Week 4

Chapter 7 Cost of Capital and Capital Budgeting

Learning Objectives

· To understand the cost of capital

· To understand basic capital budgeting

Case: Mill Pro, Inc.

As a recent graduate of a top 100 business school, Robyn Hunt was the proud possessor of a newly minted MBA. That's not all that had changed; while attending school, she had met the man of her dreams, Tom Dallin. She was now Mrs. Thomas Dallin, MBA. Tom was an engineer by training, and he was running a company his father had started back in the 1940s. The company, Mill Pro, Inc. (Mill Pro), provided custom-made parts to major firms in the aerospace industry. Mill Pro was a successful firm, but like any other firm in its position, it had razor-thin margins in order to compete. Tom was an excellent engineer but lacked business training, and he was happy to have his new bride become both part of his life and the CFO of his business.

Ten years ago, computer numeric control (CNC) machining processes had become the ascendant technology in Mill Pro's competitive landscape. Mill Pro was now using a CNC technology 10 years old, and even though the technology would last another 10 years, it was not now state of the art and was neither as flexible nor as price competitive as the next-generation technology. However, to replace the old technology with new technology was very expensive. While Tom had a general idea that some criteria should be used when making this decision, he did not know what they were. He asked Robyn if she could develop criteria and perform an analysis to decide if it was a smart move for Mill Pro to adopt and purchase the new technology. Robyn remembered that this kind of decision was made up of two parts: (1) the question of the firm's cost of capital and (2) constructing a projection and formatting the analysis. She decided she would review the cost of capital computation and the capital budgeting process.

The most basic concept of value is that any risky asset is worth the present value of all expected future cash flows discounted back to the present at an appropriate risk-adjusted required rate of return. If we accept this concept, then two problems arise: What are those future cash flows (how certain are they, at what intervals do they occur, and how long do they last), and what is the appropriate risk-adjusted rate of return? In  Chapter 6 , we indirectly considered the question of what the future cash flows may be by studying the process of making a projection of such future benefits. When entrepreneurial ventures or capital projects are valued, the inherent cash generation capacities of the firm or the capital project are the key elements that should be considered, and projections regarding the relevant future benefits must be made. The second key issue is to determine what the required rate of return should be used as a discount factor when dealing with projected future cash flows.

Chart 7.1  presents a schematic representation of the material covered in this chapter.

Chart 7.1 Schematic of  Chapter 7

Weighted Average Cost of Capital

In calculating the present value of any asset using the discounted cash flow (DCF) analysis approach, the expected free cash flows generated by that asset are discounted by a required rate of return, also known as the weighted average cost of capital (WACC). The WACC is the average cost of capital representing the expected return on all of a company's outstanding components of capital. Each source of capital, equities, bonds, and other debt is weighted in the calculation according to its prominence in the company's capital structure. A firm's WACC is the overall required return on the firm as a whole. In other words, it is a rate of return offered by investment alternatives with equivalent risk. It is important to note that the WACC embodies both the business and financial risk. The WACC is a weighted average of the cost of equity and cost of debt (including the cost of preferred stock). The cost of equity is the rate of return expected by equity holders for taking the risk for investing in a company. The cost of debt is the net of taxes cost of debt weighted by type of debt and amount.

The use of WACC is intuitively appealing because of the consistency it affords: The company's cash flows are discounted at a rate reflecting the relative cost of the various components of its long-term capital necessary to generating those cash flows. The formula used to compute WACC is shown as follows:

where

· E = the book value of equity of the target company (may be measured by its total market capitalization);

· D = the book value of debt of the target company minus the current portion (may be approximated by the market value of any outstanding long-term bonds minus the current portion);

· pfd = the book value of preferred stock of the target company (may be approximated by market value of any outstanding preferred stock);

· V = the total amount of long-term capital of the target company (i.e., the sum of E + D + pfd);

· E/V = the proportion of total firm capital represented by equity;

· D/V = the proportion of total firm capital represented by debt;

· pfd/V = the proportion of total firm capital represented by preferred stock;

· T = the target company's corporate tax rate;

· RRRequity = the target company's cost of equity funds, calculated (see below for computational methods);

· RRRdebt = the target company's cost of debt (see below for computational methods);

· RRRpfd = the target company's cost of preferred stock (see below for computational methods).

To calculate WACC at a firm, we need to attach a “cost” to each component of the firm's capital structure. Since there are three generic types of capital components that any firm may have, methodologies must be available to cost each one. These capital components are

1. Equity

2. Debt

3. Preferred stock

The Cost of Equity (RRRequity)

Virtually all firms have equity in their capital structure. There are several widely used and accepted methods of estimating the cost of equity. The most common of these are

1. The build-up method

2. The capital asset pricing model

3. The Gordon growth model

The Build-Up Method. The build-up method is an additive model in which the expected return on an asset is estimated as the sum of the risk-free rate (RFR) and one or more risk premiums. The RFR is a rate of return that a government bond with a similar maturity to the investment's time horizon earns. The RFR compensates the investor for expected inflation, the premium for forgoing consumption (often estimated to be the long-run growth rate in the economy), and the prevailing relative ease or tightness of credit. When used in its normal context, the build-up method assumes that the two key risk premiums that every risky equity investment should earn are the RFR and the equity risk premium (the required rate of return over the RFR that should be earned on a fully diversified equity portfolio—ERP).

In addition to the RFR and the ERP, two other widely accepted risk premiums can be applied to provide a complete and more specific estimate of the appropriate risk-adjusted rate of return for a single risky asset. These two commonly used risk premiums are industry risk premium (IRP) and company size premium (SP). The IRP reflects the risk that is inherent in the type of industry the company operates in. The SP may also be added in to account for the risk attributed to the company's size. Thus, the build-up method is in essence the sum of all of these historically derived risk premiums. Below is a template for visualizing the method.

The Build-up Method

Detailed studies are available for the estimation of these various risk premiums. Historical data are used to provide average values, which can be used to approximate the various premiums. One of the better providers of these data is Ibbotson's SBBI Valuation Yearbook (e.g., 2012). This data source gives estimates of each of the four premiums that have been discussed.  Tables 7.1  to  7.4  are excerpted from the 2013 edition of the Morningstar book.

Source: Ibbotson Associates (2012).

a. Compound annual return.

Source: Ibbotson Associates (2012).

Source: Ibbotson Associates (2012).

While the presentation given here is basic, it does capture the gist of the build-up process. There are various arguments about how to further process historical premium data to make them even more accurate or theoretically “pure.” For example, some academics and practitioners argue that SP data should be adjusted for the asset Beta; other arguments are made about the time frame of premium data that should be used, the length of the time frame that should be considered, or even the type of smoothing (if any) that should be applied to the data. There is always the problem of dealing with the problem of using historical data to project future performance. For more information, Ibbotson Associates (2012) provides an in-depth analysis.

Source: Ibbotson Associates (2012).

Capital Asset Pricing Model (CAPM). The capital asset pricing model (CAPM) is among the most common techniques used to estimate the cost of equity. The central insight of CAPM is that the expected return of a single risky asset is related to the relationship between its unique risk profile and the risk profile of a fully diversified portfolio of risky assets (the market portfolio [MP]). In a traditional CAPM view, there are essentially three different types of risk premiums. As was the case with the build-up method, the starting point is the premium for an appropriate maturity government security (i.e., the RFR), previously explained. Like the build-up method, CAPM is based on the assumption that taking systemic risk (risk associated with economic cycles, environmental events, and political activity) is rewarded by a risk premium that is added to the RFR. Just as with the build-up method, this additional premium is called the market's equity risk premium (ERP).

To deal with the unique risk and return characteristics of a single risky asset, the CAPM makes the assumption that the risk premium of a single risky asset is proportionate to the risk premium of the fully diversified market portfolio. Thus, a coefficient that expresses this proportionality is the best way of explaining the risk premium of the single risky asset. That coefficient (Beta) when multiplied by the ERP will yield the single asset's risk premium (ARP). (When dealing with equity securities, ERP * Beta is equal to the firm-specific risk premium [FSRP].)

The ARP is proportionate to the degree of co-movement (Beta) of the single asset's returns in excess of the RFR with the returns of a diversified market portfolio return in excess of the RFR. It is important to note that the size effect is not captured by CAPM in its traditional formulation. (However, CAPM can be modified to adjust for a unique size premium [SP]). The following is the CAPM formula:

where

· RRR = the required risk adjusted rate of return for a single risky equity asset;

· RFR = the required rate of return on an appropriate maturity government security;

· (RM - RFR) = the equity risk premium (ERP) where the total return of the market is estimated as RM;

· Betasingle asset = Beta or the unique risk coefficient for a single risky asset.

There are two main differences between the build-up method and CAPM. The first difference is that the values for the ERP are viewed in a slightly different manner. The build-up method uses historical data and either an arithmetic average or geometric average to condense that data into usable form. The CAPM method views the ERP similarly but defines the ERP as having a Beta coefficient of 1.0 along a line (it is called the security market line [SML]) defined by the CAPM equation (see above for the equation and  Chart 7.2  for the graphical representation). For assets that have Betas other than 1.0, their expected return will plot in the part of the line defined by the CAPM formula. In the CAPM equation, if the Beta is 1.0, then the RRR solution to the equation will be the model's estimate of the current required rate of return for the market portfolio.

The second difference is that the two methods deal differently with computing the RRR of a single asset. The build-up method “builds up” the sum of the RFR and the market's equity risk premium (ERP) to estimate the risky asset's unique risk premium (ARP) by adding in a premium for industry risk (IRP) and a premium for firm size (SP). CAPM relates the “volatility” of a single asset's risk premium to the “volatility” of the market risk premium via a single and unique risk coefficient (Beta). If we plot the per-period change in the risk premium of the market versus the per-period change in the risk premium of a single risky asset and perform regression analysis on the resulting data points, we will get the characteristic line (CL) for that single asset. The slope of the CL is Beta for the single asset. (Remember, Beta is the coefficient that relates the risk premium of the single asset to the risk premium of the market [ERP].)  Chart 7.3  demonstrates this concept graphically. Generally, Alpha is the average return attributed to the firm-specific risk premium (FSRP) that should be expected when the market's return attributed to the market's risk premium (ERP) is zero.

Chart 7.2 The Security Market Line

Gordon Growth Model (aka Dividend Growth Model). In addition to the build-up method and CAPM, the Gordon growth model is also used to compute the cost of equity. (This model is also referred to as a continuous growth model.) The model is based on the idea that all firms pay dividends (even if that means that they will pay only a terminating dividend). Furthermore, it assumes that all firms have dividends that will grow at some average rate over the very long term. Finally, the model requires a known or given current price or value for the equity value of the firm being analyzed.

Chart 7.3 The Characteristic Line

Because the Gordon growth model depends on knowing the current value of the firm's equity before it can be used to compute its RRR on that equity, this model is not quite as useful when trying to determine the RRR equity for firms where the firm's value is unknown and being sought. To use the Gordon growth model in situation compute the cost of equity capital (RRRequity) of a peer group of publicly traded companies and then use an average or weight value made up of these various costs of equity to infer the RRR for the equity for the target firm.

The steps in producing an estimate of an RRR on equity for a specific firm are as follows:

1. Identify some publicly traded firms that serve as a peer group (i.e., dividend paying, same industry, and similar size).

2. For each peer group firm, identify the current dividend.

3. For each peer group firm, estimate the long-run growth rate of the firm's dividends.

4. For each peer group firm, obtain the current market price.

For each peer group firm, plug the variables into the Gordon growth formula (arranged to compute RRR of equity.

where

· D0 = the firms’ current dividend;

· g = the long-term growth rate in the firm's dividends

· P0 = the firm's current market price.

Once the required rate of return for each of the peer group firms has been calculated, the required rate of return values can be averaged together, weighted based on their market capitalization, weighted together in proportion to their Beta coefficients, or otherwise combined to present a proxy for the RRR of equity of the peer group. This resulting RRR can then be used as a proxy for the RRR of the target equity.

There are potential problems with this approach:

1. There may not be a sufficient sample of dividend-paying and publicly traded peer group firms.

2. The sample of peer group firms chosen may have operating leverage, financial leverage, or exposure to foreign exchange rate movements that are uncharacteristic of the industry.

3. The target firm may have operating leverage, financial leverage, foreign exchange exposure, or a technology that is atypical of the industry.

4. It is often difficult to estimate either the dividend or the long-term dividend growth rate.

With respect to all of these methods—the build-up, CAPM, and the Gordon growth model—results are imprecise. The data that all of these methods are based on are historical; the assumptions about what time horizons to use in analyzing the data and whether to use a methodology that adjusts the data by averaging, weighting, or applying statistically based adjustments all affect the ultimate results that are computed. There is virtually no empirical proof that any of these techniques of computing RRR of equity is consistently accurate. The best data need to be used and several methods of analysis applied to generate a range of RRR values that embrace probable RRR of equity.

The Cost of Debt (RRRdebt)

Most firms have some debt in their capital structure, so calculating the RRR on this debt is a common part of the WACC computation. Unlike equity, the models for assessing the “cost” of debt are few and simple to employ. The key difference to remember when calculating the RRR on debt is that it must be done on an after-tax basis. The cost of equity capital and the cost of preferred stock are not deductible expenses for tax purposes, but the cost of debt is and, as such, needs to be adjusted for the tax subsidy that the deductibility provides, particularly in the United States.

In its most basic form, the RRR of debt is the interest rate on the debt multiplied by (1 - T), where T is the firm's overall tax rate. However, it is not always the case that interest rate multiplied by (1 - T) is the best estimate for RRR of debt. Over time, the firm's creditworthiness may change, interest rates may change or be variable, lenders may impose commitment fees or upfront lending charges, or the firm may be coming up to a point where its debt is due and it will have to refinance its debt at prevailing higher or lower rates. Some thought should be given to what interest rate will best describe the RRR on debt for the company over the foreseeable future. The basic RRR on debt is as follows:

where

· IR = interest rate on debt;

· T = the marginal tax rate at the firm.

The value of IR must be adjusted if the interest rate is stepped up or down or pegged to some index, there are upfront loan commitment fees, or there are upfront lending charges. These adjustments are specified in  Table 7.5 .

A final issue is the consideration of certain mitigating contingencies. The most often encountered contingency is that refinancing is planned or required by the firm's current situation. In this case, the renewal cost of the loan may be substituted for the current cost. Other issues that should be considered are whether the existing or the new loan will involve step-up or step-down interest rates, commitment fees, or variable loan fees. If this is the case, then the adjustments for these features should also be applied to the interest cost of the debt. These adjustments are detailed in  Table 7.5 .

Once adjustments to the basic interest cost of debt are made per  Table 7.5 , then computing the RRR on the debt can be done using the following basic equation (except that IR will now be IRadjusted):

where

· IRadjusted = interest rate on debt (IR) adjusted for contingencies;

· T = the marginal tax rate at the firm.

If different debt issues are present, then each issue should have its RRR calculated, and the resulting RRRs should be weighted proportionately with respect to their participation in the component. For example, if Debt A has an RRRdebt A = 4% and Debt A is 25% of the long-term debt portion of firm capital, and Debt B has an RRRdebt B = 8% and Debt B is 75% of the long-term debt portion of firm capital, then Debt A should contribute 1% (.25*4%) to the long-term debt portion of firm capital and Debt B should contribute 6% (.75*8%).

The Cost of Preferred Stock (RRRpfd)

Preferred stock is called a hybrid security because it has elements that make it similar to both debt and equity. Sometimes it is referred to as “quasi-debt” and sometimes “quasi-equity.” The fact that it comes behind debt in liquidation priority makes it appear to be equity. The fact that it pays a regular dividend that has precedence over the common dividend makes it appear to be a debt. Dividends paid on preferred stock are not tax deductible so, unlike with debt, there is no tax subsidy to account for when computing the required rate of return on preferred stock (RRRpfd).

The most basic model may be used to compute the RRRpfd:

where

· Dpfd = the constant dividend in dollars per preferred share;

· Parpfd = the par value in dollars of one preferred share.

Two adjustments can be made to this model if circumstances require it:

If the dividend is not constant, then Dpfd may be replaced with the average expected dividend (i.e., Daverage). If there is a market price per share or an agreed price per share that is not equal to the par value per share, then that value (MKTVALpfd) may be substituted for the par value per share. If there are different classes of preferred stock outstanding, just as was the case with different debt issues, then each class of preferred stock should have its RRR developed and should be weighted proportionately to all other preferred classes to calculate the RRR for the preferred stock component of capital.

International Issues with Respect to RRR Calculations for Capital Components

A number of issues are currently subject to debate and discussion regarding estimating WACC in an international environment.

The first issue is what the appropriate risk-free rate (RFR) is. Generally, most practitioners and many academics suggest that the choice of the RFR should be governed by two requirements.

1. It should be the rate of return on a government bond that is of a maturity that is consistent with the valuation being performed. This means it should have a maturity that is representative of the time horizon of the data being analyzed. If we are valuing an investment and anticipate liquidating it in 5 years, then the current yield-to-maturity on a 5-year maturity government security should be used as the RFR. If we are valuing the business as a going concern and the time horizon is longer, then the yield-to-maturity of a 10-year or even 20-year government security should be used as a proxy for our RFR.

2. The RFR chosen would ideally be obtained from a government debt that is indigenous to the location where the firm's capital has been raised and the asset being valued resides. If these are different locations, then the place where the capital is being raised is the venue in which to perform the calculation.

Second, a firm's WACC should be derived from data from within the markets where the firm will raise its capital. However, the country that a firm raises its capital in may or may not have information available that would allow for the computation of an equity risk premium (ERP), industry risk premiums (IRP), firm size premium (SP), and/or equity Beta (Betaequity). There are a number of possible solutions to this lack of data:

1. The appropriate RFR rate should be readily available since virtually all sovereign governments issue debt.

2. The ERP can be derived from the equity market where the capital has been raised or the asset resides.

3. If data are not available to permit the ERP calculation referenced above, sometimes it's possible to find data that present a unique country-based risk premium that can be added to the U.S.-derived ERP premium to build up to an MRP for the country in question (Ibbotson Associates, 2012).

4. Calculating Betaequity for a security cannot be done without historical prices for the security and the corresponding RFR and ERP. If the ability to calculate Betaequity is not present, then Betaequity can be estimated by computing an average Betaequity of representative U.S. peer group firms, or an average Betaequity for a peer from some other country venue can be computed.

Making the Weighted Average Cost of Capital (WACC) Computation

WACC is a computational methodology designed to identify the appropriate overall risk-adjusted rate or return on a firm's assets that compensates each capital provider on a risk-adjusted basis. That is why RRR is computed for each component of capital individually with models that are specific to the component. After all, the firm's capital comes from a wide range of providers: lenders, preferred stockholders, and equity owners. Providers of capital have different risk and return tolerances with respect to their position in the company's capital structure. WACC is the dollar-weighted combination of each capital provider's risk-adjusted RRR, and it is specific to each capital provider's investment into the various components of the capital structure of the company.

What is the Firm's Capital Structure?

The capital structure of the firm is the long-term portion of the right-hand side of the balance sheet (i.e., long-term debt, preferred stock, and shareholder equity).

The Firm's Capital Structure

All current liabilities are left out of this calculation. For example, the firm's accounts payable, notes payable, or current portion of long-term debt are not considered a part of the firm's long-term capital. These current liabilities are called “spontaneous” liabilities, and they change with day-to-day business activity. Essentially, they are internally financed at most firms with accumulated cash and ongoing accounts receivable collections. It is the providers of the long-term components that we are concerned with when we compute the firm's WACC.

Summary and Special Notes regarding the WACC Computation

For the WACC formula, the difficulty is not in computing WACC but in how to compute the required rate of return (RRR) for all components of capital that are weighted together to produce WACC. In previous sections of this chapter, some issues have been addressed that complicate the WACC computation. Some of these issues are the following:

1. How is the RRR computed on a particular component of capital?

2. How are adjustments made for special circumstances, such as when market values are available for debt or preferred stock or interest payments or preferred stock dividends are stepped up or down or pegged to a particular index?

3. What security should be used to obtain the RFR when the company is raising its capital in a country other than the United States?

4. What should be used as the Betaequity coefficient in the CAPM model when the company is raising its capital in a country other than the United States?

All of these issues and others complicate the process of determining the appropriate value for WACC is. Our advice is to try to use enough judgment so that the various RRR calculations consider as many of the unique firm circumstances as possible. Also, we suggest that the ranges of value for WACC be calculated. High, low, and expected or average possibilities can be used to produce a range of values when the WACC value is used in the DCF approach to valuing the firm.

There is much discussion about exactly what WACC is and how it should be used. It is important to understand this issue; while WACC is a useful, unique idea, there are some weaknesses embedded in the WACC concept. In addition, the related concept of the marginal cost of capital (MCC) is important to understand. Key ideas relating to WACC and MCC are the following:

1. WACC is the combined required rate of return that earns the appropriate “risk-adjusted” rate of return on each component of firm capital. WACC is constructed in such a way to ensure that all capital providers are adequately compensated for the perceived riskiness of their position within the firm's overall capital structure.

2. When using WACC as the required rate of return in capital budgeting problems, we assume that the capital structure at the firm does not change. This is not likely to be the case, particularly in the long run.

3. When changes in the capital structure of the firm are made, changes in WACC will also change by necessity. This is because (1) the relative weights of capital components will change, and (2) the costs of any or all capital components will change. When the costs of the capital components and the weights of the components within the capital structure are recalculated after such a change, the result is not called WACC but marginal cost of capital (MCC).

4. If changes made to the firm's capital structure have occurred, then the issuance cost of new debt, preferred stock, or equity needs to be considered when calculating their new costs to produce MCC.

Capital Budgeting

A capital budgeting problem can be thought of as a valuation problem; we want to value projects that consume firm capital to ensure that the projects produce positive present values when the firm's WACC or MCC is used as the discount rate. Another way to think of it is to evaluate the internal rate of return on a capital project to determine if it is equal to or higher than the firm's WACC or MCC. The classic capital budgeting example is the sell Machine A and buy Machine B problem. Indeed, this is the problem that Mill Pro is facing in the case at the beginning of this chapter.

One thing to keep in mind is that capital budgeting problems are timeline types of problems. Benefits and costs need to be projected based on both their magnitude and their place in time. Capital budgeting problems should focus on determining the amounts of cash flow for each relevant position on the timeline. The cash flows need to be computed on an after-tax basis.

Example of a Capital Budgeting Problem

Suppose that Mill Pro wants to decide if it should sell a machine (Machine A) that it currently owns and buy a new machine (Machine B), which is a machine that has improved technology and will improve Mill Pro's gross profit margin by $150,000 per year on an after-tax basis (see  Table 7.6 ). A number of steps need to be done to perform the analysis:

1. The first step in the process is to calculate the WACC at the firm (or the MCC if new capital will need to be raised). For the purposes of this example, we have assumed a capital structure and costs of each capital component as shown in  Table 7.7 . In our example, we specify that the firm does not need to seek additional capital to effect the sale of Machine A and purchase of Machine B, and thus WACC will be the appropriate rate of return we should use in the “sell Machine A and buy Machine B” analysis. (If the firm were to raise new capital, then the appropriate rate of return to use in the problem would be the MCC.) Also in  Table 7.7 , you will find the calculation of the weight for each component of capital and the product of weight times the after-tax cost for each component (W*K). By adding all of the “W*K” products, we can calculate the WACC for the capital structure found in  Table 7.7 .

2. The second step that is necessary is to assess the costs that would be incurred at the front end. This would involve estimating the after-tax consequences of the sale of Machine A.  Table 7.8  shows the analysis of the sale of Machine A. The result of selling Machine A is that the firm receives $488,000 ($600,000 in sales proceeds—$112,000 in taxes on the sale). The costs associated with the purchase of Machine B are found in  Table 7.9 .

a. The interest on debt is tax deductible. Tax rate = 28%.

b. Preferred stock is based on $2.50 annual dividend and $25 price.

3. The third step in the process is to identify the initial net after-tax costs.  Table 7.9  shows how these costs are calculated. Note from  Table 7.9  that the initial after-tax cash investment required to make the switch between Machine A and Machine B is $462,000.

4. The fourth step is to estimate the amount of the change in periodic cash flows. We already know the after-tax impact on operating revenues. This calculation is shown in  Table 7.6 . In the day-to-day world, this amount would have been determined by management's review of the impact on sales or costs that would flow from the purchase of Machine B and is case specific. Another factor that affects the periodic cash flow is the change in working capital (WC). An increase in WC represents a cash outflow, while a decrease represents a cash inflow. In this case, the increase in WC is given, but in the day-to-day world, this would also be estimated by management (see  Table 7.10 ). To solve this problem, management would analyze the impact on WC resulting from a change in sales, costs, or both sales and costs. Finally, any change in depreciation produces either a loss or gain in tax benefits associated with the depreciation. In the case we are dealing with, we see that depreciation goes up, and thus the associated tax benefit also goes up (see  Tables 7.11  and  7.12 ).

5. The final step is to calculate the impacts that occur at the end of Machine B's useful life.  Table 7.13  shows this calculation. To estimate the after-tax cash flows that occur at the terminal date of the project, the after-tax cash flow from the sale of Machine B ($450,000 – $126,000 of tax) must be calculated, resulting in the final change in WC ($25,000).

Once all of these numbers have been calculated, the next task is to place the numbers on a timeline so as to locate them at their respective places in the overall project.  Table 7.14  indicates where these various sums should be placed on the timeline.

The final task is to calculate the sum of the present value of all the cash flows at a discount rate that is equal to the firm's risk-adjusted rate of return, which is either WACC or MCC depending on whether new capital or changes in the initial capital structure were needed to fund the project.  Table 7.15  shows this calculation. As can be seen in the table, the present value of all the respective cash flows is $397,351.74. Since this sum is the combination of the present value of both costs and benefits and the sum is positive, the project should be funded. Management may also calculate the internal rate of return (IRR) on the project. IRR is the rate of return that makes the present value of project costs equal to the present value of project benefits. (Computing this number may be arrived at by iteration or by employing the aid of a basic financial calculator with the Excel function.) In this case, the IRR is found in  Table 7.15  and is 31.06%. Since this rate of return is higher than the firm's WACC, the project should be funded.

If management is faced with a capital budgeting problem where the sale of an old asset is not involved, the methodology outlined above will still work. There will just be no input for the sale of the old asset.

Summary

Cost of capital and capital budgeting are essential subjects to know when assessing the value of a firm, determining the value of an intangible asset, or contemplating making an investment in a capital project. All firms, regardless of size, need to earn the appropriate risk-adjusted rate of return on the assets they deploy. If they do not, then the firms are failing in their duty to pay each provider of capital the appropriate after-tax rate of return. If the firm has internal funds, then it should always view the investment of those funds in new capital projects in light of what the firm's WACC is. If the firm contemplates raising new capital to invest in capital projects, then it should always view the investment of those funds in new capital projects in light of what the firm's MCC is. This is because the alternative to any capital investment is to return funds to capital providers by paying off debt and/or buying back preferred stock or equity. Viewed this way, it is apparent that spending money on capital projects must be justified by earning at least WAC