Thursday, 26 January 2012

chapter 17

17.1 Adjusted Present Value Approach

When financing issues are an important part of an investment proposal, a good methodology to use is the adjusted present value method. The approach separates project cash flows from financing cash flows and values these separately. If the combined present values are positive, the project should be taken. The adjusted present value (APV) method is described by the following formula:
APV = NPV + NPVF
p. 467In words, the value of a project to a levered firm (APV) is equal to the value of the project to an unlevered firm (NPV) plus the net present value of the financing side effects (NPVF). We can generally think of four side effects:
  1. The tax subsidy to debt: This was discussed in Chapter 15, where we pointed out that for perpetual debt the value of the tax subsidy is tCB. (tC is the corporate tax rate, and B is the value of the debt.) The material about valuation under corporate taxes in Chapter 15 is actually an application of the APV approach.
  2. The costs of issuing new securities: As we shall discuss in detail in Chapter 20, bankers participate in the public issuance of corporate debt. These bankers must be compensated for their time and effort, a cost that lowers the value of the project.
  3. The costs of financial distress: The possibility of financial distress, and bankruptcy in particular, arises with debt financing. As stated in the previous chapter, financial distress imposes costs, thereby lowering value.
  4. Subsidies to debt financing: The interest on debt issued by state and local governments may not be taxable to the investor, or the tax may be discounted. Because of this, the yield on government debt can be substantially below the yield on taxable debt. Frequently corporations can obtain financing from a municipality at the tax-exempt rate because the municipality can borrow at that rate as well. As with any subsidy, this subsidy adds value.
Although each of the preceding four side effects is important, the tax deduction to debt almost certainly has the highest value in most actual situations. For this reason, the following example considers the tax subsidy but not the other three side effects. A later example will deal with all three.
Consider a project of P.B. Singer plc with the following characteristics:
  1. Cash inflows: £500,000 per year for the indefinite future.
  2. Cash costs: 72 per cent of sales.
  3. Initial investment: £520,000.
  4. tC = 28%
  5. R0 = 20 per cent, where R0 is the cost of capital for a project of an all-equity firm.
If both the project and the firm are financed with only equity, the project’s cash flows are as follows:

The distinction between present value and net present value is important for this example. The present value of a project is determined before the initial investment at date 0 is subtracted. The initial investment is subtracted for the calculation of net present value.
Given a discount rate of 20 per cent, the present value of the project is

The net present value (NPV) of the project - that is, the value of the project to an all-equity firm - is

Because the NPV is negative, the project would be rejected by an all-equity firm.
p. 468Now imagine that the firm finances the project with exactly £135,483.90 in debt, so that the remaining investment of £384,516.10 (= £520,000 - £135,483.90) is financed with equity. The net present value of the project under leverage, which we call the adjusted present value, or the APV, is

That is, the value of the project when financed with some leverage is equal to the value of the project when financed with all equity plus the tax shield from the debt. Because this number is positive, the project should be accepted.
You may be wondering why we chose such a precise amount of debt. Actually, we chose it so that the ratio of debt to the present value of the project under leverage is 0.25.1
In this example, debt is a fixed proportion of the present value of the project, not a fixed proportion of the initial investment of £520,000. This is consistent with the goal of a target debt-to-market-value ratio, which we find is followed by companies in many countries. For example, banks typically lend to property developers a fixed percentage of the appraised market value of a project, not a fixed percentage of the initial investment.

17.2 Flow to Equity Approach

The flow to equity (FTE) approach is an alternative capital budgeting approach. The formula simply calls for discounting the cash flow from the project to the shareholders of the levered firm at the cost of equity capital, RS. For a perpetuity this becomes

There are three steps to the FTE approach.

Step 1: Calculating Levered Cash Flow (LCF)2

Assuming an interest rate of 10 per cent, the perpetual cash flow to shareholders in our P.B. Singer plc example is

Alternatively, we can calculate levered cash flow (LCF) directly from unlevered cash flow (UCF). The key here is that the difference between the cash flow that shareholders receive in an unlevered firm and the cash flow that shareholders receive in a levered firm is the after-tax interest payment. (Repayment of principal does not appear in this example because the debt is perpetual.) We write this algebraically as

The term on the right side of this expression is the after-tax interest payment. Thus because cash flow to the unlevered shareholders (UCF) is £100,800 and the after-tax interest payment is £9,754.84 (= 0.72 × 0.10 × £135,483.90), cash flow to the levered shareholders (LCF) is
£100,800 - £9,755 = £91,045
p. 469which is exactly the number we calculated earlier.

Step 2: Calculating 

The next step is to calculate the discount rate, RS. Note that we assumed that the discount rate on unlevered equity, R0, is 0.20. As we saw in an earlier chapter, the formula for RS is

Note that our target debt-to-value ratio of 1/4 implies a target debt-to-equity ratio of 1/3. Applying the preceding formula to this example, we have

Step 3: Valuation

The present value of the project’s LCF is

Because the initial investment is £520,000 and £135,483.90 is borrowed, the firm must advance the project £384,516.10 (= £520,000 - £135,483.90) out of its own cash reserves. The net present value of the project is simply the difference between the present value of the project’s LCF and the investment not borrowed. Thus the NPV is

which is identical to the result found with the APV approach.

17.3 Weighted Average Cost of Capital Method

Finally, we can value a project using the weighted average cost of capital (WACC) method. Although this method was discussed in earlier chapters, it is worth while to review it here. The WACC approach begins with the insight that projects of levered firms are simultaneously financed with both debt and equity. The cost of capital is a weighted average of the cost of debt and cost of equity. The cost of equity is RS. Ignoring taxes, the cost of debt is simply the borrowing rate, RB. However, with corporate taxes, the appropriate cost of debt is (1 - tC)RB, the after-tax cost of debt.
The formula for determining the weighted average cost of capital, RWACC, is

The weight for equity, S/(S + B), and the weight for debt, B/(S + B), are target ratios. Target ratios are generally expressed in terms of market values, not accounting values. (Recall that another phrase for accounting value is book value.)
The formula calls for discounting the unlevered cash flow of the project (UCF) at the weighted average cost of capital, RWACC. The net present value of the project can be written algebraically as

If the project is a perpetuity, the net present value is

p. 470We previously stated that the target debt-to-value ratio of our project is 1/4 and the corporate tax rate is 0.28, implying that the weighted average cost of capital is

Note that RWACC, 0.186, is lower than the cost of equity capital for an all-equity firm, 0.20. This must always be the case, because debt financing provides a tax subsidy that lowers the average cost of capital.
We previously determined the UCF of the project to be £100,800, implying that the present value of the project is

This initial investment is £520,000, so the NPV of the project is:

Note that all three approaches yield the same value.

17.4 A Comparison of the APV, FTE and WACC Approaches

Capital budgeting techniques in the early chapters of this text applied to all-equity firms. Capital budgeting for the levered firm could not be handled earlier in the book, because the effects of debt on firm value were deferred until the previous two chapters. We learned there that debt increases firm value through tax benefits, but decreases value through bankruptcy and related costs.
In this chapter, we provide three approaches to capital budgeting for the levered firm. The adjusted present value (APV) approach first values the project on an all-equity basis. That is, the project’s after-tax cash flows under all-equity financing (called unlevered cash flows, or UCF) are placed in the numerator of the capital budgeting equation. The discount rate, assuming all-equity financing, appears in the denominator. At this point, the calculation is identical to that performed in the early chapters of this book. We then add the net present value of the debt. We point out that the net present value of the debt is likely to be the sum of four parameters: tax effects, flotation costs, bankruptcy costs, and interest subsidies.
The flow to equity (FTE) approach discounts the after-tax cash flow from a project going to the shareholders of a levered firm (LCF). LCF, which stands for levered cash flow, is the residual to shareholders after interest has been deducted. The discount rate is RS, the cost of capital to the shareholders of a levered firm. For a firm with leverage, RS must be greater than R0, the cost of capital for an unlevered firm. This follows from our material in Chapter 15 showing that leverage raises the risk to the shareholders.
The last approach is the weighted average cost of capital (WACC) method. This technique calculates the project’s after-tax cash flows assuming all-equity financing (UCF). The UCF is placed in the numerator of the capital budgeting equation. The denominator, RWACC, is a weighted average of the cost of equity capital and the cost of debt capital. The tax advantage of debt is reflected in the denominator, because the cost of debt capital is determined net of corporate tax. The numerator does not reflect debt at all.

Which Method Is Best?

The net present value of our project is exactly the same under each of the three methods. In theory, this should always be the case.3 However, one method usually provides an easier computation than another, and in many cases one or more of the methods are virtually impossible computationally. We first consider when it is best to use the WACC and FTE approaches.
If the risk of a project stays constant throughout its life, it is plausible to assume that R0 remains constant throughout the project’s life. This assumption of constant risk appears to be reasonable for most real-world projects. In addition, if the debt-to-value ratio remains constant over the life of the project, both RS and RWACC will remain constant as well. Under this latter assumption, either the FTE or the WACC approach is easy to apply. However, if the debt-to-value ratio varies from year to year, both RS and RWACC vary from year to year as well. Using the FTE or the WACC approach when the denominator changes every year is computationally quite complex, and when computations become complex, the error rate rises. Thus both the FTE and WACC approaches present difficulties when the debt-to-value ratio changes over time.
p. 471The APV approach is based on the level of debt in each future period. Consequently, when the debt level can be specified precisely for future periods, the APV approach is quite easy to use. However, when the debt level is uncertain, the APV approach becomes more problematic. For example, when the debt-to-value ratio is constant, the debt level varies with the value of the project. Because the value of the project in a future year cannot be easily forecast, the level of debt cannot be easily forecast either.
Thus we suggest the following guideline:
Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life. Use APV if the project’s level of debt is known over the life of the project.
There are a number of situations where the APV approach is preferred. For example, in a leveraged buyout (LBO) the firm begins with a large amount of debt but rapidly pays down the debt over a number of years. Because the schedule of debt reduction in the future is known when the LBO is arranged, tax shields in every future year can be easily forecast. Thus the APV approach is easy to use here. (An illustration of the APV approach applied to LBOs is provided in the appendix to this chapter.) By contrast, the WACC and FTE approaches are virtually impossible to apply here, because the debt-to-equity value cannot be expected to be constant over time. In addition, situations involving interest subsidies and flotation costs are much easier to handle with the APV approach. Finally, the APV approach handles the lease-versus-buy decision much more easily than does either the FTE or the WACC approach.
The preceding examples are special cases. Typical capital budgeting situations are more amenable to either the WACC or the FTE approach than to the APV approach. In many countries, financial managers think in terms of target debt-to-value ratios. If a project does better than expected, both its value and its debt capacity are likely to rise. The manager will increase debt correspondingly here. Conversely, the manager would be likely to reduce debt if the value of the project were to decline unexpectedly. Of course, because financing is a time-consuming task, the ratio cannot be adjusted daily or monthly. Rather, the adjustment can be expected to occur over the long run. As mentioned before, the WACC and FTE approaches are more appropriate than the APV approach when a firm focuses on a target debt-to-value ratio.
Because of this, we recommend that the WACC and the FTE approaches, rather than the APV approach, be used in most real-world situations. In addition, frequent discussions with business executives have convinced us that the WACC is by far the most widely used method in the real world. Thus practitioners seem to agree with us that, outside the special situations mentioned, the APV approach is a less important method of capital budgeting.4
The Three Methods of Capital Budgeting with Leverage
  1. Adjusted present value (APV) method:

    where UCFt is the project’s cash flow at date t to the equity-holders of an unlevered firm, and R0 is the cost of capital for project in an unlevered firm.
    p. 472
  2. Flow to equity (FTE) method:

    where LCFt is the project’s cash flow at date t to the equity-holders of a levered firm, and RS is the cost of equity capital with leverage.
  3. Weighted average cost of capital (WACC) method:

    where RWACC is the weighted average cost of capital.
Notes
  1. The middle term in the APV formula implies that the value of a project with leverage is greater than the value of the project without leverage. Because RWACC < R0, the WACC formula implies that the value of a project with leverage is greater than the value of the project without leverage.
  2. In the FTE method, cash flow after interest (LCF) is used. Initial investment is reduced by amount borrowed as well.
Guidelines
  1. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life.
  2. Use APV if the project’s level of debt is known over the life of the project.

17.5 Capital Budgeting when the Discount Rate Must Be Estimated

The previous sections of this chapter introduced APV, FTE and WACC - the three basic approaches to valuing a levered firm. However, one important detail remains. The example in Sections 17.1 to 17.3 assumed a discount rate. We now want to show how this rate is determined for real-world firms with leverage, with an application to the three preceding approaches. The example in this section brings together the work in Chapters 9, 10, 11 and 12 on the discount rate for unlevered firms with that in Chapter 15 on the effect of leverage on the cost of capital.
EXAMPLE 17.1Cost of Capital
World-Wide Enterprises (WWE) is a large conglomerate thinking of entering the widget business, where it plans to finance projects with a debt-to-value ratio of 25 per cent (or, alternatively, a debt-to-equity ratio of 1/3). There is currently one firm in the widget industry, Asian Widgets (AW). This firm is financed with 40 per cent debt and 60 per cent equity. The beta of AW’s equity is 1.5. AW has a borrowing rate of 12 per cent, and WWE expects to borrow for its widget venture at 10 per cent. The corporate tax rate for both firms is 0.40, the market risk premium is 8.5 per cent, and the riskless interest rate is 8 per cent. What is the appropriate discount rate for WWE to use for its widget venture?
As shown in Sections 17.1, 17.2 and 17.3, a corporation may use one of three capital budgeting approaches: APV, FTE or WACC. The appropriate discount rates for these three approaches are R0, RS and RWACC, respectively. Because AW is WWE’s only competitor in widgets, we look at AW’s cost of capital to calculate R0, RS and RWACC for WWE’s widget venture. The following four-step procedure will allow us to calculate all three discount rates:
p. 473
  1. Determining AW’s cost of equity capital: First, we determine AW’s cost of equity capital using the security market line (SML):
    AW’s cost of equity capital:

    where M is the expected return on the market portfolio and RF is the risk-free rate.
  2. Determining AW’s hypothetical all-equity cost of capital: We must standardize the preceding number in some way, because AW and WWE’s widget ventures have different target debt-to-value ratios. The easiest approach is to calculate the hypothetical cost of equity capital for AW, assuming all-equity financing. This can be determined from MM’s Proposition II under taxes:
    AW’s cost of capital if all equity:

    By solving the equation, we find that R0 = 0.1825. Of course, R0 is less than RS because the cost of equity capital would be less when the firm employs no leverage.
    At this point, firms in the real world generally make the assumption that the business risk of their venture is about equal to the business risk of the firms already in the business. Applying this assumption to our problem, we assert that the hypothetical discount rate of WWE’s widget venture if all equity financed is also 0.1825.5 This discount rate would be employed if WWE uses the APV approach because the APV approach calls for R0, the project’s cost of capital in a firm with no leverage.
  3. Determining RS for WWE’s widget venture: Alternatively, WWE might use the FTE approach, where the discount rate for levered equity is determined like this:
    Cost of equity capital for WWE’s widget venture:

    Note that the cost of equity capital for WWE’s widget venture, 0.199, is less than the cost of equity capital for AW, 0.2075. This occurs because AW has a higher debt-to-equity ratio. (As mentioned, both firms are assumed to have the same business risk.)
  4. Determining RWACC for WWE’s widget venture: Finally, WWE might use the WACC approach. Here is the appropriate calculation:
    RWACCfor WWE’s widget venture:

p. 474The preceding example shows how the three discount rates, R0, RS and RWACC, are determined in the real world. These are the appropriate rates for the APV, FTE and WACC approaches, respectively. Note that RS for Asian Widgets is determined first, because the cost of equity capital can be determined from the beta of the firm’s equity. As discussed in an earlier chapter, beta can easily be estimated for any publicly traded firm such as AW.

17.6 APV Example

As mentioned earlier in this chapter, firms generally set a target debt-to-equity ratio, allowing the use of WACC and FTE for capital budgeting. APV does not work as well here. However, as we also mentioned earlier, APV is the preferred approach when there are side benefits and side costs to debt. Because the analysis can be tricky, we now devote an entire section to an example where, in addition to the tax subsidy to debt, both flotation costs and interest subsidies come into play.
EXAMPLE 17.2APV
Bicksler Enterprises is considering a £10 million project that will last five years. The investment will be depreciated at 25 per cent reducing balance for tax purposes. At the end of the five years, the investment will be sold for its residual book value. The cash revenues less cash expenses per year are £3,500,000. The corporate tax bracket is 28 per cent. The risk-free rate is 10 per cent, and the cost of unlevered equity is 20 per cent.
First we shall calculate the depreciation in each year.

The cash flow projections each year are below. Because the investment is sold at its residual value, there are no tax implications for the final cash flow of £2,373,047. If, for example, Bicksler sold the investment for £3,000,000 it would be liable to pay tax on the profit of £626,953 (£3,000,000 - £2,373,047):

We stated before that the APV of a project is the sum of its all-equity value plus the additional effects of debt. We examine each in turn.
All-Equity Value Assuming the project is financed with all equity, we shall discount the revenues and initial outlay cash flows by the cost of unlevered equity. The depreciation tax shield should be discounted at the risk-free rate. The present value of each cash flow is given below:

p. 475The net present value is thus
-£10,000,000 + £2,736,364 + £2,183,884 + £1,754,164 + £1,416,981 + £1,135,521 + £794,729 = £21,642
This calculation uses the techniques presented in the early chapters of this book. Notice again that the depreciation tax shield is discounted at the riskless rate of 10 per cent. The revenues and expenses are discounted at the higher rate of 20 per cent.
An all-equity firm would accept the project, because the NPV is £21,642. However, equity flotation costs and economic volatility (not mentioned yet) would more than likely make the NPV negative. However, debt financing may add enough value to the project to justify acceptance. We consider the effects of debt next.
Additional Effects of Debt Bicksler Enterprises can obtain a five-year, non-amortizing loan for £7,500,000 after flotation costs at the risk-free rate of 10 per cent. Flotation costs are fees paid when equity or debt is issued. These fees may go to printers, lawyers, and bankers, among others. Bicksler Enterprises is informed that flotation costs will be 1 per cent of the gross proceeds of its loan. The previous chapter indicates that debt financing alters the NPV of a typical project. We look at the effects of debt next.
Flotation Costs Given that flotation costs are 1 per cent of the gross proceeds, we have

Thus the gross proceeds are

This implies flotation costs of £75,758 (= 1% × £7,575,758). To check the calculation, note that net proceeds are £7,500,000 (= £7,575,758 - £75,758). In other words, Bicksler Enterprises receives only £7,500,000. The flotation costs of £75,758 are received by intermediaries such as bankers.
Under International Financial Reporting Standards, flotation costs directly attributable to an investment in a particular asset should be depreciated using the same method as the asset itself. In our case, depreciation would be charged on the flotation costs using 25 per cent reducing balance. The tax shield can then be calculated accordingly. Flotation costs are paid immediately, but are deducted from taxes by amortizing on a 25 per cent reducing-balance basis over the life of the loan. The depreciation schedule on the flotation costs is presented below:

p. 476The cash flows from flotation costs are as follows:

When we discount at 10 per cent, the net cost of flotation is

The net present value of the project after the flotation costs of debt but before the benefits of debt is

Tax Subsidy Interest must be paid on the gross proceeds of the loan, even though intermediaries receive the flotation costs. Because the gross proceeds of the loan are £7,575,578, annual interest is £757,576 (= £7,575,758 × 0.10). The interest cost after taxes is £545,455 [= £757,576 × (1 − 0.28)]. Because the loan is non-amortizing, the entire debt of £7,575,758 is repaid at date 5. These terms are indicated here:

The relevant cash flows are listed in boldface in the preceding table. They are: (a) loan received, (b) annual interest cost after taxes, and (c) repayment of debt. Note that we include the gross proceeds of the loan as an inflow, because the flotation costs have previously been subtracted.
In Chapter 15 we mentioned that the financing decision can be evaluated in terms of net present value. The net present value of the loan is simply the sum of the net present values of each of the three cash flows. This can be represented as follows:

The calculations for this example are:

The NPV (loan) is positive, reflecting the interest tax shield.6
p. 477The adjusted present value of the project with this financing is

Though we previously saw that an all-equity firm would probably not accept the project (once equity flotation costs were taken into account), a firm would accept the project if a £7,500,000 (net) loan could be obtained.
Because the loan just discussed was at the market rate of 10 per cent, we have considered only two of the three additional effects of debt (flotation costs and tax subsidy) so far. We now examine another loan, where the third effect arises.
Non-Market-Rate Financing A number of companies are fortunate enough to obtain subsidized financing from a governmental authority. Suppose that the project of Bicksler Enterprises is deemed socially beneficial, and the British government grants the firm a £7,500,000 loan at 8 per cent interest. In addition, all flotation costs are absorbed by the state. Clearly, the company will choose this loan over the one we previously calculated. Here are the cash flows from the loan:

The relevant cash flows are listed in boldface in the preceding table. Using Eq. (17.1), the NPV (loan) is

Why do we discount the cash flows in Eq. (17.1″) at 10 per cent when the firm is borrowing at 8 per cent? We discount at 10 per cent because that is the fair or market-wide rate. That is, 10 per cent is the rate at which the firm could borrow without benefit of subsidization. The net present value of the subsidized loan is larger than the net present value of the earlier loan, because the firm is now borrowing at the below-market rate of 8 per cent. Note that the NPV (loan) calculation in Eq. (17.1) captures both the tax effect and the non-market-rate effect.
The net present value of the project with subsidized debt financing is

The preceding example illustrates the adjusted present value (APV) approach. The approach begins with the present value of a project for the all-equity firm. Next, the effects of debt are added in. The approach has much to recommend it. It is intuitively appealing, because individual components are calculated separately and added together in a simple way. And, if the debt from the project can be specified precisely, the present value of the debt can be calculated precisely.

17.7 Beta and Leverage

p. 478A previous chapter provides the formula for the relationship between the beta of the equity and leverage of the firm in a world without taxes. We reproduce this formula here:
The no-tax case:

As pointed out earlier, this relationship holds under the assumption that the beta of debt is zero.
Because firms must pay corporate taxes in practice, it is worth while to provide the relationship in a world with corporate taxes. It can be shown that the relationship between the beta of the unlevered firm and the beta of the levered equity is the following:7
The corporate tax case:

when (a) the corporation is taxed at the rate of tC and (b) the debt has a zero beta.
Because [1 + (1 - tC)Debt/Equity] must be more than 1 for a levered firm, it follows that βUnlevered firm < βEquity. The corporate tax case of Eq. (17.4) is quite similar to the no-tax case of Eq. (17.3), because the beta of levered equity must be greater than the beta of the unlevered firm in either case. The intuition that leverage increases the risk of equity applies in both cases.
However, notice that the two equations are not equal. It can be shown that leverage increases the equity beta less rapidly under corporate taxes. This occurs because, under taxes, leverage creates a riskless tax shield, thereby lowering the risk of the entire firm.
EXAMPLE 17.3Unlevered Betas
Ross McDermott plc is considering a scale-enhancing project. The market value of the firm’s debt is £100 million, and the market value of the firm’s equity is £200 million. The debt is considered riskless. The corporate tax rate is 28 per cent. Regression analysis indicates that the beta of the firm’s equity is 2. The risk-free rate is 10 per cent, and the expected market premium is 8.5 per cent. What would the project’s discount rate be in the hypothetical case that Ross McDermott plc is all-equity?
We can answer this question in two steps.
  1. Determining beta of hypothetical all-equity firm: Rearranging Eq. (17.4), we have this:
    Unlevered beta:
  2. Determining discount rate: We calculate the discount rate from the security market line (SML) as follows:
    Discount rate:

The Project Is not Scale Enhancing

p. 479Because the previous example assumed that the project is scale enhancing, we began with the beta of the firm’s equity. If the project is not scale enhancing, we could begin with the equity betas of firms in the industry of the project. For each firm, we could calculate the hypothetical beta of the unlevered equity by Eq. (17.5). The SML could then be used to determine the project’s discount rate from the average of these betas.
EXAMPLE 17.4More Unlevered Betas
The Irish firm J. Lowes plc, which currently manufactures staples, is considering a €1 million investment in a project in the aircraft adhesives industry. The corporation estimates unlevered after-tax cash flows (UCF) of €300,000 per year into perpetuity from the project. The firm will finance the project with a debt-to-value ratio of 0.5 (or, equivalently, a debt-to-equity ratio of 1:1).
The three competitors in this new industry are currently unlevered, with betas of 1.2, 1.3 and 1.4. Assuming a risk-free rate of 5 per cent, a market risk premium of 9 per cent, and a corporate tax rate of 12.5 per cent, what is the net present value of the project?
We can answer this question in five steps.
  1. Calculating the average unlevered beta in the industry: The average unlevered beta across all three existing competitors in the aircraft adhesives industry is
  2. Calculating the levered beta for J. Lowes’s new project: Assuming the same unlevered beta for this new project as for the existing competitors, we have, from Eq. (17.4),
    Levered beta:
  3. Calculating the cost of levered equity for the new project: We calculate the discount rate from the security market line (SML) as follows:
    Discount rate:
  4. Calculating the WACC for the new project: The formula for determining the weighted average cost of capital, RWACC, is
  5. Determining the project’s value: Because the cash flows are perpetual, the NPV of the project is

Summary and Conclusions

p. 480Earlier chapters of this text showed how to calculate net present value for projects of all-equity firms. We pointed out in the last two chapters that the introduction of taxes and bankruptcy costs changes a firm’s financing decisions. Rational corporations should employ some debt in a world of this type. Because of the benefits and costs associated with debt, the capital budgeting decision for levered firms is different from that for unlevered firms. The present chapter has discussed three methods for capital budgeting by levered firms: the adjusted present value (APV), flows to equity (FTE), and weighted average cost of capital (WACC) approaches.
  1. The APV formula can be written as

    There are four additional effects of debt:
    1. Tax shield from debt financing
    2. Flotation costs
    3. Bankruptcy costs
    4. Benefit of non-market-rate financing
  2. The FTE formula can be written as
  3. The WACC formula can be written as
  4. Corporations frequently follow this guideline:
    1. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life.
    2. Use APV if the project’s level of debt is known over the life of the project.
  5. The APV method is used frequently for special situations such as interest subsidies, LBOs, and leases. The WACC and FTE methods are commonly used for more typical capital budgeting situations. The APV approach is a rather unimportant method for typical capital budgeting situations.
  6. The beta of the equity of the firm is positively related to the leverage of the firm.

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