How is Capital Budgeting used in an Organization

how to solve capital budgeting problems and how capital budgeting could be used for evaluation purposes and how to do capital budgeting in excel
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Published Date:17-07-2017
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8 Fundamentals of Capital Budgeting LEARNING OBJECTIVES ◗ Identify the types of cash flows ◗ Recognize common pitfalls that needed in the capital budgeting arise in identifying a project’s process incremental free cash flows ◗ Forecast incremental earnings in a ◗ Assess the sensitivity of a project’s pro forma earnings statement for a NPV to changes in your assumptions project ◗ Identify the most common options ◗ Convert forecasted earnings to available to managers in projects free cash flows and compute a and understand why these options project’s NPV can be valuable notation CapEx capital expenditures NPV net present value EBIT earnings before interest and taxes NWC net working capital in year t t FCF free cash flow in year t PV present value t IRR internal rate of return r projected cost of capital 242244 Part 3 Valuation and the Firm An important responsibility of corporate financial managers is determining which projects or investments a firm should undertake. Capital budgeting, the focus of this chapter, is the process of analyzing investment opportunities and deciding which ones to accept. In doing so, we are allocating the firm’s funds to various projects—we are budgeting its capital. Chapter 7 covered the various methods for evaluating projects and proved that NPV will be the most reliable and accurate method for doing so. In retrospect, this may not be surprising as it is the only rule directly tied to the Valuation Principle. To implement the NPV rule, we must compute the NPV of our projects and accept only those projects for which the NPV is positive. We spoke in the last chapter about Sony and Toshiba each using investment decision rules to pursue competing high definition DVD standards (and eventually for Toshiba, to decide to abandon HD-DVD). In order to implement the investment decision rules, financial managers from Toshiba, for example, had to first forecast the incremental cash flows associated with the investments and later to forecast the incremental cash flows associated with the decision to stop investing in HD-DVD. The process of forecasting those cash flows, crucial inputs in the investment decision process, is our focus in this chapter. We begin by estimating the project’s expected cash flows by forecasting the project’s revenues and costs. Using these cash flows, we can compute the project’s NPV—its contribution to share- holder value. Then, 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. Finally, we examine the relationship between a project’s flexibility and its NPV. 8.1 The Capital Budgeting Process The first step in analyzing various investment opportunities is compiling a list of poten- capital budget Lists all tial projects. A capital budget lists the projects and investments that a company plans to of the projects that a com- undertake during future years. To create this list, firms analyze alternate projects and pany plans to undertake decide which ones to accept through a process called capital budgeting. This process during the next period. begins with forecasts of each project’s future consequences for the firm. Some of these consequences will affect the firm’s revenues; others will affect its costs. Our ultimate goal Answer to Concept Check 1 is to determine the effect of the decision to accept or reject a project on the firm’s cash capital budgeting The flows, and evaluate the NPV of these cash flows to assess the consequences of the decision process of analyzing for the firm’s value. Figure 8.1 depicts the types of cash flows found in a typical project. investment opportunities We will examine each of these as we proceed through our discussion of capital budgeting. and deciding which ones Of course, forecasting these cash flows is frequently challenging. We will often need to accept. to rely on different experts within the firm to obtain estimates for many of them. For example, the marketing department may provide sales forecasts, the operations manager may provide information about production costs, and the firm’s engineers may estimate the upfront research and development expenses that are required to launch the project. Another important source of information comes from looking at past projects of the firm, or those of other firms in the same industry. In particular, practitioners often base their assessments of a project’s revenues and costs using information on revenues and costs that can be learned from the historical financial statements of the firm or its competitors.Chapter 8 Fundamentals of Capital Budgeting 245 FIGURE 8.1 Start-Up On-Going Shut-Down Cash Flows in a Typical Project Purchase Incremental Sale of Equipment The diagram shows Equipment Revenues (Net of any taxes) some typical cash flows in project analy- Initial Development Incremental Shut-Down Costs Costs Costs sis and their timing. Taxes Increase in Net Working Change in Net Working Decrease in Net Working Capital (Increase Capital (Change in Capital (Decrease inventories, raw inventories, raw inventories, raw materials, etc.) materials, accounts materials, etc.) receivable and payable) incremental earnings Once we have these estimates, how do we organize them? One common starting The amount by which point is first to consider the consequences of the project for the firm’s earnings. Thus, a firm’s earnings are we will begin our analysis in Section 8.2 by determining the incremental earnings of a expected to change as project—that is, the amount by which the firm’s earnings are expected to change as a a result of an investment result of the investment decision. The incremental earnings forecast tells us how the decision. decision will affect the firm’s reported profits from an accounting perspective. However, Answer to Concept Check 2 as we emphasized in Chapter 2, earnings are not actual cash flows. We need to estimate the project’s cash flows to determine its NPV and decide whether it is a good project for the firm. Therefore, in Section 8.3, we demonstrate how to use the incremental earnings to forecast the actual cash flows of the project. Understanding how to compute the cash flow consequences of an investment based on its earning consequences is important for a number of reasons. First, as a practical matter, financial managers often begin by fore- casting earnings. Second, if we are looking at historical data, accounting information is often the only information that is readily available. Dilbert, May 05, 1994, United Features Syndicate. 1. What is capital budgeting, and what is its goal? Concept 2. Why is computing a project’s effect on the firm’s earnings insufficient for capital budgeting? Check246 Part 3 Valuation and the Firm 8.2 Forecasting Incremental Earnings Let’s begin our discussion of incremental earnings with a simple example that we will examine throughout this section. Suppose you are considering whether to upgrade your manufacturing plant and increase its capacity by purchasing a new piece of equipment. The equipment costs 1 million, plus an additional 20,000 to transport it and install it. You will also spend 50,000 on engineering costs to redesign the plant to accommodate the increased capacity. What are the initial earnings consequences of this decision? Answer to Concept Check 3 Operating Expenses Versus Capital Expenditures Most projects require some form of upfront investment—we may need to conduct a mar- keting survey, develop a prototype, or launch an ad campaign. These types of costs are accounted for as operating expenses in the year that they are incurred. However, many projects also include investments in plant, property, and/or equipment, called capital expenditures. Recall from Chapter 2 that while investments in plant, property, and equip- ment 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 depre- ciation. Financial managers use several different methods to compute depreciation. The straight-line deprecia- simplest method is straight-line depreciation, in which the asset’s cost is divided equally tion A method of depreci- over its depreciable life (we discuss another common method in Section 8.4). ation in which an asset’s In our example, the upfront costs associated with the decision to increase capacity cost is divided equally have two distinct consequences for the firm’s earnings. First, the 50,000 spent on over its life. redesigning the plant is an operating expense reported in year 0. For the 1,020,000 spent to buy, ship, and install the machine, accounting principles as well as tax rules require you to depreciate the 1,020,000 over the depreciable life of the equipment. Assuming that the equipment has a five-year depreciable life and that we use the straight-line method, we would expense 1,020,000 / 5 = 204,000 per year for five years. (The moti- vation for this accounting treatment is to match the cost of acquiring the machine to the timing of the revenues it will generate.) 1 Year 0 1 2 3 4 5 2 Operating Expenses 50,000 (Plant Redesign) 3 Depreciation 204,000 204,000 204,000 204,000 204,000 (New Equipment) As the timeline shows, the upfront cash outflow of 1,020,000 to purchase and set- up the machine is not recognized as an expense in year 0. Instead, it appears as depreci- ation expenses in years 1 through 5. Remember that these depreciation expenses do not correspond to actual cash outflows. This accounting and tax treatment of capital expen- ditures is one of the key reasons why earnings are not an accurate representation of cash flows. We will return to this issue in Section 8.3. Incremental Revenue and Cost Estimates Our next step is to estimate the ongoing revenues and costs for the project. Forecasting future revenues and costs is challenging. The most successful practitioners collect as much information as possible before tackling this task—they will talk to members ofChapter 8 Fundamentals of Capital Budgeting 247 marketing and sales teams as well as company economists to develop an estimate of sales, and they will talk to engineering and production teams to refine their estimate of costs. There are several factors to consider when estimating a project’s revenues and costs, including the following: 1. A new product typically has lower sales initially, as customers gradually become aware of the product. Sales will then accelerate, plateau, and ultimately decline as the product nears obsolescence or faces increased competition. 2. The average selling price of a product and its cost of production will generally 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. 3. For most industries, competition tends to reduce profit margins over time. Our focus here is on how to get from these forecasts to incremental earnings and then to cash flows; Chapter 17 discusses forecasting methods in more detail. All our revenue and cost estimates should be incremental, meaning that we only Answer to Concept Check 4 account for additional sales and costs generated by the project. For example, if we are evaluating the purchase of a faster manufacturing machine, we are only concerned with how many additional units of the product we will be able to sell (and at what price) and any additional costs created by the new machine. We do not forecast total sales and costs because those include our production using the old machine. Remember, we are evalu- ating how the project will change the cash flows of the firm. That is why we focus on incremental revenues and costs. Let’s return to our plant upgrade example. Assume that after we have bought and installed the machine and redesigned the plant, our additional capacity will allow us to generate incremental revenues of 500,000 per year for five years. Those incremental revenues will be associated with 150,000 per year in incremental costs. In that case our revenue, cost, and depreciation estimates for the project are as shown below (in thou- sands of dollars): 1 Year 0 1 2 3 4 5 2 Incremental Revenues 500 500 500 500 500 3 Incremental Costs 50 150 150 150 150 150 4 Depreciation 204 204 204 204 204 Now that we have these estimates, we are ready to compute the consequences of our project for the firm’s earnings. As we saw in Chapter 2, both depreciation expenses and the actual costs of producing (e.g. cost of goods sold) must be subtracted from revenues, so that: Incremental Earnings Before Interest and Taxes (EBIT) = Incremental Revenue - Incremental Costs - Depreciation (8.1) Taxes marginal corporate tax The final expense we must account for is corporate taxes. The correct tax rate to use is rate The tax rate a firm the firm’s marginal corporate tax rate, which is the tax rate it will pay on an incremental will pay on an incremental dollar of pre-tax income. The incremental income tax expense is calculated as: dollar of pre-tax income. Income Tax = EBIT the firm’s marginal corporate tax rate (8.2)248 Part 3 Valuation and the Firm Incremental Earnings Forecast We’re now ready to put the pieces together for an incremental earnings forecast. Assume our firm faces a marginal tax rate of 40%. Then the incremental earnings (or net 1 income) are as follows (in thousands of dollars): 1 Year 0 1 2 3 4 5 2 Incremental Revenues 500 500 500 500 500 3 Incremental Costs 150 150 150 150 50 150 4 Depreciation 204 204 204 204 204 5 EBIT 50 146 146 146 146 146 6 Income Tax at 40% 20 58.4 58.4 58.4 58.4 58.4 7 Incremental Earnings 30 87.6 87.6 87.6 87.6 87.6 We can also combine Eq. 8.1 and Eq. 8.2 to compute incremental earnings directly. For example, in years 1 through 5 we have: Incremental Earnings = (Incremental Revenues - Incremental Cost - Depreciation) (1 - Tax Rate) (8.3) Incremental Earnings = (500,000 - 150,000 - 204,000) (1 - 0.4) = 87,600 Problem EXAMPLE 8.1 Suppose that Linksys is considering the development of a wireless home networking appli- Incremental Earnings ance, 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 PCs and printers, HomeNet will control new Internet-capable stereos, digital video recorders, heating and air- conditioning units, major appliances, telephone and security systems, office equipment, and so on. The major competitor for HomeNet is a product being developed by Brandt-Quigley Corporation. Based on extensive marketing surveys, the sales forecast for HomeNet is 50,000 units per year. Given the pace of technological change, Linksys expects the product will have a four-year life and an expected wholesale price of 260 (the price Linksys will receive from stores). Actual production will be outsourced at a cost (including packaging) of 110 per unit. To verify the compatibility of new consumer Internet-ready appliances, as they become available, with the HomeNet system, Linksys must also establish a new lab for testing pur- poses. It will rent the lab space, but will need to purchase 7.5 million of new equipment. The equipment will be depreciated using the straight-line method over a five-year life. The lab will be operational at the end of one year. At that time, HomeNet will be ready to ship. Linksys expects to spend 2.8 million per year on rental costs for the lab space, as well as marketing and support for this product. Forecast the incremental earnings from the HomeNet project. 1 While revenues and costs occur throughout the year, the standard convention, which we adopt here, is to list revenues and costs in the year in which they occur. Thus, cash flows that occur at the end of one year will be listed in a different column than those that occur at the start of the next year, even though they may occur only weeks apart. When additional precision is required, cash flows are often estimated on a quarterly or monthly basis.Chapter 8 Fundamentals of Capital Budgeting 249 Solution ◗ Plan We need 4 items to calculate incremental earnings: (1) incremental revenues, (2) incremental costs, (3) depreciation, and (4) the marginal tax rate: Incremental Revenues are additional units sold price = 50,000 260 = 13,000,000 Incremental Costs are: additional units sold production costs = 50,000 110 = 5,500,000 Selling, General, and Administrative = 2,800,000 for rent, marketing and support Depreciation is: Depreciable base / Depreciable Life = 7,500,000 / 5 = 1,500,000 Marginal Tax Rate: 40% Note that even though the project lasts for four years, the equipment has a five-year life, so we must account for the final depreciation charge in the fifth year. ◗ Execute (in 000s) 1 Year 05 1 2 3 4 2 Revenues 13,000 13,000 13,000 13,000 – 3 Cost of Goods Sold 5,500 5,500 5,500 5,500 – 4 Gross Profit 7,500 7,500 7,500 7,500 – 5 Selling, General, and Administrative 2,800 2,800 2,800 2,800 – 6 Depreciation 1,500 1,500 1,500 1,500 1,500 7 EBIT 3,200 3,200 3,200 3,200 1,500 8 Income Tax at 40% 1,280 1,280 1,280 1,280 600 9 Incremental Earnings 1,920 1,920 1,920 1,920 900 ◗ Evaluate These incremental earnings are an intermediate step on the way to calculating the incremen- tal cash flows that would form the basis of any analysis of the HomeNet project. The cost of the equipment does not affect earnings in the year it is purchased, but does so through the depre- ciation expense in the following five years. Note that the depreciable life, which is based on accounting rules, does not have to be the same as the economic life of the asset—the period over which it will have value. Here, the firm will use the equipment for four years, but will depre- ciate it over five years. Pro Forma Statement. The table calculating incremental earnings that we produced Answer to Review Question 1 for our plant upgrade, and again in Example 8.1, is often referred to as a pro forma state- pro forma Describes ment, because it is not based on actual data but rather depicts the firm’s financials under a statement that is not a given set of hypothetical assumptions. In the HomeNet example, the firm’s forecasts of based on actual data but revenues and costs were assumptions that allowed Linksys to forecast incremental earn- rather depicts a firm’s ings in a pro forma statement. financials under a given set of hypothetical Taxes and Negative EBIT. Notice that in year 0 of our plant upgrade project, and in assumptions. year 5 of the HomeNet example, EBIT is negative. Why are taxes relevant in this case? Consider the HomeNet example. HomeNet will reduce Linksys’s taxable income in year 5 by 1.5 million. As long as Linksys earns taxable income elsewhere in year 5 against which it can offset HomeNet’s losses, Linksys will owe 1.5 million 40% = 600,000 less in taxes in year 5 than if it were not undertaking the project. Because the tax sav- ings come from the depreciation expense on equipment for the HomeNet project, the firm should credit this tax savings to the HomeNet project.250 Part 3 Valuation and the Firm Problem EXAMPLE 8.2 Kellogg Company plans to launch a new line of high-fiber, zero-trans-fat breakfast pastries. The Taxing Losses for heavy advertising expenses associated with the new product launch will generate operating Projects in Profitable losses of 15 million next year for the product. Kellogg expects to earn pre-tax income of 460 Companies million from operations other than the new pastries next year. If Kellogg pays a 40% tax rate on its pre-tax income, what will it owe in taxes next year without the new pastry product? What will it owe with the new product? Solution ◗ Plan We need Kellogg’s pre-tax income with and without the new product losses and its tax rate of 40%. We can then compute the tax without the losses and compare it to the tax with the losses. ◗ Execute Without the new product, Kellogg will owe 460 million 40% = 184 million in corporate taxes next year. With the new product, Kellogg’s pre-tax income next year will be only 460 mil- lion - 15 million = 445 million, and it will owe 445 million 40% = 178 million in tax. ◗ Evaluate Thus, launching the new product reduces Kellogg’s taxes next year by 184 million - 178 mil- lion = 6 million. Because the losses on the new product reduce Kellogg’s taxable income dol- lar for dollar, it is the same as if the new product had a tax bill of negative 6 million. What About 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, however, we generally do not include interest expenses. Any incre- mental interest expenses will be related to the firm’s decision regarding how to finance the project, which is a separate decision. Here, we wish to evaluate the earnings contri- butions from the project on its own, separate from the financing decision. Ultimately, managers may also look at the additional earnings consequences associated with differ- ent methods of financing the project. Thus, we evaluate a project as if the company will not use any debt to finance it (whether or not that is actually the case), and we postpone the consideration of alterna- tive financing choices until Part V of this book. Because we calculate the net income unlevered net income assuming no debt (no leverage), we refer to the net income we compute using Eq. 8.3, Net income that does not as in the pro forma in Example 8.1, as the unlevered net income of the project, to indi- include interest expenses associated with debt. cate that it does not include any interest expenses associated with debt. 3. How are operating expenses and capital expenditures treated differently when calculating Concept incremental earnings? Check 4. Why do we focus only on incremental revenues and costs, rather than all revenues and costs of the firm? 8.3 Determining Incremental Free Cash Flow As discussed in Chapter 2, earnings are an accounting measure of the firm’s performance. 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,Chapter 8 Fundamentals of Capital Budgeting 251 the firm needs cash. Thus, to evaluate a capital budgeting decision, we must determine free cash flow The incre- its consequences for the firm’s available cash. The incremental effect of a project on the mental effect of a project on a firm’s available cash. firm’s available cash is the project’s incremental free cash flow. Calculating Free Cash Flow from Earnings As discussed in Chapter 2, there are important differences between earnings and cash Answer to Review Question 2 flow. Earnings include non-cash charges, such as depreciation, but do not include the cost of capital investment. To determine a project’s free cash flow from its incremental earnings, we must adjust for these differences. Capital Expenditures and Depreciation. As we have noted, depreciation is not a cash expense that is paid by the firm. Rather, it is a method used for accounting and tax pur- poses to allocate the original purchase cost of the asset over its life. Because deprecia- Answer to Concept Check 5 tion is not a cash flow, we do not include it in the cash flow forecast. However, that does not mean we can ignore depreciation. The depreciation expense reduces our taxable earnings and in doing so reduces our taxes. Taxes are cash flows, so because depreciation affects our cash flows, it still matters. Our approach for handling depreciation is to add it back to the incremental earnings to recognize the fact that we still have the cash flow associated with it. For example, a project has incremental gross profit (revenues minus costs) of 1 million and a 200,000 depreciation expense. If the firm’s tax rate is 40%, then the incremental earnings will be (1,000,000 - 200,000) (1 - 0.40) = 480,000. However, the firm will still have 680,000 because the 200,000 depreciation expense is not an actual cash outflow. Table 8.1 shows the calculation to get the incremental free cash flow in this case. Blue boxes surround all of the actual cash flows in the column labeled “Correct.” A good way to check to make sure the incremental free cash flow is correct is to sum the actual cash flows. In this case, the firm generated 1,000,000 in gross profit (a positive cash flow), paid 320,000 in taxes (a negative cash flow), and was left with 1,000,000 - 320,000 = 680,000, which is the amount shown as the incremental free cash flow. In the last column, labeled “Incorrect,” we show what would happen if you just ignored depreciation altogether. Because EBIT would be too high, the taxes would be too high as well and consequently, the incremental free cash flow would be too low. (Note that the difference of 80,000 between the two cases is entirely due to the differ- ence in tax payments.) Correct Incorrect TABLE 8.1 Incremental Gross Profit 1,000,000 1,000,000 Deducting and then Adding Back Depreciation -200,000 Depreciation EBIT 800,000 1,000,000 Tax at 40% -320,000 -400,000 Incremental Earnings 480,000 600,000 Add Back depreciation 200,000 Incremental Free Cash Flow 680,000 600,000252 Part 3 Valuation and the Firm Problem EXAMPLE 8.3 Let’s return to the HomeNet example. In Example 8.1, we computed the incremental earnings Incremental Free for HomeNet, but we need the incremental free cash flows to decide whether Linksys should Cash Flows proceed with the project. Solution ◗ Plan The difference between the incremental earnings and incremental free cash flows in the HomeNet example will be driven by the equipment purchased for the lab. We need to recognize the 7.5 million cash outflow associated with the purchase in year 0 and add back the 1.5 mil- lion depreciation expenses from year 1 to 5 as they are not actually cash outflows. ◗ Execute (in 000s) 1 Year 0 1 2 3 4 5 2 Revenues 13,000 13,000 13,000 13,000 – 3 Cost of Goods Sold 5,500 5,500 5,500 5,500 – 4 Gross Profit 7,500 7,500 7,500 7,500 – 5 Selling, General, and Administrative 2,800 2,800 2,800 2,800 – 6 Depreciation 1,500 1,500 1,500 1,500 1,500 7 EBIT 3,200 3,200 3,200 3,200 1,500 8 Income Tax at 40% 1,280 1,280 1,280 1,280 600 9 Incremental Earnings 1,920 1,920 1,920 1,920 900 10 Add Back Depreciation 1,500 1,500 1,500 1,500 1,500 11 Purchase of Equipment 7,500 12 Incremental Free Cash Flows 7,500 3,420 3,420 3,420 3,420 600 ◗ Evaluate By recognizing the outflow from purchasing the equipment in year 0, we account for the fact that 7.5 million left the firm at that time. By adding back the 1.5 million depreciation expenses in years 1–5, we adjust the incremental earnings to reflect the fact that the depreci- ation expense is not a cash outflow. Net Working Capital (NWC). Another way that incremental earnings and free cash flows can differ is if there are changes in net working capital. We defined net working capital in Answer to Review Question 3 Chapter 2 as the difference between current assets and current liabilities. The main com- ponents of net working capital are cash, inventory, receivables, and payables: Net Working Capital = Current Assets - Current Liabilities = Cash + Inventory + Receivables - Payables (8.4) Most projects will require the firm to invest in net working capital. Firms may need 2 to maintain a minimum cash balance to meet unexpected expenditures, and inventories of raw materials and finished product to accommodate production uncertainties and demand fluctuations. Also, customers may not pay for the goods they purchase immedi- ately. While sales are immediately counted as part of earnings, the firm does not receive any cash until the customers actually pay. In the interim, the firm includes the amount 2 The cash included in net working capital is cash that is not invested to earn a market rate of return. It includes cash held in the firm’s checking account, in a company safe or cash box, in cash registers (for retail stores), and other sites.Chapter 8 Fundamentals of Capital Budgeting 253 trade credit The differ- that customers owe in its receivables. Thus, the firm’s receivables measure the total ence between receivables credit that the firm has extended to its customers. In the same way, payables measure and payables that is the the credit the firm has received from its suppliers. The difference between receivables net amount of a firm’s cap- and payables is the net amount of the firm’s capital that is consumed as a result of these ital consumed as a result credit transactions, known as trade credit. of those credit transac- We care about net working capital because it reflects a short-term investment that tions; the credit that a firm ties up cash flow that could be used elsewhere. For example, when a firm holds a lot of extends to its customers. unsold inventory or has a lot of outstanding receivables, cash flow is tied up in the form Answer to Review Question 4 of inventory or in the form of credit extended to customers. It is costly for the firm to tie up that cash flow because it delays the time until the cash flow is available for reinvest- ment or distribution to shareholders. Since we know that money has time value, we can- not ignore this delay in our forecasts for the project. Thus, whenever net working capital Answer to Concept Check 6 increases, reflecting additional investment in working capital, it represents a reduction in cash flow that year. It is important to note that only changes in net working capital impact cash flows. For example, consider a three-year project that causes the firm to build up initial inventory by 20,000 and maintain that level of inventory in years 1 and 2, before drawing it down as the project ends and the last product is sold. It is often necessary for the initial increase in inventory to occur prior to the first sale so that the higher level of inventory would be achieved by the end of year 0. The level of the incremental net working capital in each year, the associated change in net working capital and the cash flow implications, would be: 1 Year 0 1 2 3 2 Level of Incremental NWC 20,000 20,000 20,000 0 3 Change in Incremental NWC 20,000 0 0 20,000 4 Cash Flow from Change in NWC 20,000 0 0 20,000 Note that the cash flow effect from a change in net working capital is always equal and opposite in sign to the change in net working capital. For example, an increase in inventory represents an investment or cash outflow, while a reduction in that inventory frees up that investment of capital and represents a cash inflow. Thus in capital budget- ing we subtract changes in net working capital to arrive at the cash flows. Also notice that since the level of incremental net working capital did not change in years 1 and 2, there was no new cash flow effect. Intuitively, as the firm is using up inventory and replenish- ing it, the net new investment in inventory is zero, so no additional cash outflow is required. Finally, note that over the life of the project, the incremental net working cap- ital returns to zero so that the changes (+20,000 in year 0 and -20,000 in year 3) sum to zero. Accounting principles ensure this by requiring the recapture of working capital over the life of the project. More generally, we define the change in net working capital in year t as: Change in NWC in year t = NWC - NWC (8.5) t t- 1 When a project causes a change in NWC, that change must be subtracted from incre- mental earnings to arrive at incremental free cash flows. Problem EXAMPLE 8.4 Suppose that HomeNet will have no incremental cash or inventory requirements (products will Incorporating be shipped directly from the contract manufacturer to customers). However, receivables Changes in Net related to HomeNet are expected to account for 15% of annual sales, and payables are Working Capital expected to be 15% of the annual cost of goods sold (COGS). Fifteen percent of 13 million in254 Part 3 Valuation and the Firm sales is 1.95 million and 15% of 5.5 million in COGS is 825,000. HomeNet’s net working capital requirements are shown in the following table: 1 Year 0 1 2 3 4 5 2 Net Working Capital Forecast (000s) 3 Cash Requirements 0 0 4 Inventory 0 0 5 Receivables (15% of Sales) 0 0 6 Payables (15% of COGS) 0 0 7 Net Working Capital 0 0 How does this requirement affect the project’s free cash flow? Solution ◗ Plan Any increases in net working capital represent an investment that reduces the cash available to the firm and so reduces free cash flow. We can use our forecast of HomeNet’s net working capital requirements to complete our estimate of HomeNet’s free cash flow. In year 1, net work- ing capital increases by 1.125 million. This increase represents a cost to the firm. This reduc- tion of free cash flow corresponds to the fact that 1.950 million of the firm’s sales in year 1, and 0.825 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, when the project is shut down, net working capital falls by 1.125 million as the payments of the last customers are received and the final bills are paid. We add this 1.125 million to free cash flow in year 5. ◗ Execute (in 000s) 1 Year 0 1 2 3 4 5 2 Net Working Capital 0 1,125 1,125 1,125 1,125 0 3 Change in NWC 1,125 0 0 0 1,125 4 Cash Flow Effect 1,125 0 0 0 1,125 The incremental free cash flows would then be: 1 Year 0 1 2 3 4 5 2 Revenues 13,000 13,000 13,000 13,000 0 3 Costs of Goods Sold 5,500 5,500 5,500 5,500 0 4 Gross Profit 7,500 7,500 7,500 7,500 0 5 Selling, General, and Administrative 2,800 2,800 2,800 2,800 0 6 Depreciation 1,500 1,500 1,500 1,500 1,500 7 EBIT 3,200 3,200 3,200 3,200 1,500 8 Income Tax at 40% 1,280 1,280 1,280 1,280 600 9 Incremental Earnings 1,920 1,920 1,920 1,920 900 10 Add Back Depreciation 1,500 1,500 1,500 1,500 1,500 11 Purchase of Equipment 7,500 12 Subtract Changes in NWC 1,125 0 0 0 1,125 13 Incremental Free Cash Flows 7,500 2,295 3,420 3,420 3,420 1,725 ◗ Evaluate The free cash flows differ from unlevered net income by reflecting the cash flow effects of capi- tal expenditures on equipment, depreciation, and changes in net working capital. Note that in the first two years, free cash flow is lower than unlevered net income, reflecting the upfront invest- ment in equipment and net working capital required by the project. In later years, free cash flow exceeds unlevered net income because depreciation is not a cash expense. In the last year, the firm ultimately recovers the investment in net working capital, further boosting the free cash flow.Chapter 8 Fundamentals of Capital Budgeting 255 Calculating Free Cash Flow Directly As we noted at the outset of this chapter, because practitioners usually begin the capital budgeting process by first forecasting earnings, we have chosen to do the same. However, we can calculate a project’s free cash flow directly by using the following shorthand formula: Free Cash Flow Unlevered Net Income '''''''''''%'''''''''''& Free Cash Flow = (Revenues - Costs - Depreciation) (1 - tax rate) + Depreciation - CapEx - Change in NWC (8.6) Note that we first deduct depreciation when computing the project’s incremental earn- ings and then add it back (because it is a non-cash expense) when computing free cash flow. Thus, the only effect of depreciation is to reduce the firm’s taxable income. Indeed, we can rewrite Eq. 8.6 as: Free Cash Flow = (Revenues - Costs) (1 - tax rate) - CapEx - Change in NWC + tax rate Depreciation (8.7) The last term in Eq. 8.7, tax rate Depreciation, is called the depreciation tax shield, depreciation tax shield The tax savings that result which is the tax savings that results from the ability to deduct depreciation. As a con- from the ability to deduct sequence, depreciation expenses have a positive impact on free cash flow. Returning to depreciation. our example in Table 8.1, if the firm ignored depreciation, its taxes were 400,000 instead of 320,000, leaving it with incremental free cash flow of 600,000 instead of 680,000. Notice that the 80,000 difference is exactly equal to the tax rate (40%) mul- tiplied by the depreciation expense (200,000). Every dollar of depreciation expense saves the firm 40 cents in taxes, so the 200,000 depreciation expense translates into an 80,000 tax savings. Firms often report a different depreciation expense for accounting and for tax pur- poses. Because only the tax consequences 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. For tax purposes, many firms use a system called Modified Accelerated Cost Recovery System, which we discuss in the next section. Calculating the NPV The goal of forecasting the incremental free cash flows is to have the necessary inputs to calculate the project’s NPV. To compute a project’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 invest- ment with similar risk and maturity. We will develop the techniques needed to estimate the cost of capital in Part IV of the text, when we discuss risk and return. For now, we take the cost of capital as given. We compute the present value of each free cash flow in the future by discounting it at the project’s cost of capital. As explained in Chapter 4, using r to represent the cost of capital, the present value of the free cash flow in year t (or FCF ) is: t FCF 1 t PV(FCF ) = = FCF (8.8) t t t t (1 + r) (1 + r) (')' t-year discount factor256 Part 3 Valuation and the Firm Problem EXAMPLE 8.5 Assume that Linksys’s managers believe that the HomeNet project has risks similar to its exist- Calculating the ing projects, for which it has a cost of capital of 12%. Compute the NPV of the HomeNet project. Project’s NPV Solution ◗ Plan From Example 8.4, the incremental free cash flows for the HomeNet project are (in 000s): 1 Year 0 1 2 3 4 5 2 Incremental Free Cash Flows 7,500 2,295 3,420 3,420 3,420 1,725 To compute the NPV, we sum the present values of all of the cash flows, noting that the year 0 cash outflow is already a present value. ◗ Execute Using Eq. 8.8, 2295 3420 3420 3420 1725 NPV=-7500 + + + + + = 2862 1 2 3 4 5 (1.12) (1.12) (1.12) (1.12) (1.12) ◗ Evaluate Based on our estimates, HomeNet’s NPV is 2.862 million. While HomeNet’s upfront cost is 7.5 million, the present value of the additional free cash flow that Linksys will receive from the project is 10.362 million. Thus, taking the HomeNet project is equivalent to Linksys hav- ing an extra 2.862 million in the bank today. 5. If depreciation expense is not a cash flow, why do we have to subtract it and add it back? Concept Why not just ignore it? Check 6. Why does an increase in net working capital represent a cash outflow? 8.4 Other Effects on Incremental Free Cash Flows When computing the incremental free cash flows of an investment decision, we should include all changes between the firm’s free cash flows with the project versus without the project. These include opportunities forgone due to the project and effects of the project on other parts of the firm. In this section, we discuss these other effects, some of the pitfalls and common mistakes to avoid, and finally the complications that can arise when forecasting incremental free cash flows. 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 opportunity cost The the resource is available for free. However, in many cases the resource could provide value a resource could value for the firm in another opportunity or project. The opportunity cost of using a have provided in its best 3 alternative use. resource is the value it could have provided in its best alternative use. Because this 3 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.Chapter 8 Fundamentals of Capital Budgeting 257 The Opportunity Cost of an Idle Asset Common Mistake A common mistake is to conclude that if an asset is cur- firm. Even if the firm has no alternative use for the asset, rently idle, its opportunity cost is zero. For example, the the firm could choose to sell or rent the asset. The value firm might have a warehouse that is currently empty or obtained from the asset’s alternative use, sale, or rental a machine that is not being used. Often, the asset may represents an opportunity cost that must be included as have been idled in anticipation of taking on the new proj- part of the incremental cash flows. ect, and would have otherwise been put to use by the value is lost when the resource is used by another project, we should include the oppor- tunity cost as an incremental cost of the project. For example, your company may be considering building a retail store on some land that it owns. Even though it already owns the land, it is not free to the store project. If it did not put its store on the land, the project externalities company could sell the land, for example. This forgone market price for the land is an Indirect effects of a project opportunity cost of the retail store project. that may increase or decrease the profits of Project Externalities other business activities of a firm. Project externalities are indirect effects of a project that may increase or decrease the Answer to Review Question 5 profits of other business activities of the firm. For instance, some purchasers of Apple’s iPhone would otherwise have bought Apple’s iPod nano. When sales of a new product displace sales of an existing product, the situation is often referred to cannibalization When as cannibalization. The lost sales of the existing sales of a firm’s new prod- project are an incremental cost to the company of uct displace sales of one of its existing products. going forward with the new product. Sunk Costs sunk cost Any unrecov- erable cost for which a A sunk cost is any unrecoverable cost for which the firm is already liable. Sunk costs firm is already liable. have been or will be paid regardless of the decision whether or not to proceed with the Answer to Concept Check 7 project. Therefore, they are not incremental with respect to the current decision and should not be included in its analysis. You may hire a market research firm to do mar- ket analysis to determine whether there is demand for a new product you are consider- ing and the analysis may show that there is not enough demand, so you decide not to go forward with the project. Does that mean you do not have to pay the research firm’s bill? Of course you still have to pay the bill, emphasizing that the cost was sunk and incurred whether you went forward with the project or not. A good rule to remember is that if your decision does not affect a cash flow, then the cash flow should not affect your decision. If the cash flow is the same regardless of the decision, then it is not relevant to your decision. Following are some common exam- ples of sunk costs you may encounter. overhead expenses Fixed Overhead Expenses. Overhead expenses are associated with activities that are Those expenses associ- not directly attributable to a single business activity but instead affect many different areas ated with activities that of the corporation. Examples include the cost of maintaining the company’s headquarters are not directly attributa- and the salary of the CEO. These expenses are often allocated to the different business ble to a single business activities for accounting purposes. To the extent that these overhead costs are fixed and activity but instead affect will be incurred in any case, they are not incremental to the project and should not be many different areas of a included. Only include as incremental expenses the additional overhead expenses that corporation. arise because of the decision to take on the project.258 Part 3 Valuation and the Firm The Sunk Cost Fallacy Common Mistake Being influenced by sunk costs is such a widespread continue funding the joint development of the Concorde mistake that it has a special name: sunk cost fallacy. aircraft even after it was clear that sales of the plane The most common problem is that people “throw good would fall far short of what was necessary to justify its money after bad.” That is, people sometimes continue continued development. The project was viewed by the to invest in a project that has a negative NPV because British government as a commercial and financial disas- they have already invested a large amount in the proj- ter. However, the political implications of halting the ect and feel that by not continuing it, the prior invest- project—and thereby publicly admitting that all past ment will be wasted. The sunk cost fallacy is also expenses on the project would result in nothing— sometimes called the “Concorde effect,” a term that ultimately prevented either government from abandon- refers to the British and French governments’ decision to ing the project. Past Research and Development Expenditures. A pharmaceutical company may spend tens of millions of dollars developing a new drug, but if it fails to produce an effect in tri- als (or worse, has only negative effects), should it proceed? The company cannot get its development costs back and the amount of those costs should have no bearing on whether to continue developing a failed drug. When a firm has already devoted significant 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 that is 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. Adjusting Free Cash Flow Here, we describe a number of complications that can arise when estimating a project’s free cash flow. Timing of Cash Flows. For simplicity, we have treated the cash flows in our examples as if they occur at annual intervals. In reality, cash flows will be spread throughout the year. While it is common to forecast at the annual level, we can forecast free cash flow on a quarterly or monthly basis when greater accuracy is required. In practice, firms often choose shorter intervals for riskier projects so that they might forecast cash flows at the monthly level for projects that carry considerable risk. For example, cash flows for a new facility in Europe may be forecasted at the quarterly or annual level, but if that same facility were located in a politically unstable country, the forecasts would likely be at the monthly level. MACRS depreciation The Answer to Concept Check 8 most accelerated cost Accelerated Depreciation. Because depreciation contributes positively to the firm’s recovery system allowed cash flow through the depreciation tax shield, it is in the firm’s best interest to use the by the IRS. Based on the most accelerated method of depreciation that is allowable for tax purposes. By doing so, recovery period, MACRS  the firm will accelerate its tax savings and increase their present value. In the United depreciation tables assign States, the most accelerated depreciation method allowed by the IRS is MACRS (Modified a fraction of the purchase Accelerated Cost Recovery System) depreciation. With MACRS depreciation, the firm price that the firm can depreciate each year. first categorizes assets according to their recovery period. Based on the recovery period, Answer to Review Question 6Chapter 8 Fundamentals of Capital Budgeting 259 MACRS depreciation tables assign a fraction of the purchase price that the firm can recover each year. We provide MACRS tables and recovery periods for common assets in the appendix. Problem EXAMPLE 8.6 What depreciation deduction would be allowed for HomeNet’s 7.5 million lab equipment using Computing the MACRS method, assuming the lab equipment is designated to have a five-year recovery Accelerated period? (See the appendix for information on MACRS depreciation schedules.) Depreciation Solution ◗ Plan Table 8.4 in this chapter’s Appendix A provides the percentage of the cost that can be depreci- ated each year. Under MACRS, we take the percentage in the table for each year and multiply it by the original purchase price of the equipment to calculate the depreciation for that year. ◗ Execute Based on the table, the allowable depreciation expense for the lab equipment is shown below (in thousands of dollars): 1 Year 0 1 2 3 4 5 2 MACRS Depreciation 3 Lab Equipment Cost 7,500 4 MACRS Depreciation Rate 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% 5 Depreciation Expense 1,500 2,400 1,440 864 864 432 ◗ Evaluate 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 thus will raise the project’s NPV. In the case of HomeNet, computing the NPV using MACRS depreciation leads to an NPV of 3.179 million. 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 neg- ative liquidation value. For example, it may cost money to remove and dispose of the used equipment. 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 capital gain is taxed as income. We calculate the capital gain as the difference between the sale price and the book value of the asset: Capital Gain = Sale Price - Book Value (8.9) The book value is equal to the asset’s original cost less the amount it has already been depreciated for tax purposes: Book Value = Purchase Price - Accumulated Depreciation (8.10) We must adjust the project’s free cash flow to account for the after-tax cash flow that would result from an asset sale: After-Tax Cash Flow from Asset Sale = Sale Price - (Tax Rate Capital Gain) (8.11)260 Part 3 Valuation and the Firm Problem EXAMPLE 8.7 As production manager, you are overseeing the shutdown of a production line for a discontin- Computing After-Tax ued product. Some of the equipment can be sold for a total price of 50,000. The equipment Cash Flows from an was originally purchased four years ago for 500,000 and is being depreciated according to the Asset Sale five-year MACRS schedule. If your marginal tax rate is 35%, what is the after-tax cash flow you can expect from selling the equipment? Solution ◗ Plan In order to compute the after-tax cash flow, you will need to compute the capital gain, which, as Eq. 8.9 shows requires you to know the book value of the equipment. The book value is given in Eq. 8.10 as the original purchase price of the equipment less accumulated depreciation. Thus, you need to follow these steps: 1. Use the MACRS schedule to determine the accumulated depreciation. 2. Determine the book value as purchase price minus accumulated depreciation. 3. Determine the capital gain as the sale price less the book value. 4. Compute the tax owed on the capital gain and subtract it from the sale price, following Eq. 8.11. ◗ Execute From the chapter appendix, we see that the first five rates of the five-year MACRS schedule (including year 0) are: 1 Year 0 1 2 3 4 2 20.00% 32.00% 19.20% 11.52% 11.52% Depreciation Rate 3 Depreciation Amount 100,000 160,000 96,000 57,600 57,600 Thus, the accumulated depreciation is 100,000 + 160,000 + 96,000 + 57,600 + 57,600 = 471,200, such that the remaining book value is 500,000 - 471,200 = 28,800. (Note we could have also calculated this by summing the rates for years remaining on the MACRS sched- ule (Year 5 is 5.76%, so .0576 500,000 = 28,800). The capital gain is then 50,000 - 28,800 = 21,200 and the tax owed is 0.35 21,200 = 7,420. Your after-tax cash flow is then found as the sale price minus the tax owed: 50,000 - 7,420 = 42,580. ◗ Evaluate Because you are only taxed on the capital gain portion of the sale price, figuring the after-tax cash flow is not as simple as subtracting the tax rate multiplied by the sale price. Instead, you have to determine the portion of the sale price that represents a gain and compute the tax from there. The same procedure holds for selling equipment at a loss relative to book value—the loss creates a deduction for taxable income elsewhere in the company. tax loss carryforwards and carrybacks Two fea- tures of the U.S. tax code Tax Carryforwards. A firm generally identifies its marginal tax rate by determining the that allow corporations to tax bracket that it falls into based on its overall level of pre-tax income. Two additional take losses during a cur- features of the tax code, called tax loss carryforwards and carrybacks, allow corporations rent year and offset them to take losses during a current year and offset them against gains in nearby years. against gains in nearby Since 1997, companies can “carry back” losses for two years and “carry forward” losses years. Since 1997, com- for 20 years. This tax rule means that a firm can offset losses during one year against panies can “carry back” income for the last two years, or save the losses to be offset against income during the losses for two years and next 20 years. When a firm can carry back losses, it receives a refund for back taxes in “carry forward” losses for 20 years. the current year. Otherwise, the firm must carry forward the loss and use it to offsetChapter 8 Fundamentals of Capital Budgeting 261 future taxable income. When a firm has tax loss carryforwards well in excess of its cur- rent pre-tax income, then additional income it earns today will simply increase the taxes it owes after it exhausts its carryforwards. Replacement Decisions Often the financial manager must decide whether to replace an existing piece of equip- ment. The new equipment may allow increased production, resulting in incremental revenue, or it may simply be more efficient, lowering costs. The typical incremental effects associated with such a decision are salvage value from the old machine, purchase of the new machine, cost savings and revenue increases, and depreciation effects. Problem EXAMPLE 8.8 You are trying to decide whether to replace a machine on your production line. The new Replacing an Existing machine will cost 1 million, but will be more efficient than the old machine, reducing costs by Machine 500,000 per year. Your old machine is fully depreciated, but you could sell it for 50,000. You would depreciate the new machine over a five-year life using MACRS. The new machine will not change your working capital needs. Your tax rate is 35%. Solution ◗ Plan Incremental revenues: 0 Incremental costs: - 500,000 (a reduction in costs will appear as a positive number in the costs line of our analysis) Depreciation schedule (from the appendix): 1 Year 0 1 2 3 4 5 2 Depreciation Rate 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% 3 200,000 320,000 192,000 115,200 115,200 57,600 Depreciation Amount Capital gain on salvage = 50,000 - 0 = 50,000 Cash flow from salvage value: +50,000 - (50,000)(.35) = 32,500 ◗ Execute 1 Year 0 1 2 3 4 5 2 Incremental Revenues 3 Incremental Costs of Goods Sold 500 500 500 500 500 4 Incremental Gross Profit 500 500 500 500 500 5 Depreciation 200 320 192 115.2 115.2 57.6 6 EBIT 200 180 308 384.8 384.8 442.4 7 Income Tax at 35% 70 63 107.8 134.68 134.68 154.84 8 Incremental Earnings 130 117 200.2 250.12 250.12 287.56 9 Add Back Depreciation 200 320 192 115.2 115.2 57.6 10 Purchase of Equipment 1,000 11 Salvage Cash Flow 32.5 12 Incremental Free Cash Flows 897.5 437 392.2 365.32 365.32 345.16 ◗ Evaluate Even though the decision has no impact on revenues, it still matters for cash flows because it reduces costs. Further, both selling the old machine and buying the new machine involve cash flows with tax implications.262 Part 3 Valuation and the Firm 7. Should we include sunk costs in the cash flows of a project? Why or why not? Concept 8. Explain why it is advantageous for a firm to use the most accelerated depreciation schedule Check possible for tax purposes. 8.5 Analyzing the Project When evaluating a capital budgeting project, financial managers should make the deci- sion that maximizes NPV. As we have discussed, to compute the NPV for a project you need to estimate the incremental free cash flows and choose a discount rate. Given these inputs, the NPV calculation is relatively straightforward. The most difficult part of capital budgeting is deciding how to estimate the cash flows and cost of capital. These estimates are often subject to significant uncertainty. In this section, we look at methods that assess sensitivity analysis An the importance of this uncertainty and identify the drivers of value in the project. important capital budget- ing tool that determines Sensitivity Analysis how the NPV varies as a An important capital budgeting tool for assessing the effect of uncertainty in forecasts is single underlying assump- tion is changed. sensitivity analysis. Sensitivity analysis breaks the NPV calculation into its component Answer to Concept Check 9 assumptions and shows how the NPV varies as the underlying assumptions change. In Answer to Review Question 7 this way, sensitivity analysis allows us to explore the effects of errors in our NPV esti- mates for a project. By conducting a sensitivity analysis, we learn which assumptions are the most important; we can then invest further resources and effort to refine these assumptions. Such an analysis also reveals which aspects of a project are most critical when we are actually managing the project. In fact, we have already performed a type of sensitivity analysis in Chapter 7 when we constructed an NPV profile. By graphing the NPV of a project as a function of the discount rate, we are assessing the sensitivity of our NPV calculation to uncertainty about the cor- rect cost of capital to use as a discount rate. In practice, financial managers explore the sensitivity of their NPV calculation to many more factors than just the discount rate. To illustrate, consider the assumptions underlying the calculation of HomeNet’s NPV in Example 8.5. There is likely to be significant uncertainty surrounding each revenue and cost assumption. In addition to the base case assumptions about units sold, sale price, cost of goods sold, net working capital, and cost of capital, Linksys’s managers would also identify best and worst case scenarios for each. For example, assume that they identified the best and worst case assumptions listed in Table 8.2. Note that these are best and worst case scenarios for each parameter rather than representing one worst case scenario and one best case scenario. To determine the importance of this uncertainty, we recalculate the NPV of the HomeNet project under the best- and worst-case assumptions for each parameter. For example, if the number of units sold is only 35,000 per year, the NPV of the project falls Parameter Initial Assumption Worst Case Best Case TABLE 8.2 Units Sold (thousands) 50 35 65 Best- and Worst-Case Sale Price (/unit) 260 240 280 Assumptions for Each Cost of Goods (/unit) 110 120 100 Parameter in the NWC ( thousands) 1125 1525 725 HomeNet Project Cost of Capital 12% 15% 10%

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