Capital Budgeting (PDF)

CH APTE R Fundamentals of Capital Budgeting 8 IN EARLY 2017, NINTENDO RELEASED ITS SEVENTH MAJOR VIDEO NOTATION gam...

CH APTE R Fundamentals of Capital Budgeting 8 IN EARLY 2017, NINTENDO RELEASED ITS SEVENTH MAJOR VIDEO NOTATION game console, the Nintendo Switch. The Switch was developed after Nintendo’s IRR   internal rate of return previous game console, the Wii U, had disappointing sales that led to several EBIT earnings before interest quarters of financial losses in 2014. The Switch took four years to develop and and taxes consumed a significant portion of the company’s $2.4 billion R&D budget during τ c   marginal corporate that time. It distinguished itself with a unique controller and portability features tax rate designed to appeal to more casual gamers. While investors were initially skepti- NPV net present value cal, sales immediately exceeded expectations with nearly 18 million units in the NWC t   net working capital in first year, causing Nintendo’s stock price to almost double. year t Nintendo’s decision to invest hundreds of millions of dollars in the Switch is ∆NWC t   increase in net working a classic capital budgeting decision. To make such a decision, firms like Nintendo capital between year t use the NPV rule to assess the potential impact on the firm’s value. How do man- and year t − 1 agers quantify the cost and benefits of a project like this one to compute the NPV? CapEx   capital expenditures An important responsibility of corporate financial managers is determining FCFt   free cash flow in year t which projects or investments a firm should undertake. Capital budgeting, the PV present value focus of this chapter, is the process of analyzing investment opportunities and deciding which ones to accept. As we learned in Chapter 7, the NPV rule is the most r   projected cost of capital accurate and reliable method for allocating the firm’s resources so as to maximize its value. To implement the NPV rule, financial managers must compute the NPV of the firm’s projects and only accept those for which the NPV is positive. The first step in this process is to forecast the project’s revenues and costs, and from these forecasts, estimate the project’s expected future cash flows. In this chapter, we will consider in detail the process of estimating a project’s expected cash flows, which are crucial inputs in the investment decision process. Using these cash flows, we can then compute the project’s NPV—its contribution to shareholder value. Finally, because the cash flow forecasts almost always contain uncertainty, we demonstrate how to compute the sensitivity of the NPV to the uncertainty in the forecasts. 275 M08_BERK6318_06_GE_C08.indd 275 26/04/23 6:16 PM  276 Chapter 8 Fundamentals of Capital Budgeting 8.1 Forecasting Earnings A capital budget lists the projects and investments that a company plans to undertake during the coming year. To determine this list, firms analyze alternative projects and decide which ones to accept through a process called capital budgeting. This process begins with forecasts of the project’s future consequences for the firm. Some of these conse- quences will affect the firm’s revenues; others will affect its costs. Our ultimate goal is to determine the effect of the decision on the firm’s cash flows, and evaluate the NPV of these cash flows to assess the consequences of the decision for the firm’s value. As we emphasized in Chapter 2, earnings are not actual cash flows. However, as a practical matter, to derive the forecasted cash flows of a project, financial managers often begin by forecasting earnings. Thus, we begin by determining the incremental earnings of a project—that is, the amount by which the firm’s earnings are expected to change as a result of the investment decision. Then, in Section 8.2, we demonstrate how to use the incremen- tal earnings to forecast the cash flows of the project. Let’s consider a hypothetical capital budgeting decision faced by managers of the router division of Cisco Systems, a maker of networking hardware. Cisco is considering the de- velopment of a wireless home networking appliance, called HomeNet, that will provide both the hardware and the software necessary to run an entire home from any Internet connection. In addition to connecting computers and smartphones, HomeNet will con- trol Internet-based telepresence and phone systems, home entertainment systems, heating and air-conditioning units, major appliances, security systems, office equipment, and so on. Cisco has already conducted an intensive, $300,000 feasibility study to assess the attractive- ness of the new product. Revenue and Cost Estimates We begin by reviewing the revenue and cost estimates for HomeNet. HomeNet’s target market is upscale residential “smart” homes and home offices. Based on extensive market- ing surveys, the sales forecast for HomeNet is 100,000 units per year. Given the pace of technological change, Cisco expects the product will have a four-year life. It will be sold through high-end electronics stores for a retail price of $375, with an expected wholesale price of $260. Developing the new hardware will be relatively inexpensive, as existing technologies can be simply repackaged in a newly designed, home-friendly box. Industrial design teams will make the box and its packaging aesthetically pleasing to the residential market. Cisco ex- pects total engineering and design costs to amount to $5 million. Once the design is final- ized, actual production will be outsourced at a cost (including packaging) of $110 per unit. In addition to the hardware requirements, Cisco must build a new software application to allow virtual control of the home from the Web. This software development project requires coordination with each of the Web appliance manufacturers and is expected to take a dedicated team of 50 software engineers a full year to complete. The cost of a software engineer (including benefits and related costs) is $200,000 per year. To verify the compatibility of new consumer Internet-ready appliances with the HomeNet system as they become available, Cisco must also install new equipment that will require an up-front investment of $7.5 million. The software and hardware design will be completed, and the new equipment will be operational, at the end of one year. At that time, HomeNet will be ready to ship. Cisco expects to spend $2.8 million per year on marketing and support for this product. M08_BERK6318_06_GE_C08.indd 276 26/04/23 6:16 PM  8.1 Forecasting Earnings 277 Incremental Earnings Forecast Given the revenue and cost estimates, we can forecast HomeNet’s incremental earnings, as shown in the spreadsheet in Table 8.1. After the product is developed in year 0, it will generate sales of 100,000 units × $260 unit = $26 million each year for the next four years. The cost of produc- ing these units is 100,000 units × $110/unit = $11 million per year. Thus, HomeNet will pro- duce a gross profit of $26 million − $11 million = $15 million per year, as shown in line 3 of Table 8.1. Note that while revenues and costs occur throughout the year, we adopt the standard accounting convention of listing revenues and costs at the end of the year in which they occur.1 The project’s operating expenses include $2.8 million per year in marketing and support costs, which are listed as selling, general, and administrative expenses. In year 0, Cisco will spend $5 million on design and engineering, together with 50 × $200,000 = $10 million on software, for a total of $15 million in research and development expenditures. Capital Expenditures and Depreciation. HomeNet also requires $7.5 million in equipment that will be required to allow third-party manufacturers to upload the specifications and verify the compatibility of any new Internet-ready appliances that they might produce. To encourage the development of compatible products and provide service for existing customers, Cisco ex- pects to continue to operate this equipment even after they phase out the current version of the product. Recall from Chapter 2 that while investments in plant, property, and equipment are a cash expense, they are not directly listed as expenses when calculating earnings. Instead, the firm deducts a fraction of the cost of these items each year as depreciation. Several different meth- ods are used to compute depreciation. The simplest method is straight-line depreciation, in which the asset’s cost ( less any expected salvage value) is divided equally over its estimated useful life (we discuss other methods in Section 8.4). If we assume the equipment is purchased just before the end of year 0, and then use straight-line depreciation over a five-year life for the new equipment, HomeNet’s depreciation expense is $1.5 million per year in years 1 through 5.2 TABLE 8.1 HomeNet’s Incremental Earnings Forecast SPREADSHEET Year 0 1 2 3 4 5 Incremental Earnings Forecast ($000s) 1 Sales — 26,000 26,000 26,000 26,000 — 2 Cost of Goods Sold — (11,000) (11,000) (11,000) (11,000) — 3 Gross Profit — 15,000 15,000 15,000 15,000 — 4 Selling, General, and Administrative — (2,800) (2,800) (2,800) (2,800) — 5 Research and Development (15,000) — — — — 6 Depreciation — (1,500) (1,500) (1,500) (1,500) (1,500) 7 EBIT (15,000) 10,700 10,700 10,700 10,700 (1,500) 8 Income Tax at 20% 3,000 (2,140) (2,140) (2,140) (2,140) 300 9 Unlevered Net Income (12,000) 8,560 8,560 8,560 8,560 (1,200) 1 Note that for our cash flow timeline, we will associate each year as a “point” in the timeline (i.e., Year 0 = date 0, etc.). Doing so mixes cash flows that may occur at the beginning or the end of the year. When additional precision is required, cash flows are often estimated on a quarterly or monthly basis. (See also the appendix to Chapter 5 for a method of converting continuously arriving cash flows to annual ones.) 2 Recall that although new product sales have ceased, the equipment will remain in use in year 5. Note also that as in Chapter 2, we list depreciation expenses separately rather than include them with other expenses (i.e., COGS, SG&A, and R&D are “clean” and do not include non-cash expenses. Using clean expenses is preferred in financial models.) M08_BERK6318_06_GE_C08.indd 277 26/04/23 6:16 PM  278 Chapter 8 Fundamentals of Capital Budgeting Deducting these depreciation expenses leads to the forecast for HomeNet’s earnings before interest and taxes (EBIT) shown in line 7 of Table 8.1. This treatment of capital expenditures is one of the key reasons why earnings are not an accurate representation of cash flows.3 Interest Expenses. In Chapter 2, we saw that to compute a firm’s net income, we must first deduct interest expenses from EBIT. When evaluating a capital budgeting decision like the HomeNet project, however, we generally do not include interest expenses. Any incremental interest expenses will be related to the firm’s decision regarding how to finance the project. Here we wish to evaluate the project on its own, separate from the financing decision, as we will incorporate the appropriate cost of capital in our NPV calculation.4 Thus, we evaluate the HomeNet project as if Cisco will not use any debt to finance it (whether or not that is actually the case), and we postpone the consideration of alternative financing choices until Part 5 of the book. For this reason, we refer to the net income we compute in Table 8.1 as the unlevered net income of the project, to indicate that it does not include any interest expenses associated with debt. Taxes. The final expense we must account for is corporate taxes. The correct tax rate to use is the firm’s marginal corporate tax rate, which is the tax rate it will pay on an incremental dollar of pretax income. In Table 8.1, we assume the marginal corporate tax rate for the HomeNet project is 20% each year. The incremental income tax expense is calculated in line 8 as Income Tax = EBIT × τ c (8.1) where τ c is the firm’s marginal corporate tax rate. In year 1, HomeNet will contribute an additional $10.7 million to Cisco’s EBIT, which will result in an additional $10.7 million × 20% = $2.14 million in corporate tax that Cisco will owe. We deduct this amount to determine HomeNet’s after-tax contribution to net income. In year 0, however, HomeNet’s EBIT is negative. Are taxes relevant in this case? Yes. HomeNet will reduce Cisco’s taxable income in year 0 by $15 million. As long as Cisco earns taxable income elsewhere in year 0 against which it can offset HomeNet’s losses, Cisco will owe $15 million × 20% = $3 million less in taxes in year 0. The firm should credit this tax savings to the HomeNet project. A similar credit applies in year 5, when the firm claims its final depreciation expense for the equipment. EXAMPLE 8.1 Taxing Losses for Projects in Profitable Companies Problem Kellogg plans to launch a new line of high-fiber, gluten-free breakfast pastries. The heavy adver- tising expenses associated with the product launch will generate operating losses of $20 million next year. Kellogg expects to earn pretax income of $460 million from operations other than the new pastries next year. If Kellogg pays a 25% tax rate on its pretax income, what will it owe in taxes next year without the new product? What will it owe with it? 3 Starting in 2022, the 2017 TCJA requires that firms also capitalize and depreciate R&D expenses over five years, though it is expected that Congress will act to delay this tax change. 4 This approach is motivated by the Separation Principle (see Chapter 3): When securities are fairly priced, the NPV of financing is zero, and so the NPV of an investment is independent of how it is financed. Later in the text, we consider cases in which financing may influence the project’s value, and extend our capital budgeting techniques accordingly in Chapter 18. M08_BERK6318_06_GE_C08.indd 278 26/04/23 6:16 PM  8.1 Forecasting Earnings 279 Solution Without the new pastries, Kellogg will owe $460 million × 25% = $115 million in corporate taxes next year. With the new pastries, Kellogg’s pretax income next year will be only $460 million  − $20 million = $440 million, and it will owe $440 million × 25% = $110 million in tax. Thus, launching the new product reduces Kellogg’s taxes next year by $115 million − $110 million = $5 million, which equals the tax rate (25%) times the loss ($20 million). Unlevered Net Income Calculation. We can express the calculation in the Table 8.1 spreadsheet as the following shorthand formula for unlevered net income: Unlevered Net Income = EBIT × ( 1 − τ c ) = ( Revenues − Costs − Depreciation ) × ( 1 − τ c ) (8.2) That is, a project’s unlevered net income is equal to its incremental revenues less costs and depreciation, evaluated on an after-tax basis.5 Indirect Effects on Incremental Earnings When computing the incremental earnings of an investment decision, we should include all changes between the firm’s earnings with the project versus without the project. Thus far, we have analyzed only the direct effects of the HomeNet project. But HomeNet may have indirect consequences for other operations within Cisco. Because these indirect effects will also affect Cisco’s earnings, we must include them in our analysis. Opportunity Costs. Many projects use a resource that the company already owns. Because the firm does not need to pay cash to acquire this resource for a new project, it is tempting to assume that the resource is available for free. However, in many cases the resource could provide value for the firm in another opportunity or project. The opportunity cost of using a resource is the value it could have provided in its best alternative use.6 Because this value is lost when the resource is used by another project, we should include the opportunity cost as an incremental cost of the project. In the case of the HomeNet project, suppose the project will require space for a new lab. Even though the lab will be housed in an existing facility, we must include the opportunity cost of not using the space in an alternative way. EXAMPLE 8.2 The Opportunity Cost of HomeNet’s Lab Space Problem Suppose HomeNet’s new lab will be housed in office space that the company would have oth- erwise rented out for $200,000 per year during years 1–4. How does this opportunity cost affect HomeNet’s incremental earnings? Solution In this case, the opportunity cost of the office space is the foregone rent. This cost would reduce HomeNet’s incremental earnings during years 1– 4 by $200,000 × ( 1 − 20% ) = $160,000, the after-tax benefit of renting out the office space. 5 Unlevered net income is sometimes also referred to as net operating profit after tax (NOPAT). 6 In Chapter 5, we defined the opportunity cost of capital as the rate you could earn on an alternative investment with equivalent risk. We similarly define the opportunity cost of using an existing asset in a project as the cash flow generated by the next-best alternative use for the asset. M08_BERK6318_06_GE_C08.indd 279 26/04/23 6:16 PM  280 Chapter 8 Fundamentals of Capital Budgeting COMMON MISTAKE The Opportunity Cost of an Idle Asset A common mistake is to conclude that if an asset is currently otherwise been put to use by the firm. Even if the firm has idle, its opportunity cost is zero. For example, the firm might no alternative use for the asset, the firm could choose to sell have a warehouse that is currently empty or a machine that or rent the asset. The value obtained from the asset’s alterna- is not being used. Often, the asset may have been idled in tive use, sale, or rental represents an opportunity cost that anticipation of taking on the new project, and would have must be included as part of the incremental cash flows. Project Externalities. Project externalities are indirect effects of the project that may increase or decrease the profits of other business activities of the firm. For instance, in the Nintendo example in the chapter introduction, purchasers of the Switch are also likely to buy additional games and accessories from Nintendo. On the other hand, when sales of a new product displace sales of an existing product, the situation is often referred to as can- nibalization. Suppose that approximately 25% of HomeNet’s sales come from customers who would have purchased an existing Cisco device if HomeNet were not available. If this reduction in sales of the existing product is a consequence of the decision to develop HomeNet, then we must include it when calculating HomeNet’s incremental earnings. The spreadsheet in Table 8.2 recalculates HomeNet’s incremental earnings forecast in- cluding the opportunity cost of the office space and the expected cannibalization of the existing product. The opportunity cost of the office space in Example 8.2 increases selling, general, and administrative expenses from $2.8 million to $3.0 million. For the cannibaliza- tion, suppose that the existing device wholesales for $100 so the expected loss in sales is 25% × 100,000 units × $100 unit = $2.5 million Compared to Table 8.1, the sales forecast falls from $26 million to $23.5 million. In addi- tion, suppose the cost of the existing device is $60 per unit. Then, because Cisco will no longer need to produce as many of its existing product, the incremental cost of goods sold attributable to the HomeNet project is reduced by 25% × 100,000 units × ( $60 cost per unit ) = $1.5 million from $11 million to $9.5 million. HomeNet’s incremental gross profit therefore declines by $2.5 million − $1.5 million = $1 million once we account for this externality. Thus, comparing the spreadsheets in Table 8.1 and Table 8.2, our forecast for HomeNet’s unlevered net income in years 1–4 declines from $8.56 million to $7.6 million due to the lost rent of the lab space and the lost sales of the existing router. TABLE 8.2 HomeNet’s Incremental Earnings Forecast (Including SPREADSHEET       Cannibalization and Lost Rent) Year 0 1 2 3 4 5 Incremental Earnings Forecast ($000s) 1 Sales — 23,500 23,500 23,500 23,500 — 2 Cost of Goods Sold — (9,500) (9,500) (9,500) (9,500) — 3 Gross Profit — 14,000 14,000 14,000 14,000 — 4 Selling, General, and Administrative — (3,000) (3,000) (3,000) (3,000) — 5 Research and Development (15,000) — — — — — 6 Depreciation — (1,500) (1,500) (1,500) (1,500) (1,500) 7 EBIT (15,000) 9,500 9,500 9,500 9,500 (1,500) 8 Income Tax at 20% 3,000 (1,900) (1,900) (1,900) (1,900) 300 9 Unlevered Net Income (12,000) 7,600 7,600 7,600 7,600 (1,200) M08_BERK6318_06_GE_C08.indd 280 26/04/23 6:16 PM  8.1 Forecasting Earnings 281 Sunk Costs and Incremental Earnings A sunk cost is any unrecoverable cost for which the firm is already liable. Sunk costs have been or will be paid regardless of the decision about whether or not to proceed with the project. Therefore, they are not incremental with respect to the current decision and should not be included in its analysis. For this reason, we did not include in our analysis the $300,000 already expended on the marketing and feasibility studies for HomeNet. Because this $300,000 has already been spent, it is a sunk cost. A good rule to remember is that if our decision does not affect the cash flow, then the cash flow should not affect our decision. Below are some common examples of sunk costs you may encounter. Fixed Overhead Expenses. Overhead expenses are associated with activities that are not directly attributable to a single business activity but instead affect many different areas of the corporation. These expenses are often allocated to the different business activities for accounting purposes. To the extent that these overhead costs are fixed and will be in- curred in any case, they are not incremental to the project and should not be included. Only include as incremental expenses the additional overhead expenses that arise because of the decision to take on the project. Past Research and Development Expenditures. When a firm has already devoted sig- nificant resources to develop a new product, there may be a tendency to continue investing in the product even if market conditions have changed and the product is unlikely to be viable. The rationale sometimes given is that if the product is abandoned, the money that has already been invested will be “wasted.” In other cases, a decision is made to abandon a project because it cannot possibly be successful enough to recoup the investment that has already been made. In fact, neither argument is correct: Any money that has already been spent is a sunk cost and therefore irrelevant. The decision to continue or abandon should be based only on the incremental costs and benefits of the product going forward. Unavoidable Competitive Effects. When developing a new product, firms often worry about the cannibalization of their existing products. But if sales are likely to decline in any case as a result of new products introduced by competitors, then these lost sales are a sunk cost and we should not include them in our projections. COMMON MISTAKE The Sunk Cost Fallacy Sunk cost fallacy is a term used to describe the tendency of c­ ommercial and financial disaster, the political implications people to be influenced by sunk costs and to “throw good of halting the project—and thereby publicly admitting that money after bad.” That is, people sometimes continue to in- all past expenses on the project would result in nothing— vest in a project that has a negative NPV because they have ultimately prevented either government from abandoning already invested a large amount in the project and feel that the project. by not continuing it, the prior investment will be wasted. It is important to note that sunk costs need not always The sunk cost fallacy is also sometimes called the “Con- be in the past. Any cash flows, even future ones, that will corde effect,” a term that refers to the British and French not be affected by the decision at hand are effectively sunk, governments’ decision to continue funding the joint devel- and should not be included in our incremental forecast. For opment of the Concorde aircraft even after it was clear that example, if Cisco believes it will lose some sales on its other sales of the plane would fall far short of what was necessary products whether or not it launches HomeNet, these lost to justify the cost of continuing its development. Although sales are a sunk cost that should not be included as part of the project was viewed by the British government as a the cannibalization adjustments in Table 8.2. M08_BERK6318_06_GE_C08.indd 281 26/04/23 6:16 PM  282 Chapter 8 Fundamentals of Capital Budgeting Real-World Complexities We have simplified the HomeNet example in an effort to focus on the types of effects that financial managers consider when estimating a project’s incremental earnings. For a real project, however, the estimates of these revenues and costs are likely to be much more complicated. For instance, our assumption that the same number of HomeNet units will be sold each year is probably unrealistic. A new product typically has lower sales initially, as customers gradually become aware of the product. Sales will then acceler- ate, plateau, and ultimately decline as the product nears obsolescence or faces increased competition. Similarly, the average selling price of a product and its cost of production will gener- ally change over time. Prices and costs tend to rise with the general level of inflation in the economy. The prices of technology products, however, often fall over time as newer, superior technologies emerge and production costs decline. For most industries, competi- tion tends to reduce profit margins over time. These factors should be considered when estimating a project’s revenues and costs. EXAMPLE 8.3 Product Adoption and Price Changes Problem Suppose sales of HomeNet were expected to be 100,000 units in year 1, 125,000 units in years 2 and 3, and 50,000 units in year 4. Suppose also that HomeNet’s sale price and manufacturing cost are expected to decline by 10% per year, as with other networking products. By contrast, selling, general, and administrative expenses (including lost rent) are expected to rise with inflation by 4% per year. Update the incremental earnings forecast in the spreadsheet in Table 8.2 to account for these effects. Solution HomeNet’s incremental earnings with these new assumptions are shown in the spreadsheet below: Year 0 1 2 3 4 5 Incremental Earnings Forecast ($000s) 1 Sales — 23,500 26,438 23,794 8,566 — 2 Cost of Goods Sold — (9,500) (10,688) (9,619) (3,463) — 3 Gross Profit — 14,000 15,750 14,175 5,103 — 4 Selling, General, and Administrative — (3,000) (3,120) (3,245) (3,375) — 5 Research and Development (15,000) — — — — — 6 Depreciation — (1,500) (1,500) (1,500) (1,500) (1,500) 7 EBIT (15,000) 9,500 11,130 9,430 228 (1,500) 8 Income Tax at 20% 3,000 (1,900) (2,226) (1,886) (46) 300 9 Unlevered Net Income (12,000) 7,600 8,904 7,544 183 (1,200) For example, sale prices in year 2 will be $260 × 0.90 = $234 per unit for HomeNet, and $100 × 0.90 = $90 per unit for the cannibalized product. Thus, incremental sales in year 2 are equal to 125, 000 units × ( $234 per unit ) − 31, 250 cannibalized units × ( $90 per unit ) = $26.438 million. CONCEPT CHECK 1. How do we forecast unlevered net income? 2. Should we include sunk costs in the cash flow forecasts of a project? Why or why not? 3. Explain why you must include the opportunity cost of using a resource as an incremental cost of a project. M08_BERK6318_06_GE_C08.indd 282 26/04/23 6:16 PM  8.2 Determining Free Cash Flow and NPV 283 8.2 Determining Free Cash Flow and NPV As discussed in Chapter 2, earnings are an accounting measure of the firm’s perfor- mance. They do not represent real profits: The firm cannot use its earnings to buy goods, pay employees, fund new investments, or pay dividends to shareholders. To do those things, a firm needs cash. Thus, to evaluate a capital budgeting decision, we must deter- mine its consequences for the firm’s available cash. The incremental effect of a project on the firm’s available cash, separate from any financing decisions, is the project’s free cash flow. In this section, we forecast the free cash flow of the HomeNet project using the earn- ings forecasts we developed in Section 8.1. We then use this forecast to calculate the NPV of the project. Calculating Free Cash Flow from Earnings As discussed in Chapter 2, there are important differences between earnings and cash flow. Earnings include non-cash charges, such as depreciation, but do not include the cost of capital investment. To determine HomeNet’s free cash flow from its incremental earnings, we must adjust for these differences. Capital Expenditures and Depreciation. Depreciation is not a cash expense that is paid by the firm. Rather, it is a method used for accounting and tax purposes to allocate the original purchase cost of the asset over its life. Because depreciation is not a cash flow, we do not include it in the cash flow forecast. Instead, we include the actual cash cost of the asset when it is purchased. To compute HomeNet’s free cash flow, we must add back to earnings the depreciation expense for the new equipment (a non-cash charge) and subtract the actual capital expen- diture of $7.5 million that will be paid for the equipment in year 0. We show these adjust- ments in lines 10 and 11 of the spreadsheet in Table 8.3 (which is based on the incremental earnings forecast of Table 8.2). TABLE 8.3 Calculation  of HomeNet’s Free Cash Flow (Including SPREADSHEET      Cannibalization and Lost Rent) Year 0 1 2 3 4 5 Incremental Earnings Forecast ($000s) 1 Sales — 23,500 23,500 23,500 23,500 — 2 Cost of Goods Sold — (9,500) (9,500) (9,500) (9,500) — 3 Gross Profit — 14,000 14,000 14,000 14,000 — 4 Selling, General, and Administrative — (3,000) (3,000) (3,000) (3,000) — 5 Research and Development (15,000) — — — — — 6 Depreciation — (1,500) (1,500) (1,500) (1,500) (1,500) 7 EBIT (15,000) 9,500 9,500 9,500 9,500 (1,500) 8 Income Tax at 20% 3,000 (1,900) (1,900) (1,900) (1,900) 300 9 Unlevered Net Income (12,000) 7,600 7,600 7,600 7,600 (1,200) Free Cash Flow ($000s) 10 Plus: Depreciation — 1,500 1,500 1,500 1,500 1,500 11 Less: Capital Expenditures (7,500) — — — — — 12 Less: Increases in NWC — (2,100) — — — 2,100 13 Free Cash Flow (19,500) 7,000 9,100 9,100 9,100 2,400 M08_BERK6318_06_GE_C08.indd 283 26/04/23 6:16 PM  284 Chapter 8 Fundamentals of Capital Budgeting Net Working Capital (NWC). In Chapter 2, we defined net working capital as the difference between current assets and current liabilities. The main components of net working capital are cash, inventory, receivables, and payables: Net Working Capital = Current Assets − Current Liabilities = Cash + Inventory + Receivables − Payables (8.3) Most projects will require the firm to invest in net working capital. Firms may need to maintain a minimum cash balance7 to meet unexpected expenditures, and inventories of raw materials and finished product to accommodate production uncertainties and demand fluc- tuations. Also, customers may not pay for the goods they purchase immediately. While sales are immediately counted as part of earnings, the firm does not receive any cash until the cus- tomers actually pay. In the interim, the firm includes the amount that customers owe in its receivables. Thus, the firm’s receivables measure the total credit that the firm has extended to its customers. In the same way, payables measure the credit the firm has received from its suppliers. The difference between receivables and payables is the net amount of the firm’s capital that is consumed as a result of these credit transactions, known as trade credit. Suppose that HomeNet will have no incremental cash or inventory requirements ­( products will be shipped directly from the contract manufacturer to customers). However, receivables related to HomeNet are expected to account for 15% of annual sales, and pay- ables are expected to be 15% of the annual cost of goods sold (COGS).8 HomeNet’s net working capital requirements are shown in the spreadsheet in Table 8.4. Table 8.4 shows that the HomeNet project will require no net working capital in year 0, $2.1 million in net working capital in years 1–4, and no net working capital in year 5. How does this requirement affect the project’s free cash flow? Any increases in net working capi- tal represent an investment that reduces the cash available to the firm and so reduces free cash flow. We define the increase in net working capital in year t as ∆NWC t = NWC t − NWC t −1 (8.4) TABLE 8.4 HomeNet’s Net Working Capital Requirements SPREADSHEET Year 0 1 2 3 4 5 Net Working Capital Forecast ($000s) 1 Cash Requirements — — — — — — 2 Inventory — — — — — — 3 Receivables (15% of Sales) — 3,525 3,525 3,525 3,525 — 4 Payables (15% of COGS) — (1,425) (1,425) (1,425) (1,425) — 5 Net Working Capital — 2,100 2,100 2,100 2,100 — 7 The cash included in net working capital is cash that is not invested to earn a market rate of return. It includes non-invested cash held in the firm’s checking account, in a company safe or cash box, in cash registers (for retail stores), and other sites, which is needed to run the business. 8 If customers take N days to pay, then accounts receivable will consist of those sales that occurred in the last N days. If sales are evenly distributed throughout the year, receivables will equal (N/365) times annual sales. Thus, receivables equal to 15% of sales corresponds to an average payment period of N = 15% × 365 = 55 accounts receivable days. The same is true for payables. (See also Eq. 2.11 in Chapter 2.) M08_BERK6318_06_GE_C08.indd 284 26/04/23 6:16 PM  8.2 Determining Free Cash Flow and NPV 285 We can use our forecast of HomeNet’s net working capital requirements to complete our estimate of HomeNet’s free cash flow in Table 8.3. In year 1, net working capital in- creases by $2.1 million. This increase represents a cost to the firm as shown in line 12 of Table 8.3. This reduction of free cash flow corresponds to the fact that $3.525 million of the firm’s sales in year 1 and $1.425 million of its costs have not yet been paid. In years 2–4, net working capital does not change, so no further contributions are needed. In year 5, after the project is shut down, net working capital falls by $2.1 million as the payments of the last customers are received and the final bills are paid. We add this $2.1 million to free cash flow in year 5, as shown in line 12 of Table 8.3. Now that we have adjusted HomeNet’s unlevered net income for depreciation, capital expenditures, and increases to net working capital, we compute HomeNet’s free cash flow as shown in line 13 of the spreadsheet in Table 8.3. Note that in the first two years, free cash flow is lower than unlevered net income, reflecting the up-front investment in equipment and net working capital required by the project. In later years, free cash flow exceeds unle- vered net income because depreciation is not a cash expense. In the last year, the firm ulti- mately recovers the investment in net working capital, further boosting the free cash flow. EXAMPLE 8.4 Net Working Capital with Changing Sales Problem Forecast the required investment in net working capital for HomeNet under the scenario in Example 8.3. Solution Required investments in net working capital are shown below: Year 0 1 2 3 4 5 Net Working Capital Forecast ($000s) 1 Receivables (15% of Sales) — 3,525 3,966 3,569 1,285 — 2 Payables (15% of COGS) — (1,425) (1,603) (1,443) (519) — 3 Net Working Capital — 2,100 2,363 2,126 765 — 4 Increases in NWC — 2,100 263 (237) (1,361) (765) In this case, working capital changes each year. A large initial investment in working capital is required in year 1, followed by a small investment in year 2 as sales continue to grow. Working capital is recovered in years 3–5 as sales decline. Calculating Free Cash Flow Directly As we noted at the outset of this chapter, because practitioners usually begin the capital budget- ing process by first forecasting earnings, we have chosen to do the same. However, we could have calculated the HomeNet’s free cash flow directly by using the following shorthand formula: Free Cash Flow Unlevered Net Income    Free Cash Flow = ( Revenues − Costs − Depreciation ) × ( 1 − τ c )  + Depreciation − CapEx − ∆ NWC (8.5) Note that we first deduct depreciation when computing the project’s incremental e­ arnings, and then add it back (because it is a non-cash expense) when computing free cash flow. M08_BERK6318_06_GE_C08.indd 285 26/04/23 6:16 PM  286 Chapter 8 Fundamentals of Capital Budgeting Thus, the only effect of depreciation is to reduce the firm’s taxable income. Indeed, we can rewrite Eq. 8.5 as Free Cash Flow = ( Revenues − Costs ) × ( 1 − τ c ) − CapEx − ∆ NWC  + τ c × Depreciation (8.6) The last term in Eq. 8.6, τ c × Depreciation, is called the depreciation tax shield. It is the tax savings that results from the ability to deduct depreciation. As a consequence, depreciation expenses have a positive impact on free cash flow. Firms often report a differ- ent depreciation expense for accounting and for tax purposes. Because only the tax con- sequences of depreciation are relevant for free cash flow, we should use the depreciation expense that the firm will use for tax purposes in our forecast. Calculating the NPV To compute HomeNet’s NPV, we must discount its free cash flow at the appropriate cost of capital. As discussed in Chapter 5 the cost of capital for a project is the expected return that investors could earn on their best alternative investment with similar risk and maturity. We will develop the techniques needed to estimate the cost of capital in Part 4. For now, we assume that Cisco’s managers believe that the HomeNet project will have similar risk to other projects within Cisco’s router division, and that the appropriate cost of capital for these projects is 12%. Given this cost of capital, we compute the present value of each free cash flow in the future. As explained in Chapter 4 if the cost of capital r = 12%, the present value of the free cash flow in year t (or FCFt ) is9 FCFt 1 PV ( FCFt ) = = FCFt × (8.7) ( 1 + r )t ( ) t 1+r t -year discount factor We compute the NPV of the HomeNet project in the spreadsheet in Table 8.5. Line 3 calculates the discount factor, and line 4 multiplies the free cash flow by the discount factor to get the present value. The NPV of the project is the sum of the present values of each free cash flow, reported on line 5:10 7000 9100 9100 9100 2400 NPV = −19,500 + + + + + = $7627 1.12 1.12 2 1.12 3 1.12 4 1.12 5 TABLE 8.5 SPREADSHEET   Computing HomeNet’s NPV Year 0 1 2 3 4 5 Net Present Value ($000s) 1 Free Cash Flow (19,500) 7,000 9,100 9,100 9,100 2,400 2 Project Cost of Capital 12% 3 Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567 4 PV of Free Cash Flow (19,500) 6,250 7,254 6,477 5,783 1,362 5 NPV 7,627 6 IRR 27.9% 9 When discounting, we adopt the standard convention and interpret each year as a date in the timeline and discount to year 0. This approach effectively treats the cash flows as occurring at the midpoint of each year. For additional precision, we could forecast the cash flows on a quarterly or monthly basis (see also footnote 1). 10 We can also compute the NPV using the Excel NPV function to calculate the present value of the cash flows in year 1 through 5, and then add the cash flow in year 0 (i.e., “ = NPV ( r , FCF1 :FCF5 ) + FCF0 ” ). M08_BERK6318_06_GE_C08.indd 286 26/04/23 6:16 PM  8.2 Determining Free Cash Flow and NPV 287 USING EXCEL Capital budgeting forecasts and analysis are most easily performed in a spreadsheet program. Here we highlight a few best practices when developing your own capital budgets. Capital Budgeting Using Excel Create a Project Dashboard All capital budgeting analyses begin with a set of assumptions regarding future revenues and costs associated with the investment. Centralize these assumptions within your spreadsheet in a project dashboard so they are easy to locate, review, and potentially modify. Here we show an example for the HomeNet project. Color Code for Clarity In spreadsheet models, use a blue font color to distinguish numerical assumptions from formu- las. For example, HomeNet’s revenue and cost estimates are set to a numerical value in year 1, whereas estimates in later years are set to equal to the year 1 estimates. It is therefore clear which cells contain the main assumptions, should we wish to change them at a later date. Maintain Flexibility In the HomeNet dashboard, note that we state all assumptions on an annual basis even if we expect them to remain constant. For example, we specify HomeNet’s unit volume and average sale price for each year. We can then calculate HomeNet revenues each year based on the corre- sponding annual assumptions. Doing so provides flexibility if we later determine that HomeNet’s adoption rate might vary over time or if we expect prices to follow a trend, as in Example 8.3. Never Hardcode So that your assumptions are clear and easy to modify, reference any numerical values you need to develop your projections in the project dashboard. Never “hardcode,” or enter numerical values directly into formulas. For example, in the computation of taxes in cell E34 below, we use the formula “ = − E21*E33” rather than “ = −0.20*E33”. While the latter formula would compute the same answer, because the tax rate is hardcoded it would be difficult to update the model if the forecast for the tax rate were to change. M08_BERK6318_06_GE_C08.indd 287 26/04/23 6:16 PM  288 Chapter 8 Fundamentals of Capital Budgeting Based on our estimates, HomeNet’s NPV is $7.627 million. While HomeNet’s up-front cost is $19.5 million, the present value of the additional free cash flow that Cisco will re- ceive from the project is $27.1 million. Thus, taking the HomeNet project is equivalent to Cisco having an extra $7.6 million in the bank today—this amount is the value of the additional cash flows the project generates above and beyond what investors could earn investing the same amount, with the same risk, on their own. CONCEPT CHECK 1. What adjustments must you make to a project’s unlevered net income to determine its free cash flows? 2. What is the depreciation tax shield? 8.3 Choosing among Alternatives Thus far, we have considered the capital budgeting decision to launch the HomeNet prod- uct line. To analyze the decision, we computed the project’s free cash flow and calculated the NPV. Because not launching HomeNet produces an additional NPV of zero for the firm, launching HomeNet is the best decision for the firm if its NPV is positive. In many situations, however, we must compare mutually exclusive alternatives, each of which has consequences for the firm’s cash flows. As we explained in Chapter 7, in such cases we can make the best decision by first computing the free cash flow associated with each alterna- tive and then choosing the alternative with the highest NPV. Evaluating Manufacturing Alternatives Suppose Cisco is considering an alternative manufacturing plan for the HomeNet product. The current plan is to fully outsource production at a cost of $110 per unit. Alternatively, Cisco could assemble the product in-house at a cost of $95 per unit. However, the latter option will require $5 million in up-front operating expenses to reorganize the assembly facility, and Cisco will need to maintain inventory equal to one month’s production starting in year 1. To choose between these two alternatives, we compute the free cash flow associated with each choice and compare their NPVs to see which is most advantageous for the firm. When comparing alternatives, we only need to compare those cash flows that differ between them. We can ignore any cash flows that are the same under either scenario (e.g., HomeNet’s revenues). The spreadsheet in Table 8.6 compares the two assembly options, computing the NPV of the cash costs for each. The difference in EBIT results from the up-front cost of setting up the in-house facility in year 0, and the differing assembly costs: $110 unit × 100,000 units yr = $11 million yr outsourced, versus $95 unit × 100,000 units yr = $9.5 million yr in-house. Adjusting for taxes, we see the consequences for unlevered net income on lines 3 and 9. Because the options do not differ in terms of capital expenditures (there are none as- sociated with assembly), to compare the free cash flow for each, we only need to adjust for their different net working capital requirements. If assembly is outsourced, payables account for 15% of the cost of goods, or 15% × $11 million = $1.65 million. This amount is the credit Cisco will receive from its supplier in year 1 and will maintain until year 5. Because Cisco will borrow this amount from its supplier, net working capital falls by $1.65 million in year 1, adding to Cisco’s free cash flow. In year 5, Cisco’s net working capital will increase as Cisco pays its suppliers, and free cash flow will fall by an equal amount. If assembly is done in-house, payables are 15% × $9.5 million = $1.425 million. However, Cisco will need to maintain inventory equal to one month’s production, which requires an investment in net working capital of $9.5 million ÷ 12 = $0.792 million. Thus, M08_BERK6318_06_GE_C08.indd 288 26/04/23 6:16 PM  8.4 Further Adjustments to Free Cash Flow 289 TABLE 8.6  NPV Cost of Outsourced Versus In-House SPREADSHEET Assembly of HomeNet Year 0 1 2 3 4 5 Outsourced Assembly 1 EBIT — (11,000) (11,000) (11,000) (11,000) — 2 Income Tax at 20% — 2,200 2,200 2,200 2,200 — 3 Unlevered Net Income — (8,800) (8,800) (8,800) (8,800) — 4 Less: Increases in NWC — 1,650 — — — (1,650) 5 Free Cash Flow — (7,150) (8,800) (8,800) (8,800) (1,650) 6 NPV at 12% (26,192) Year 0 1 2 3 4 5 In-House Assembly 7 EBIT (5,000) (9,500) (9,500) (9,500) (9,500) — 8 Income Tax at 20% 1,000 1,900 1,900 1,900 1,900 — 9 Unlevered Net Income (4,000) (7,600) (7,600) (7,600) (7,600) — 10 Less: Increases in NWC — 633 — — — (633) 11 Free Cash Flow (4,000) (6,967) (7,600) (7,600) (7,600) (633) 12 NPV at 12% (26,878) Cisco will reduce its net working capital by $1.425 million − $0.792 million = $0.633 million in year 1 and will increase net working capital by the same amount in year 5.11 Comparing Free Cash Flows for Cisco’s Alternatives Adjusting for increases to net working capital, we compare the free cash flow of each ­alternative on lines 5 and 11 and compute their NPVs using the project’s 12% cost of ­capital.12 In each case, the NPV is negative, as we are evaluating only the costs of production. Outsourcing, however, is a little cheaper, with a present value cost of $26.2 million versus $26.9 million if the units are produced in-house.13 CONCEPT CHECK 1. How do you choose between mutually exclusive capital budgeting decisions? 2. When choosing between alternatives, what cash flows can be ignored? 8.4 Further Adjustments to Free Cash Flow In this section, we consider a number of complications that can arise when estimating a project’s free cash flow, such as non-cash charges, alternative depreciation methods, liqui- dation or continuation values, and tax loss carryforwards. 11 While inventory may be needed before production starts, we assume it will not be paid for until year 1. 12 In some settings the risks of these options might differ from the risk of the project overall or from each other, requiring a different cost of capital for each case. 13 It is also possible to compare these two cases in a single spreadsheet in which we compute the difference in the free cash flows directly, rather than compute the free cash flows separately for each option. We prefer to do them separately, as it is clearer and generalizes to the case when there are more than two options. M08_BERK6318_06_GE_C08.indd 289 26/04/23 6:16 PM  290 Chapter 8 Fundamentals of Capital Budgeting Other Non-Cash Items. In general, other non-cash items that appear as part of incre- mental earnings should not be included in the project’s free cash flow. The firm should include only actual cash revenues or expenses. For example, the firm adds back any amorti- zation of intangible assets (such as patents) to unlevered net income when calculating free cash flow. Timing of Cash Flows. For simplicity, we have treated the cash flows for HomeNet as if they occur at the end of each year. In reality, cash flows will be spread throughout the year. We can forecast free cash flow on a quarterly, monthly, or even continuous basis when greater accuracy is required. Accelerated Depreciation. Because depreciation contributes positively to the firm’s cash flow through the depreciation tax shield, it is in the firm’s best interest to use the most accel- erated method of depreciation that is allowable for tax purposes. By doing so, the firm will accelerate its tax savings and increase their present value. For example, U.S. firms can use the Modified Accelerated Cost Recovery System or MACRS ­depreciation which catego- rizes assets according to their recovery period and specifies a fraction of the purchase price the firm can depreciate each year. We provide MACRS tables for common assets in the ap- pendix to this chapter. In addition, the tax code sometimes provides for bonus depreciation which allows firms to deduct an additional portion of the purchase price when the asset is first placed into service. The Tax Cut and Jobs Act enacted in 2017 currently allows firms to take 100% bonus depreciation for qualified assets, which means that the full purchase price can be deducted immediately (though this provision is set to expire in 2023). Liquidation or Salvage Value. Assets that are no longer needed often have a resale value, or some salvage value if the parts are sold for scrap. Some assets may have a negative liqui- dation value. For example, it may cost money to remove and dispose of the used equipment. EXAMPLE 8.5 Computing Accelerated Depreciation Problem What depreciation deduction would be allowed for HomeNet’s equipment using the MACRS method, assuming the equipment is put into use by the end of year 0 and designated to have a five-year recovery period? What depreciation deduction would be allowed for HomeNet’s equip- ment with 100% bonus depreciation? (Assume that the equipment is put into use immediately.) Solution Table 8A.1 in the appendix provides the percentage of the cost that can be depreciated each year. Based on the table, the allowable depreciation expense for the lab equipment is shown below: Year 0 1 2 3 4 5 MACRS Depreciation ($000s) 1 Lab Equipment Cost (7,500) 2 MACRS Depreciation Rate 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% 3 Depreciation Expense (1,500) (2,400) (1,440) (864) (864) (432) As long as the equipment is put into use by the end of year 0, the tax code allows us to take our first depreciation expense in the same year. Compared with straight-line depreciation, the MACRS method allows for larger depreciation deductions earlier in the asset’s life, which increases the present value of the depreciation tax shield and so will raise the project’s NPV (see Problem 17). Bonus depreciation would allow us to deduct the full $7.5 million cost of the equipment in year 0, accelerating the tax shield and increasing NPV even further. M08_BERK6318_06_GE_C08.indd 290 26/04/23 6:16 PM  8.4 Further Adjustments to Free Cash Flow 291 In the calculation of free cash flow, we include the liquidation value of any assets that are no longer needed and may be disposed of. When an asset is liquidated, any gain on sale is taxed. We calculate the gain on sale as the difference between the sale price and the book value of the asset: Gain on Sale = Sale Price − Book Value (8.8) The book value is equal to the asset’s original cost less the amount it has already been de- preciated for tax purposes: Book Value = Purchase Price − Accumulated Depreciation (8.9) We must adjust the project’s free cash flow to account for the after-tax cash flow that would result from an asset sale:14 After-Tax Cash Flow from Asset Sale = Sale Price − ( τ c × Gain on Sale ) (8.10) EXAMPLE 8.6 Adding Salvage Value to Free Cash Flow Problem Suppose that in addition to the $7.5 million in new equipment required for HomeNet, some equipment will be transferred to the lab from another Cisco facility. This equipment has a resale value of $2 million and a book value of $1 million. If the equipment is kept rather than sold, its remaining book value can be depreciated next year. When the lab is shut down in year 5, the equipment will have a salvage value of $800,000. What adjustments must we make to HomeNet’s free cash flow in this case? Solution The existing equipment could have been sold for $2 million. The after-tax proceeds from this sale are an opportunity cost of using the equipment in the HomeNet lab. Thus, we must reduce HomeNet’s free cash flow in year 0 by the sale price less any taxes that would have been owed had the sale occurred: $2 million − 20% × ( $2 million − $1 million ) = $1.8 million. In year 1, the remaining $1 million book value of the equipment can be depreciated, creating a depreciation tax shield of 20% × $1 million = $200,000. In year 5, the firm will sell the equip- ment for a salvage value of $800,000. Because the equipment will be fully depreciated at that time, the entire amount will be taxable as a capital gain, so the after-tax cash flow from the sale is $800,000 × ( 1 − 20% ) = $640,000. The spreadsheet below shows these adjustments to the free cash flow from the spreadsheet in Table 8.3 and recalculates HomeNet’s free cash flow and NPV in this case. Year 0 1 2 3 4 5 Free Cash Flow and NPV ($000s) 1 Free Cash Flow w/o equipment (19,500) 7,000 9,100 9,100 9,100 2,400 Adjustments for use of existing equipment 2 After-Tax Salvage Value (1,800) — — — 640 3 Depreciation Tax Shield — 200 — — — 4 7,200 5 NPV at 12% 6,368 14 When the sale price is less than the original purchase price of the asset, the gain on sale is treated as a recapture of depreciation and taxed as ordinary income. If the sale price exceeds the original purchase price, then this portion of the gain on sale is considered a capital gain, and in some cases may be taxed at a lower capital gains tax rate. M08_BERK6318_06_GE_C08.indd 291 26/04/23 6:16 PM  292 Chapter 8 Fundamentals of Capital Budgeting Terminal or Continuation Value. Sometimes the firm explicitly forecasts free cash flow over a shorter horizon than the full horizon of the project or investment. This is necessarily true for investments with an indefinite life, such as an expansion of the firm. In this case, we estimate the value of the remaining free cash flow beyond the forecast horizon by including an additional, one-time cash flow at the end of the forecast horizon called the terminal or continuation value of the project. This amount represents the market value (as of the last forecast period) of the free cash flow from the project at all future dates. Depending on the setting, we use different methods for estimating the continuation value of an investment. For example, when analyzing investments with long lives, it is com- mon to explicitly calculate free cash flow over a short horizon, and then assume that cash flows grow at some constant rate beyond the forecast horizon. EXAMPLE 8.7 Continuation Value with Perpetual Growth Problem Base Hardware is considering opening a set of new retail stores. The free cash flow projections for the new stores are shown below (in millions of dollars): 0 1 2 3 4 5 6... 2+10.5 2+5.5 +0.8 +1.2 +1.3 +1.3 3 1.05 +1.3 3 (1.05)2 After year 4, Base Hardware expects free cash flow from the stores to increase at a rate of 5% per year. If the appropriate cost of capital for this investment is 10%, what continuation value in year 4 captures the value of future free cash flows in year 5 and beyond? What is the NPV of the new stores? Solution Because the future free cash flow beyond year 4 is expected to grow at 5% per year, the continu- ation value in year 4 of the free cash flow in year 5 and beyond can be calculated as a constant growth perpetuity: Continuation Value in Year 4 = PV (FCF in Year 5 and Beyond ) FCF4 × ( 1 + g ) 1.05 = = $1.30 million × r− g 0.10 − 0.05 = $1.30 million × 21 = $27.3 million Notice that under the assumption of constant growth, we can compute the continuation value as a multiple of the project’s final free cash flow. We can restate the free cash flows of the investment as follows (in thousands of dollars): Year 0 1 2 3 4 Free Cash Flow (Years 0–4) (10,500) (5,500) 800 1,200 1,300 Continuation Value 27,300 Free Cash Flow (10,500) (5,500) 800 1,200 28,600 The NPV of the investment in the new stores is 5500 800 1200 28,600 NPV = −10,500 − + 2 + + = $5597 1.10 1.10 1.10 3 1.10 4 or $5.597 million. M08_BERK6318_06_GE_C08.indd 292 26/04/23 6:16 PM  8.4 Further Adjustments to Free Cash Flow 293 Tax Carryforwards. A firm generally identifies its marginal tax rate by determining the tax bracket that it falls into based on its overall level of pretax income. If pretax income is negative, the firm is said to have a net operating loss (NOL). In that case, no tax is due, and a feature of the tax code, called a tax loss carryforward, allows corpo- rations to use past NOLs as a deduction to reduce their taxable income in future years. The Tax Cut and Jobs Act of 2017 limits the amount of the NOL deduction to be at most 80% of the firm’s current pretax income, and any excess NOLs can be carried forward to future years.15 Past NOLs that are carried forward thus provide future tax credits for the firm, and the anticipated value of these credits is listed as a deferred tax asset on the balance sheet. EXAMPLE 8.8 Tax Loss Carryforwards Problem Verian Industries has a net operating loss of $140 million this year. If Verian earns $50 million per year in pretax income from now on, what will its taxable income be over the next 4 years? If Verian earns an extra $10 million in the coming year, in which years will its taxable income increase? Solution With pretax income of $50 million per year, Verian will be able to use its tax loss carryforwards to reduce its taxable income by 80% × 50 = $40 million each year: Year 0 1 2 3 4 5 Pretax Income (140) 50 50 50 50 50 Tax Loss Carryforward — (40) (40) (40) (20) — Taxable Income — 10 10 10 30 50 If Verian earns an additional $10 million the first year, it will owe taxes on an extra $2 million next year and $8 million in year 4: Year 0 1 2 3 4 5 Pretax Income (140) 60 50 50 50 50 Tax Loss Carryforward — (48) (40) (40) (12) — Taxable Income — 12 10 10 38 50 Thus, when a firm has tax loss carryforwards, the tax impact of a portion of current earnings will be delayed until the carryforwards are exhausted. This delay reduces the present value of the tax impact, and firms sometimes approximate the effect of tax loss carryforwards by using a lower marginal tax rate. CONCEPT CHECK 1. Explain why it is advantageous for a firm to use the most accelerated depreciation schedule possible for tax purposes. 2. What is the continuation or terminal value of a project? 15 Prior to 2018, firms could also carryback NOLs to obta