsgrad)

2. Predetermined debt levels

When a firm keeps its interest payments equal to a target fraction of its FCFs, we say it has a constant interest coverage ratio

If the target fraction is k, then:

Interest paid in year t = k*FCFt

To implement the APV approach, the PV of the ITS under this policy needs to be computed. Because the ITS is proportional to the project’s FCF, it has the same risk as the project’s cash flow and so should be discounted at the same rate - that is the unlevered cost of capital.

With a constant interest coverage policy, the value of the ITS is proportional to the project’s unlevered value

if the investment’s free cash flows are expected to grow at a constant rate, then the assumption of constant interest coverage and a constant debt-equity ratio are equivalent, as in the following example.

Rather than set debt according to a target debt-equity ratio or interest coverage level, a firm may adjust its debt according to a fixed schedule that is known in advance

When the debt levels are known in advance, it is straightforward to compute the interest payments and the corresponding tax shield the firm will obtain. The question is, at what rate should we discount this tax shield to determine the present value? In Section 18.3, we used the project’s unlevered cost of capital because the amount of debt—and, therefore, the tax shield—fluctuated with the value of the project itself and so had similar risk. However, with a fixed debt schedule, the amount of the debt will not fluctuate. In this case, the tax shield is less risky than the project, so it should be discounted at a lower rate.

When debt levels are set according to a fixed schedule, we can discount the predetermined interest tax shields using the debt cost of capital

A Cautionary Note: When debt levels are predetermined, the firm will not adjust its debt based on fluctuations to its cash flows or value according to a target leverage ratio. Because the risk of the interest tax shield now differs from the risk of the cash flows, the overall risk of the firm depends on leverage. As a result, the firm’s pre-tax WACC no longer coincides with its unlevered cost of capital, and Eq. 18.6, Eq. 18.10, and Eq. 18.11 do not apply.

We have introduced three methods for valuing levered investments: WACC, APV, and FTE.

• When used consistently, each method produces the same valuation for the investment.

• Typically, the WACC method is the easiest to use when the firm will maintain a fixed debt-to-value ratio over the life of the investment.

• For alternative leverage policies, the APV method is usually the simplest approach.

• The FTE method is typically used only in complicated settings where the values in the firm‘s capital structure or the interest tax shield are difficult to determine.

We adjust the valuation to account for imperfections such as issuance costs, security mispricing, and financial distress and agency costs

When a firm takes out a loan or raises capital by issuing securities, the banks that provide the loan or underwrite the sale of the securities charge fees. Table 18.9 lists the typical fees for common transactions. The fees associated with the financing of the project are a cost that should be included as part of the project’s required investment, reducing the NPV of the project.

This calculation presumes the cash flows generated by the project will be paid out. If instead they will be reinvested in a new project, and thereby save future issuance costs, the present value of these savings should also be incorporated and will offset the current issu- ance costs.

If so, the NPV of the transaction, which is the difference between the actual money raised and the true value of the securities sold, should be included when evaluating the decision. For example, if the financing of the project involves an equity issue, and if management believes that the equity will sell at a price that is less than its true value, this mispricing is a cost of the project for the existing shareholders. It can be deducted from the project NPV in addition to other issuance costs.

When the debt level—and, therefore, the probability of financial distress—is high, the expected free cash flow will be reduced by the expected costs associated with financial distress and agency problems.

Financial distress and agency costs also have consequences for the cost of capital. For example, financial distress is more likely to occur when economic times are bad. As a result, the costs of distress cause the value of the firm to fall further in a market downturn. Financial distress costs, therefore, tend to increase the sensitivity of the firm’s value to market risk, further raising the cost of capital for highly levered firms.