КФ / Лекции / Brealey Myers - Principles Of Corporate Finance 7th Ed (eBook)

Cost of debt (rD)

Debt–equity ratio (D/E )

of equity rE is less, because financial risk is reduced. The cost of debt may be lower too.

Figure 19.1 plots WACC and the costs of debt and equity as a function of the debt–equity ratio. The flat line is r, the opportunity cost of capital. Remember, this is the expected rate of return that investors would want from the project if it were all-equity-financed. The opportunity cost of capital depends only on business risk and is the natural reference point.

Suppose Sangria or the perpetual crusher project were all-equity-financed (D/V 0). At that point WACC equals cost of equity, and both equal the opportunity cost of capital. Start from that point in Figure 19.1. As the debt ratio increases, the cost of equity increases, because of financial risk, but notice that WACC declines. The decline is not caused by use of “cheap” debt in place of “expensive” equity. It falls because of the tax shields on debt interest payments. If there were no corporate income taxes, the weighted-average cost of capital would be constant, and equal to the opportunity cost of capital, at all debt ratios. We showed this in Chapters 9 and 17.

Figure 19.1 shows the shape of the relationship between financing and WACC, but we have numbers only for Sangria’s current 40 percent debt ratio. We want to recalculate WACC at a 20 percent ratio.

Here is the simplest way to do it. There are three steps.

Step 1 Calculate the opportunity cost of capital. In other words, calculate WACC and the cost of equity at zero debt. This step is called unlevering the WACC. The simplest unlevering formula is

Opportunity cost of capital r rD D/V rE E/V

This formula comes directly from Modigliani and Miller’s proposition I (see Section 17.1). If taxes are left out, the weighted-average cost of capital equals the opportunity cost of capital and is independent of leverage.

Step 1. Calculate the unlevered opportunity cost of capital

r .0721.3732 .1291.6272 .108

Step 2. Assume that the cost of debt increases to 8 percent at 45 percent debt. The cost of equity is

rE .108 1.108 .080245/55 .13

Step 3. Recalculate WACC. If the marginal tax rate stays at 35 percent,

WACC .08011 .352.45 .1301.552 .095 or 9.5%

The cost of capital drops by more than one half percentage point. Is this a great deal? Not as good as it looks. In these simple calculations, the cost of capital drops as financial leverage increases, but only because of corporate interest tax shields. In Chapter 18 we reviewed all the reasons why just focusing on corporate interest tax shields overstates the advantages of debt. For example, costs of financial distress encountered at high debt levels appear nowhere in the WACC formula or in the standard formulas relating the cost of equity for leverage.14

Unlevering and Relevering Betas

Our three-step procedure (1) unlevers and then (2) relevers the cost of equity. Some financial managers find it convenient to (1) unlever and then (2) relever the equity beta. Given the beta of equity at the new debt ratio, the cost of equity is determined from the capital asset pricing model. Then WACC is recalculated.

The formula for unlevering beta was given in Section 9.2.

asset debt1D/V 2 equity1E/V 2

This equation says that the beta of a firm’s assets is revealed by the beta of a portfolio of all of the firm’s outstanding debt and equity securities. An investor who bought such a portfolio would own the assets free and clear and absorb only business risks.

The formula for relevering beta closely resembles MM’s proposition II, except that betas are substituted for rates of return:

equity asset 1 asset debt 2D/E

The Importance of Rebalancing

The formulas for WACC and for unlevering and relevering expected returns are simple, but we must be careful to remember underlying assumptions. The most important point is rebalancing.

Calculating WACC for a company at its existing capital structure requires that the capital structure not change; in other words, the company must rebalance its capital structure to maintain the same market-value debt ratio for the relevant future. Take Sangria Corporation as an example. It starts with a debt-to-value ratio of 40 percent and a market value of $125 million. Suppose that Sangria’s products do unexpectedly

14Some financial managers and analysts argue that the costs of debt and equity increase rapidly at high debt ratios because of costs of financial distress. This in turn would cause the WACC curve in Figure 19.1 to flatten out, and finally increase, as the debt ratio climbs. For practical purposes, this can be a sensible end result. However, formal modeling of the interactions between the cost of financial distress and the expected rates of return on the company’s securities is not easy.

well in the marketplace and that market value increases to $150 million. Rebalancing means that it will then increase debt to .4 150 $60 million,15 thus regaining a 40 percent ratio. If market value instead falls, Sangria would have to pay down debt proportionally.

Of course real companies do not rebalance capital structure in such a mechanical and compulsive way. For practical purposes, it’s sufficient to assume gradual but steady adjustment toward a long-run target. But if the firm plans significant changes in capital structure (for example, if it plans to pay off its debt), the WACC formula won’t work. In such cases, you should turn to the APV method, which we describe in the next section.

Our three-step procedure for recalculating WACC makes a similar rebalancing assumption.16 Whatever the starting debt ratio, the firm is assumed to rebalance to maintain that ratio in the future. The unlevering and relevering in steps 1 and 2 also ignore any impact of investors’ personal income taxes on the costs of debt and equity.17

19.4 ADJUSTED PRESENT VALUE

We now take a different tack. Instead of messing around with the discount rate, we explicitly adjust cash flows and present values for costs or benefits of financing. This approach is called adjusted present value, or APV.

The adjusted-present-value rule is easiest to understand in the context of simple numerical examples. We start by analyzing a project under base-case assumptions and then consider possible financing side effects of accepting the project.

The Base Case

The APV method begins by valuing the project as if it were a mini-firm financed solely by equity. Consider a project to produce solar water heaters. It requires a $10 million investment and offers a level after-tax cash flow of $1.8 million per year for 10 years. The opportunity cost of capital is 12 percent, which reflects the project’s business risk. Investors would demand a 12 percent expected return to invest in the mini-firm’s shares.

Thus the mini-firm’s base-case NPV is

10 1.8

NPV 10 ta1 11.122t $.17 million, or $170,000

Considering the project’s size, this figure is not much greater than zero. In a pure MM world where no financing decision matters, the financial manager would lean toward taking the project but would not be heartbroken if it were discarded.

15The proceeds of the additional borrowing would be paid out to shareholders or used, along with additional equity investment, to finance Sangria’s growth.

16Similar, but not identical. The basic WACC formula assumes that rebalancing occurs at the end of each period. The unlevering and relevering formulas used in steps 1 and 2 of our three-step procedure are exact only if rebalancing is continuous so that the debt ratio stays constant day-to-day and week-to- week. However, the errors introduced from annual rebalancing are very small and can be ignored for practical purposes.

17The response of the cost of equity to changes in financial leverage can be affected by personal taxes. This is not covered here and is rarely adjusted for in practice.

Issue Costs

But suppose that the firm actually has to finance the $10 million investment by issuing stock (it will not have to issue stock if it rejects the project) and that issue costs soak up 5 percent of the gross proceeds of the issue. That means the firm has to issue $10,526,000 in order to obtain $10,000,000 cash. The $526,000 difference goes to underwriters, lawyers, and others involved in the issue process.

The project’s APV is calculated by subtracting the issue cost from base-case NPV:

APV base-case NPV issue cost

170,000 526,000 $356,000

The firm would reject the project because APV is negative.

Additions to the Firm’s Debt Capacity

Consider a different financing scenario. Suppose that the firm has a 50 percent target debt ratio. Its policy is to limit debt to 50 percent of its assets. Thus, if it invests more, it borrows more; in this sense investment adds to the firm’s debt capacity.18 Is debt capacity worth anything? The most widely accepted answer is yes because of the tax shields generated by interest payments on corporate borrowing. (Look back to our discussion of debt and taxes in Chapter 18.) For example, MM’s theory states that the value of the firm is independent of its capital structure except

for the present value of interest tax shields:

Firm value value with all-equity financing PV1tax shield2

This theory tells us to compute the value of the firm in two steps: First compute its base-case value under all-equity financing, and then add the present value of taxes saved due to a departure from all-equity financing. This procedure is like an APV calculation for the firm as a whole.

We can repeat the calculation for a particular project. For example, suppose that the solar heater project increases the firm’s assets by $10 million and therefore prompts it to borrow $5 million more. Suppose that this $5 million loan is repaid in equal installments, so that the amount borrowed declines with the depreciating book value of the solar heater project. We also assume that the loan carries an interest rate of 8 percent. Table 19.1 shows how the value of the interest tax shields is calculated. This is the value of the additional debt capacity contributed to the firm by the project. We obtain APV by adding this amount to the project’s NPV:

APV base-case NPV PV1tax shield2170,000 576,000 $746,000

With these numbers, the solar heater project looks like a “go.” But notice the differences between this APV calculation and an NPV calculated with a WACC used as the discount rate. The APV calculation assumes debt equal to 50 percent of book value, paid down on a fixed schedule. NPV using WACC assumes debt is a constant fraction of market value in each year of the project’s life. Since the project’s value will inevitably turn out higher or lower than expected, using WACC also assumes that

18Debt capacity is potentially misleading because it seems to imply an absolute limit to the amount the firm is able to borrow. That is not what we mean. The firm limits borrowing to 50 percent of assets as a rule of thumb for optimal capital structure. It could borrow more if it wanted to run increased risks of costs of financial distress.

T A B L E 1 9 . 1

Calculating the present value of interest tax shields on debt supported by the solar heater project (dollar figures in thousands).

Assumptions:

1.Marginal tax rate Tc .35; tax shield Tc interest.

2.Debt principal is repaid at end of year in ten $500,000 installments.

3.Interest rate on debt is 8 percent.

4.Present value is calculated at the 8 percent borrowing rate. The assumption here is that the tax shields are just as risky as the interest payments generating them.

future debt levels will be increased or reduced as necessary to keep the future debt ratio constant.

APV can be used when debt supported by a project is tied to the project’s book value or has to be repaid on a fixed schedule. For example, Kaplan and Ruback used APV to analyze the prices paid for a sample of leveraged buyouts (LBOs). LBOs are takeovers, typically of mature companies, financed almost entirely with debt. However, the new debt is not intended to be permanent. LBO business plans call for generating extra cash by selling assets, shaving costs, and improving profit margins. The extra cash is used to pay down the LBO debt. Therefore you can’t use WACC as a discount rate to evaluate an LBO because its debt ratio will not be constant.

APV works fine for LBOs. The company is first evaluated as if it were all-equity- financed. That means that cash flows are projected after tax, but without any interest tax shields generated by the LBO’s debt. The tax shields are then valued separately. The debt repayment schedule is set down in the same format as Table 19.1 and the present value of interest tax shields is calculated and added to the allequity value. Any other financing side effects are added also. The result is an APV valuation for the company.19 Kaplan and Ruback found that APV did a pretty good job explaining prices paid in these hotly contested takeovers, considering that not all the information available to bidders had percolated into the public domain. Kaplan and Ruback were restricted to publicly available data.

19Kaplan and Ruback actually used “compressed” APV, in which all cash flows, including interest tax shields, are discounted at the opportunity cost of capital. S. N. Kaplan and R. S. Ruback, “The Valuation of Cash Flow Forecasts: An Empirical Analysis,” Journal of Finance 50 (September 1995), pp. 1059–1093.

The Value of Interest Tax Shields

In Table 19.1, we boldly assume that the firm can fully capture interest tax shields of $.35 on every dollar of interest. We also treat the interest tax shields as safe cash inflows and discount them at a low 8 percent rate.

The true present value of the tax shields is almost surely less than $576,000:

•You can’t use tax shields unless you pay taxes, and you don’t pay taxes unless you make money. Few firms can be sure that future profitability will be sufficient to use up the interest tax shields.

•The government takes two bites out of corporate income: the corporate tax and the tax on bondholders’ and stockholders’ personal income. The corporate tax favors debt; the personal tax favors equity.

•A project’s debt capacity depends on how well it does. When profits exceed expectations, the firm can borrow more; if the project fails, it won’t support any debt. If the future amount of debt is tied to future project value, then the interest tax shields given in Table 19.1 are estimates, not fixed amounts.

In Chapter 18, we argued that the effective tax shield on interest was probably not 35 percent (Tc .35) but some lower figure, call it T*. We were unable to pin down an exact figure for T*.

Suppose, for example, that we believe T* .25. We can easily recalculate the APV of the solar heater project. Just multiply the present value of the interest tax shields by 25/35. The bottom line of Table 19.1 drops from $576,000 to 576,000125/352 $411,000. APV drops to

APV base-case NPV PV1tax shield2170,000 411,000 $581,000

PV(tax shield) drops still further if the tax shields are treated as forecasts and discounted at a higher rate. Suppose the firm ties the amount of debt to actual future project cash flows. Then the interest tax shields become just as risky as the project and should be discounted at the 12 percent opportunity cost of capital. PV(tax shield) drops to $362,000 at T* .25.

Review of the Adjusted-Present-Value Approach

If the decision to invest in a capital project has important side effects on other financial decisions made by the firm, those side effects should be taken into account when the project is evaluated. They include interest tax shields on debt supported by the project (a plus), any issue costs of raising financing for the project (a minus), or perhaps other side effects such as the value of a government-subsidized loan tied to the project.

The idea behind APV is to divide and conquer. The approach does not attempt to capture all the side effects in a single calculation. A series of present value calculations is made instead. The first establishes a base-case value for the project: its value as a separate, all-equity-financed mini-firm. Then each side effect is traced out, and the present value of its cost or benefit to the firm is calculated. Finally, all the present values are added together to estimate the project’s total contribution to the value of the firm. Thus, in general,

Project APV base-case NPV sum of the present values of the side effects of accepting the project

tion that the only financing side effects are the interest tax shields on debt supported by the perpetual crusher project, and we consider corporate taxes only. (In other words, T* Tc .) As in Section 19.1, we assume that the perpetual crusher is an exact match, in business risk and financing, to its parent, the Sangria Corporation.

Base-case NPV is found by discounting after-tax project cash flows of $1.355 million at the opportunity cost of capital r of 12 percent and then subtracting the $12.5 million outlay. The cash flows are perpetual, so

Base-case NPV 12.5 1.355.12 $1.21 million

Thus the project would not be worthwhile with all-equity financing. But it actually supports debt of $5 million. At an 8 percent borrowing rate (rD .08) and a 35 percent tax rate (Tc .35), annual interest tax shields are .35 .08 5 .14, or $140,000.

What are those tax shields worth? It depends on the financing rule the company follows. There are two common rules:

•Financing Rule 1: Debt fixed. Borrow a fraction of initial project value and make any debt repayments on a predetermined schedule. We followed this rule in Table 19.1.

•Financing Rule 2: Debt rebalanced. Adjust the debt in each future period to keep it at a constant fraction of future project value.

What do these rules mean for the perpetual crusher project? Under Financing Rule 1, debt stays at $5 million come hell or high water, and interest tax shields stay at $140,000 per year. The tax shields are tied to fixed interest payments, so the 8 percent cost of debt is a reasonable discount rate:

PV1tax shields, debt fixed2 140,000 $1,750,000, or $1.75 million

.08

APV base-case NPV PV1tax shield21.21 1.75 $.54 million

If the perpetual crusher were financed solely by equity, project value would be $11.29 million. With fixed debt of $5 million, value increases by PV(tax shield) to 11.29 1.75 $13.04 million.

Under Financing Rule 2, debt is rebalanced to 40 percent of actual project value. That means future debt levels are not known at the start of the project. They shift up or down depending on the success or failure of the project. Interest tax shields therefore pick up the project’s business risk.

If interest tax shields are just as risky as the project, they should be discounted at the project’s opportunity cost of capital, in this case 12 percent.

PV1tax shields, debt rebalanced2 140,000 1, 170,000, or $1.17 million

.12

APV 1debt rebalanced2 1.21 1.17 $.04 million

We have now valued the perpetual crusher project three different ways:

1.APV (debt fixed) $.54 million.

2.APV (debt rebalanced) $.04 million.

3.NPV (discounting at WACC) $0 million.

The first APV is the highest, because it assumes that debt is fixed, not rebalanced, and that interest tax shields are as safe as the interest payments generating them.