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:
Consider a project of P.B. Singer plc with the following characteristics:
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 allequity firm  is
Because the NPV is negative, the project would be rejected by an allequity 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 debttomarketvalue 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.
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:
 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 t_{C}B. (t_{C} 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.
 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.
 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.
 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 taxexempt rate because the municipality can borrow at that rate as well. As with any subsidy, this subsidy adds value.
Consider a project of P.B. Singer plc with the following characteristics:
 Cash inflows: £500,000 per year for the indefinite future.
 Cash costs: 72 per cent of sales.
 Initial investment: £520,000.
 t_{C} = 28%
 R_{0} = 20 per cent, where R_{0} is the cost of capital for a project of an allequity firm.
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 allequity firm  is
Because the NPV is negative, the project would be rejected by an allequity 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 debttomarketvalue 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, R_{S}. For a perpetuity this becomes
There are three steps to the FTE approach.
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 aftertax 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 aftertax interest payment. Thus because cash flow to the unlevered shareholders (UCF) is £100,800 and the aftertax 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.
Note that our target debttovalue ratio of 1/4 implies a target debttoequity ratio of 1/3. Applying the preceding formula to this example, we have
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.
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 isAlternatively, 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 aftertax 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 aftertax interest payment. Thus because cash flow to the unlevered shareholders (UCF) is £100,800 and the aftertax 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, R_{S}. Note that we assumed that the discount rate on unlevered equity, R_{0}, is 0.20. As we saw in an earlier chapter, the formula for R_{S} isNote that our target debttovalue ratio of 1/4 implies a target debttoequity ratio of 1/3. Applying the preceding formula to this example, we have
Step 3: Valuation
The present value of the project’s LCF isBecause 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 R_{S}. Ignoring taxes, the cost of debt is simply the borrowing rate, R_{B}. However, with corporate taxes, the appropriate cost of debt is (1  t_{C})R_{B}, the aftertax cost of debt.
The formula for determining the weighted average cost of capital, R_{WACC}, 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, R_{WACC}. 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 debttovalue 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 R_{WACC}, 0.186, is lower than the cost of equity capital for an allequity 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.
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 allequity basis. That is, the project’s aftertax cash flows under allequity financing (called unlevered cash flows, or UCF) are placed in the numerator of the capital budgeting equation. The discount rate, assuming allequity 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 aftertax 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 R_{S}, the cost of capital to the shareholders of a levered firm. For a firm with leverage, R_{S} must be greater than R_{0}, 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 aftertax cash flows assuming allequity financing (UCF). The UCF is placed in the numerator of the capital budgeting equation. The denominator, R_{WACC}, 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.
If the risk of a project stays constant throughout its life, it is plausible to assume that R_{0} remains constant throughout the project’s life. This assumption of constant risk appears to be reasonable for most realworld projects. In addition, if the debttovalue ratio remains constant over the life of the project, both R_{S} and R_{WACC} will remain constant as well. Under this latter assumption, either the FTE or the WACC approach is easy to apply. However, if the debttovalue ratio varies from year to year, both R_{S} and R_{WACC} 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 debttovalue 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 debttovalue 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 debttovalue 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 debttoequity 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 leaseversusbuy 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 debttovalue 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 timeconsuming 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 debttovalue ratio.
Because of this, we recommend that the WACC and the FTE approaches, rather than the APV approach, be used in most realworld 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 formula for determining the weighted average cost of capital, R_{WACC}, 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, R_{WACC}. 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 debttovalue 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 R_{WACC}, 0.186, is lower than the cost of equity capital for an allequity 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 allequity 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 allequity basis. That is, the project’s aftertax cash flows under allequity financing (called unlevered cash flows, or UCF) are placed in the numerator of the capital budgeting equation. The discount rate, assuming allequity 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 aftertax 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 R_{S}, the cost of capital to the shareholders of a levered firm. For a firm with leverage, R_{S} must be greater than R_{0}, 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 aftertax cash flows assuming allequity financing (UCF). The UCF is placed in the numerator of the capital budgeting equation. The denominator, R_{WACC}, 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 R_{0} remains constant throughout the project’s life. This assumption of constant risk appears to be reasonable for most realworld projects. In addition, if the debttovalue ratio remains constant over the life of the project, both R_{S} and R_{WACC} will remain constant as well. Under this latter assumption, either the FTE or the WACC approach is easy to apply. However, if the debttovalue ratio varies from year to year, both R_{S} and R_{WACC} 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 debttovalue 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 debttovalue 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 debttovalue 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 debttoequity 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 leaseversusbuy 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 debttovalue 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 timeconsuming 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 debttovalue ratio.
Because of this, we recommend that the WACC and the FTE approaches, rather than the APV approach, be used in most realworld 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  

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
realworld 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.
p. 474The preceding example shows how the three discount rates, R_{0}, R_{S} and R_{WACC}, are determined in the real world. These are the appropriate rates for the APV, FTE and WACC approaches, respectively. Note that R_{S} 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.

p. 474The preceding example shows how the three discount rates, R_{0}, R_{S} and R_{WACC}, are determined in the real world. These are the appropriate rates for the APV, FTE and WACC approaches, respectively. Note that R_{S} 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
debttoequity 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.
The preceding example illustrates the adjusted present value (APV) approach. The approach begins with the present value of a project for the allequity 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.
The notax 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 t_{C} and (b) the debt has a zero beta.
Because [1 + (1  t_{C})Debt/Equity] must be more than 1 for a levered firm, it follows that β_{Unlevered firm} < β_{Equity}. The corporate tax case of Eq. (17.4) is quite similar to the notax 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.

The preceding example illustrates the adjusted present value (APV) approach. The approach begins with the present value of a project for the allequity 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 notax 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 t_{C} and (b) the debt has a zero beta.
Because [1 + (1  t_{C})Debt/Equity] must be more than 1 for a levered firm, it follows that β_{Unlevered firm} < β_{Equity}. The corporate tax case of Eq. (17.4) is quite similar to the notax 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.

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 17.4  More 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 aftertax cash
flows (UCF) of €300,000 per year into perpetuity from the project. The
firm will finance the project with a debttovalue ratio of 0.5 (or,
equivalently, a debttoequity 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 riskfree 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.

Summary and Conclusions
p. 480Earlier chapters of this text showed how to calculate net present value for projects of allequity 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. The APV formula can be written as
There are four additional effects of debt:
 Tax shield from debt financing
 Flotation costs
 Bankruptcy costs
 Benefit of nonmarketrate financing
 The FTE formula can be written as
 The WACC formula can be written as
 Corporations frequently follow this guideline:
 Use WACC or FTE if the firm’s target debttovalue 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.
 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.
 The beta of the equity of the firm is positively related to the leverage of the firm.
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