Chapter 11 Cash Flows and Capital Budgeting Learning Objectives 1. Explain why incremental after-tax free cash flows are relevant in evaluating a project, and be able to calculate them for a project. 2. Discuss the five general rules for incremental after-tax free cash flow calculations, and explain why cash flows stated in nominal (real) dollars should be discounted using a nominal (real) discount rate. 3. Describe how distinguishing between variable and fixed costs can be useful in forecasting operating expenses. 4. Explain the concept of equivalent annual cost, and be able to use it to compare projects with unequal lives, decide when to replace an existing asset, and calculate the opportunity cost of using an existing asset. 5. Determine the appropriate time to harvest an asset. I. Chapter Outline 1
Calculating Project Cash Flows In capital budgeting, we estimate the NPV of the cash flows that a project is expected to produce in the future. All of the cash flow estimates are forward-looking. A. Incremental After-Tax Free Cash Flows The cash flows we discount in an NPV analysis are the incremental after-tax free cash flows, which refers to the fact that these cash flows reflect the amount by which the firm s total after-tax free cash flows will change if the project is adopted. See Equation 11.1: o FCF Project = FCF Firm with project FCF Firm without project The term free cash flows (FCF) refers to the fact that the firm is free to distribute these cash flows to creditors and stockholders because these are the cash flows that are left over after a firm has made necessary investments in working capital and long-term assets. B. The FCF Calculation Referring to 11.2, which is a more detailed version of 11.1: FCF = [(Revenue Op Exp D&A) x (1 t)] + D&A Cap Ex Add WC We first compute the incremental cash flow from operations (CF Opns), which is the cash flow that the project is expected to generate after all operating expenses and taxes have been paid. We then subtract the incremental capital expenditures (Cap Ex) and incremental additions to working capital (Add WC) required for the project to obtain FCF. 2
The FCF is therefore a measure of the after-tax cash flows from operations over and above what is necessary to make any required investments. The idea that we can evaluate the cash flows from a project independently of the cash flows for the firm is known as the stand-alone principle. It is another way of saying that we can treat the project as if it is a stand-alone firm that has its own revenue, expenses, and investment requirements. C. Cash Flows from Operations Note that the incremental cash flow from operations, CF Opns, equals the incremental net operating profits after tax (NOPAT) plus the incremental depreciation and amortization (D&A) associated with the project. We exclude interest expenses when calculating NOPAT because the cost of financing a project is reflected in the discount rate that is used in the NPV calculation. We use the firm s marginal tax rate (t) to calculate NOPAT because the profits from a project are assumed to be incremental to the firm. We add incremental depreciation and amortization (D&A) to NOPAT when calculating CF Opns because, as in the accounting statement of cash flows, D&A represents a noncash charge that reduces the firm s tax obligation. However, since D&A is a noncash charge, we have to add it back to NOPAT in order to get the cash flow from operations right. D. Cash Flows Associated with Investments Once we have estimated CF Opns, we simply subtract cash flows associated with required investment to obtain FCF for a project in a particular period. 3
Investments can be required to purchase long-term tangible assets and intangible assets, or to fund current assets. E. FCF versus Accounting Earnings The impact of a project on a firm s overall value or on its stock price does not depend on how the project affects the company s accounting earnings. It depends only on how the project affects the company s free cash flows. Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project. Accounting earnings also reflect noncash charges, such as depreciation and amortization, which are intended to account for the costs associated with deterioration of the assets in a business as those assets are used. 11.2 Estimating Cash Flows in Practice A. Five General Rules for Incremental Cash Flow Calculations Rule 1: Include cash flows and only cash flows in your calculations. Do not include allocated costs or overhead unless they reflect cash flows. Rule 2: Include the impact of the project on cash flows from other product lines. If the product associated with a project is expected to cannibalize or boost sales of another product, you must include the expected impact of the new project on the cash flows from the other product in the analysis. Rule 3: Include all opportunity costs. By opportunity costs, we mean the cost of giving up another opportunity. 4
Rule 4: Forget sunk costs. Sunk costs are costs that have already been incurred, but all that matters when you evaluate a project at a particular point in time is how much you have to invest in the future and what you could expect to receive in return for that investment; this means that past investments are irrelevant. Rule 5: Include only after-tax cash flows in the cash flow calculations. The incremental pretax earnings of a project only matter to the extent that they affect the after-tax cash flows that the firm s investors receive. B. Nominal versus Real Cash Flows Nominal dollars are the dollars that we typically think of. They represent the actual dollar amounts that we expect a project to generate in the future, without any adjustments. When prices are going up, a given nominal dollar amount will buy less and less over time. o Real dollars represent dollars stated in terms of constant purchasing power. We can write the cost of capital, k, as o 1 + k = (1 + P e ) x (1 + r) r is the real cost of capital ( P e ) is the expected rate of inflation (r) is the real rate of return It is important to make sure that all cash flows are stated in either nominal dollars or real dollars. C. Tax Rates and Depreciation 5
A progressive tax system, which we have in the United States, is one in which the marginal tax rate at low levels of income is lower than the marginal tax rate at high levels of income. One especially important difference from a capital budgeting perspective is that the depreciation methods allowed by GAAP differ from those allowed by the IRS. o The straight-line depreciation method illustrated earlier in this chapter in the NASCAR racetrack example is allowed by GAAP and is often used for financial reporting. o An accelerated method of depreciation, called the Modified Accelerated Cost Recovery System (MACRS), has been in use for U.S. federal tax calculations since the Tax Reform Act of 1986 went into effect. MACRS thus enables a firm to deduct depreciation charges sooner, thereby realizing the tax savings sooner and increasing the present value of the tax savings. D. Computing the Terminal-Year FCF The FCF in the last, or terminal, year of a project often includes cash flows that are not typically included in the calculations for other years. o For instance, in the final year of a project, the assets acquired during the life of the project may be sold and the working capital that has been invested may be recovered. Add WC = Change in cash and cash equivalents + Change in accounts receivable + Change in inventories Change in accounts payable. 6
o When an asset is expected to have a salvage value, we must include the salvage value realized from the sale (net of any tax consequences) of the asset and the impact of the sale on the firm s taxes in the terminal-year FCF calculations. E. Expected Cash Flows We are estimating when we forecast FCF in an NPV analysis. o The expected FCF for a particular year equals the sum of the products of the possible outcomes (FCFs) and the probabilities that those outcomes will be realized. 11.3.1 Forecasting Free Cash Flows A. Cash Flows from Operations To forecast incremental cash flows from operations we must forecast the incremental net revenue, operating expenses, and depreciation and amortization associated with the project, as well as the firm s marginal tax rate When forecasting operating expenses, analysts often distinguish between variable costs and fixed costs B. Investment Cash Flows We must consider two general classes of investments when calculating FCF: incremental capital expenditures and incremental additions to working capital 1. Capital Expenditures o Capital expenditure forecasts in an NPV analysis reflect the expected level of investment during each year of the project s life. 7
o Capital expenditures are typically required at the beginning of a project 2. Working Capital o Cash flow forecasts in an NPV analysis include four working capital items: 1)cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable 11.4 Special Cases A. Projects with Different Lives A problem that arises quite often in capital budgeting involves choosing between two mutually exclusive investments where the investments have different lives. o In a situation like this, we can effectively make the lives of the mowers the same by assuming repeated investments over some identical period and then comparing the NPVs of their costs. o A less cumbersome and more powerful method to handle the problem is to compute the equivalent annual cost (EAC). The EAC can be calculated as follows: EAC i = knpv i [(1 + k) t / (1 + k) t t 1] (11.5) ( 1+ k ) EACi = k NPVi t ( 1 + k ) 1 k is the opportunity cost of capital NPV i is the normal NPV of the investment i t is the life of the investment 8
EAC simply reflects the annuity that has the same present value as the FCFs of an investment over the investment period we are considering. B. When to Harvest an Asset The optimal time to harvest is the point in time at which the rate of increase in cash flows, from period to period, is no longer greater than the cost of capital. At this point in time, it becomes optimal to harvest the trees and invest the proceeds in alternative investments that yield the opportunity cost of capital. C. When to Replace an Existing Asset Two fundamental questions: Do the benefits of replacing the existing asset exceed the costs, and, if they do not now, when will they? Solving this problem is simply a matter of computing the EAC for the new asset and comparing it with the annual cash inflows from the old asset. D. The Cost of Using an Existing Asset The third rule of calculating incremental after-tax cash flows is to include all opportunity costs that are not always directly observable. o Sometimes they have to be computed by first figuring the EAC for a given set of cash flows and then adjusting the EAC by the appropriate discount rate and time, if the EAC is not in present value form. 9
II. Suggested and Alternative Approaches to the Material This is a very important chapter for all students. Finance majors will need the basic capital budgeting concepts introduced here for their more advanced course work, whereas nonmajors will require a basic foundation for the material in their professional lives as they will undoubtedly be involved in project analysis at some point in their careers. The chapter begins with a general framework for capital budgeting, so that the overall approach to capital budgeting can be seen before proceeding to the detailed aspects of the subject matter. Free cash flow (FCF) is then formally introduced, along with individual subcalculations that make it up. The chapter includes a number of examples to accompany the individual aspects of the material and finishes by introducing cases where the net present value of the projects FCFs will require further adjustments. Thorough coverage of the material is recommended before proceeding to the next chapter where the tools are then applied further. As such, it may be necessary to allocate additional time for this chapter as the material is central to Finance while it also incorporates a number of tools that were learned in earlier chapters. 10
III. Summary of Learning Objectives 1. Explain why incremental after-tax cash flows are relevant in evaluating a project, and be able to calculate them for a project. The incremental after-tax cash flows, also called the incremental free cash flows (FCFs), for a project equal the expected change in the total after-tax cash flows of the firm if the project is adopted. The impact of a project on the firm s total cash flows is the appropriate measure of cash flows because these are the cash flows that reflect all of the costs and benefits from the project and only the costs and benefits from the project. The incremental after-tax cash flows are calculated using Equation 11.2. The calculation is also illustrated in Exhibit 11.1. 2. List and explain the five general rules for incremental after-tax free cash flow calculations and why cash flows stated in nominal (real) dollars should be discounted using a nominal (real) discount rate. The five general rules are: Rule 1: Include cash flows and only cash flows in your calculations. Stockholders only care about the impact of a project on the firm s cash flows. Rule 2: Include the impact of the project on cash flows from other product lines. If a project affects the cash flows from other projects, we must take this fact into account in NPV analysis in order to fully capture the impact of the project on the firm s total cash flows. Rule 3: Include all opportunity costs. If an asset is used for a project, the relevant cost for that asset is the value that could be realized from its most valuable alternative use. By 11
including this cost in the NPV analysis, we capture the change in the firm s cash flows that is attributable to the use of this asset for the project. Rule 4: Forget sunk costs. The only costs that matter are those to be incurred from this point on. Rule 5: Include only after-tax cash flows in the cash flow calculations. Since stockholders receive cash flows after taxes have been paid, they are only concerned about after-tax cash flows. Since a nominal rate reflects both the expected rate of inflation and a real return, we would be overadjusting for inflation if we discounted a real cash flow with a nominal rate. Similarly, if we discounted a nominal cash flow using a real discount rate, we would be undercompensating for expected inflation in the discounting process. This is why we discount nominal cash flows using only a nominal discount rate and we discount real cash flows using only a real discount rate. 3. Describe how distinguishing between variable and fixed costs can be useful in forecasting operating expenses. Variable costs vary directly with the number of units sold, while fixed costs do not. When forecasting operating expenses, it is often useful to treat variable and fixed costs separately. We can forecast variable costs by multiplying unit variable costs by the number of units sold. Fixed costs are more accurately based on the specific characteristics of those costs, rather than as a function of sales. Separating fixed costs from the variable also makes it easier to identify the factors that will cause them to change over time and therefore easier to forecast them. 12
4. Explain the concept of equivalent annual cost, and be able to use it to compare projects with unequal lives, decide when to replace an existing asset, and calculate the opportunity cost of using an existing asset. The equivalent annual cost (EAC) is the annualized cost of an investment that is stated in nominal dollars. In other words, it is the annual payment from an annuity that has the same NPV and the same life as the project. Since it is a measure of the annual cost or cash inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects. Applications of the EAC concept are presented in Section 11.4. 5. Determine the appropriate time to harvest an asset. The appropriate time to harvest an asset is that point in time where harvesting the asset yields the largest present value, in today s dollars, of the project NPV. 13
IV. Summary of Key Equations Equation Description Formula 11.1 Incremental free cash flow definition FCF Project = FCF Firm with project FCF Firm without project 11.2 Incremental free dash flow calculation FCF = [(Revenue Op Exp D&A) x (1 t)] + D&A Cap Ex Add WC 11.3 Inflation and real components of cost of capital 1 + k = (1 + P e ) x (1 + r) 11.4 Incremental additions to working capital Add WC = Change in cash and cash equivalents + Change in accounts receivable + Change in inventories Change in accounts payable 11.5 Equivalent annual cost EAC i = knpv i [(1 + k) t / (1 + k) t 1] 14
V. Before You Go On Questions and Answers Section 11.1 1. Why do we care about incremental cash flows at the firm level when we evaluate a project? We care about incremental cash flows at the firm level because they reflect the impact of the project on the total cash flows that the firm produces. This is what the stockholders care about. The difference between the present value of the expected cash flows from the firm with the project and the present value of the expected cash flows from the firm without the project is precisely what the NPV of a project is. Our NPV estimate will be incorrect if we do not account for all of the incremental cash flows at the firm level. 2. Why is D&A first subtracted and then added back in FCF calculations? By subtracting D&A, calculating the tax obligation, and then adding back D&A, we are accounting for the fact that D&A is a noncash charge that reduces the firm s tax obligation by the product of D&A and the tax rate (D&A x t). If we did not do this, we would overstate the tax obligation and understate FCF. 3. What types of investments should be included in FCF calculations? All investments directly associated with the project should be included in FCF calculations. These can include both investments in tangible and intangible assets. They can also include investments 15
in additions to working capital, such as for the credit a firm extends to its customers and inventories. Section 11.2 1. What are the five general rules for calculating FCF? (1) Include cash flows and only cash flows in your calculations. (2) Include the impact of the project on cash flows from other product lines. (3) Include all opportunity costs. (4) Forget sunk costs. (5) Include only after-tax cash flows in the cash flow calculations. 2. What is the difference between nominal and real dollars? Why is it important not to mix them in an NPV analysis? When most people talk about dollar amounts, they are referring to nominal dollars. Nominal dollars do not take into account changes in purchasing power. Real dollars are dollar amounts that are adjusted for changes in purchasing power. For example, 100 real dollars have the same purchasing power whether they are received today or at some future date. It is important not to mix nominal and real dollars in an NPV analysis because the discount rate is either a nominal rate, which is used to discount nominal dollars, or a real rate, which is used to discount real dollars. Since the discount rate must be either a nominal rate or a real rate, if real and nominal dollars are mixed in an NPV analysis, the NPV will be calculated incorrectly. 16
3. What is a progressive tax system? What is the difference between a firm s marginal and average tax rates? A progressive tax system is one in which the marginal tax rate at low levels of income is lower than the marginal tax rate at high levels of income. A firm s marginal tax rate is the rate that it pays on the last dollar earned while the average tax rate is the average rate paid on the firm s total earnings (tax paid divided by taxable income). 4. How can FCF in the terminal year of a project s life differ from FCF in the other years? FCF in the terminal year can differ from FCF in other years in several ways. The terminal year cash flows can include cash flows from the asset sales, including the actual proceeds from the sales themselves and taxes due or received if there is a gain or loss on the sale. Terminal year cash flows can also include cash flows associated with recovery of working capital. 5. Why is it important to understand that cash flow forecasts in an NPV analysis are expected values? It is important to recognize that we are forecasting expected cash flows in an NPV analysis because uncertainties regarding project cash flows that are unique to the project should be reflected in the cash flow forecasts. Section 11.3 17
1. What is the difference between variable and fixed costs, and what are examples of each? Variable costs vary directly with unit sales. Fixed costs do not vary with unit sales. For an example of each, see the video game player scenario on page 379. Variable costs are those associated with purchasing the components for the player, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses. 2. How are working capital items forecast? Why are accounts receivable typically forecast as a percentage of revenue and accounts payable, and inventories as percentages of the cost of good sold? Working capital items are forecast using 1) cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable Inventories are forecast as a percentage of the cost of goods sold because the COGS represent a measure of the amount of money invested in inventories. Accounts payable are forecast this way because the COGS is a measure of the amount of money actually owed to suppliers. Section 11.4 1. When can we not simply compare the NPVs of two mutually exclusive projects? If we expect to replace at least one of the projects at the end of its life, we cannot simply compare the NPVs. Doing so would ignore the subsequent investment(s). You can only directly compare the NPVs of mutually exclusive projects under one condition that is, if you expect to terminate 18
the project that is chosen (e.g., sell the lawn mower) on or before the end of the life of the shorterlived project. 2. How do we decide when to harvest an asset? We choose the harvest date that maximizes the NPV of the asset. To identify this date, we compare the NPVs expected from harvesting the asset for each of the feasible harvest dates. The best date to harvest the asset is the date that produces the largest NPV, once the NPVs for all of the alternative harvest dates have been discounted to the same point in time. 3. Under what circumstance would you replace an old machine that is still operating with a new one? You should replace the old machine when the EAC of the new machine is lower than the EAC of the old machine (if revenues are the same for both machines) or when the annualized cash inflow from the replacement is greater. 19
VI. Self Study Problems 11.1 Explain why the announcement of a new investment is usually accompanied by a change in the firm s stock price. A firm s investments cause changes in its future after-tax cash flows and stockholders are the residual claimants (owners) of those cash flows. Therefore, the stock price should increase when stockholders expect an investment to have a positive NPV, and decrease when it is expected to have a negative NPV. 11.2 In calculating the NPV of a project, should we use all of the cash flows associated with the project, or incremental cash flows of the project? Why? We should use incremental cash flows of the project. Incremental cash flows reflect the amount by which the firm s total cash flows will change if the project is adopted. In other words, incremental cash flows represent the net difference in cash revenues, costs, and investment outlays at the firm level with and without the project, which is precisely what the stockholders care about. 11.3 You are considering opening another restaurant in the food chain of TexasBurgers. The new restaurant will have annual revenue of $300,000 and operating expenses of $150,000. The 20
annual depreciation and amortization for the assets used in the restaurant will equal $50,000. An annual capital expenditure of $10,000 will be required to offset wear-and-tear on the assets used in the restaurant, but no additions to working capital will be required. The marginal tax rate will be 40 percent. Calculate the incremental annual free cash flow for the project The incremental annual free cash flow is calculated as: FCF = ($300,000-$150,000-$50,000) x (1-0.4) + $50,000-$10,000 = $100,000 11.4 Sunglass Heaven, Inc., is launching a new store in a shopping mall in Houston. The store s annual revenue depends on Houston s weather conditions in the summer. The annual revenue will be $240,000 in a sizzling summer, with probability of 0.3; $80,000 in a cool summer, with probability of 0.2; and $150,000 in a normal summer, with probability of 0.5. What is the expected annual revenue of the store? The expected annual revenue is: (0.3 x $240,000) + (0.2 x $80,000) + (0.5 x $150,000) = $163,000 11.5 Sprigg Lane needs to purchase a new central air-conditioning system for a plant. There are two choices. The first system costs $50,000 and is expected to last 10 years, and the second 21
system costs $72,000 and is expected to last 15 years. Assume that the opportunity cost of capital is 10 percent. Which air-conditioning system should you purchase? The equivalent annual cost for each system is: EAC 1 = (0.1)($50,000)[((1.1) 10 )/((1.1) 10-1)] = $8,137.27 EAC 2 = (0.1)($72,000)[((1.1) 15 )/((1.1) 15-1)] = $9,466.11 Therefore Sprigg Lane should purchase the first one. 22
VII. Critical Thinking Questions 11.1 Do you agree or disagree with the following statement: given the techniques discussed in this chapter? We can estimate future cash flows precisely and obtain an exact value for the NPV of an investment. The statement is not true. Given the nature of the real business world, it is almost certain that the cash flows generated by a project will differ from the forecasts used to decide whether to proceed with the project. However, techniques discussed in this chapter provide an important and useful framework that helps minimize errors and ensures that forecasts are internally consistent. 11.2 What are the differences between forecasted cash flows used in capital budgeting calculations and past accounting earnings? Cash flows used in capital budgeting calculations are forward looking; they are incremental after-tax cash flows based on forecast. Accounting earnings are backward looking; they represent a record of past performance and may not accurately reflect cash flows. 11.3 Suppose that FRA Corporation already has divisions in both Dallas and Houston. FRA is now considering setting up a third division in Austin. This expansion will require one senior manager from Dallas and one from Houston to relocate to Austin. Ignore relocation expenses. Is their annual compensation relevant to the decision to expand? 23
The annual compensations of existing senior managers are not incremental to the new investment and therefore are not relevant for capital budgeting analysis. This is consistent with our Rule 1 for incremental cash flow calculations: Include cash flows and only cash flows; do not include allocated costs unless they reflect cash flows. 11.4 MusicHeaven, Inc., is a producer of MP3 players which currently have either 20 gigabytes or 30 gigabytes of storage. Now the company is considering launching a new production line making mini MP3 players with 5 gigabytes of storage. Analysts forecast that your company will be able to sell 1 million such mini MP3 players if the investment is taken. In making the investment decision, discuss what the company should consider other than the sales of the mini MP3 players. The company s launch of the new mini MP3 players may reduce its current sales of MP3 players of bigger storage. This impact has to be considered. This is consistent with our Rule 2 for incremental cash flow calculations: Include the impact of the project on cash flows from other product lines. 11.5 QualityLiving Trust is a real estate investment company that builds and remodels apartment buildings in northern California. It is currently considering remodeling a few idle buildings in its possession into luxury apartment buildings in San Jose. The company bought those buildings eight months ago. How should the market value of the buildings be treated in evaluating this project? 24
Although the buildings are not currently in use, the company can sell them at their market value rather than remodel them into apartments. Therefore, the market value of the buildings is the opportunity cost of the project and should be considered as cash outflow in the investment decision. This is consistent with our Rule 3 for incremental cash flow calculations: Include all opportunity costs. 11.6 High-End Fashions, Inc., bought a production line of ankle-length skirts last year at a cost of $500,000. This year, however, miniskirts are hot in the market and ankle-length skirts are completely out of fashion. High-End has the option to rebuild the production line and use it to produce miniskirts, with a cost of $300,000 and expected revenue of $700,000. How should the company treat the cost of $500,000 of the old production line in evaluating the rebuilding plan? The cost of the old production line occurred in the past. It cannot be changed whether or not the company rebuilds it into the miniskirt production line. Therefore, High-End should not consider the cost of $500,000. This is consistent with our Rule 4 for incremental cash flow calculations: Forget sunk costs. 11.7 How is the MACRS depreciation method under IRS rules different from that under GAAP rules? What is the implication of incremental after-tax cash flows from firms investments? 25
GAAP allows the straight-line depreciation method. In contrast, an accelerated method of depreciation, Modified Accelerated Cost Recovery System (MACRS), has been used for U.S. federal tax calculations. The advantage of MACRS, relative to straight-line depreciation, is that it enables a firm to deduct depreciation changes sooner, thereby realizing the tax saving sooner and increasing the present value of the tax savings. 11.8 Explain the difference between marginal and average tax rates, and identify which of these rates is used in capital budgeting and why. The marginal tax rate is the rate paid on the next dollar earned. The average tax rate is the dollar value of total taxes paid divided by total income. The marginal tax rate is the appropriate rate to use in capital budgeting analysis because this is the tax rate that will be paid on the incremental income earned by the project. 11.9 When two mutually exclusive projects have different lives, how should we make the capital budgeting decision? What is the underlying assumption in this method? When we choose from mutually exclusive projects with different lives, instead of electing the project with higher NPV or lower net present value of costs, we should choose the project with higher Equivalent Annual Revenue or lower Equivalent Annual Cost. The underlying assumption is that we will continue to operate with the same equivalent annual revenue or equivalent annual cost in the future. 26
11.10 What is the opportunity cost of using an existing asset? Give an example of the opportunity cost of using the excess capacity of a machine. The opportunity cost of using an existing asset in a project is the present value of the change in the firm s cash flows that is attributed to the fact that this asset is being used in the project. For example, by using the excess capacity of a machine, you may accelerate the wear-andtear of the machine and hence will need to replace it sooner. The present value of the added annualized costs is the opportunity cost of using the excess capacity. 11.11 You are providing financial advice to a shrimp farmer who will be harvesting his last crop of farm-raised shrimp. His current shrimp crop is very young and will therefore grow and become more valuable as their weight increases. Describe how you would determine the appropriate time to harvest the entire crop of shrimp. Assuming that the price of shrimp is directly (and linearly) related to the weight of the shrimp, then the optimal point in time to harvest the shrimp would be where the rate of weight increase is no longer greater than the opportunity cost of capital for the shrimp farmer. Alternatively, the appropriate time is when the value increase of the shrimp is no longer greater than the opportunity cost of capital. VIII. Questions and Problems BASIC 27
11.1 Calculating project cash flows: Why do we use forecasted cash flows instead of forecasted accounting earnings in estimating the NPV of a project? Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project. For example, ease of manipulating earnings components such as accounts receivable and depreciation may result in distorted estimation of capital budgeting; using forecasted cash flows eliminates such possibilities. In addition, because there is time value of money, cash flows better reflect the actual available funds to be distributed to shareholders at each point in time. 11.2 The FCF calculation: How do we calculate incremental free cash flow from the forecasted earnings of a project? What are the common adjustment items? We need to adjust for the depreciation and amortization tax shield, capital expenditures, and changes in working capital (including receivables and payables). 11.3 The FCF calculation: How do we adjust for depreciation when we calculate incremental aftertax cash flow from EBITDA? What is the intuition for the adjustment? 28
There are two ways to adjust for depreciation: (1) subtract depreciation from EBITDA, multiply it by (1 tax rate), and then add depreciation back; (2) add the tax shield from depreciation (depreciation multiplied by tax rate) to revenue. These two methods yield the same results. The intuition is that although depreciation itself is not a cash flow inflow or outflow, increase in depreciation will result in a decrease in taxable income. This saving on tax is treated as cash inflow in calculating incremental after-tax cash flows. 11.4 Nominal versus real cash flows: What is the difference between nominal and real dollars? Which rate of return should we use to discount each type of these cash flows in the future? Nominal dollars are dollars stated as we usually think of them, without any adjustment for changes in purchasing power over time. Real dollars are dollars stated so that their purchasing power remains constant. We should use nominal rate of return to discount future nominal dollars and real rate of return to discount future real dollars. By doing this, we will get meaningful present values in today s dollars and purchasing power. 11.5 Taxes and depreciation: What is the difference between the average tax rate and the marginal tax rate? Which one should we use in calculating the incremental after-tax cash flows? 29
In a progressive tax system, the marginal tax rate is different from the average tax rate. The average tax rate is the total amount of tax divided by total amount of money earned, while the marginal tax rate is the rate paid on the last dollar earned. Since a firm already pays taxes, the appropriate tax rate used for the firm s new project is the tax rate that the firm will pay on any additional profits that are earned because the project is adopted. Therefore, we use the marginal tax rate in calculating incremental after-tax cash flows. 11.6 Computing terminal-year FCF: Five years ago, a pharmaceutical company bought a machine that produces pain-reliever medicine at a cost of $2 million. The machine has been depreciated over the past five years, and the current book value is $800,000. The company decides to sell the machine now at its market price of $1 million. The marginal tax rate is 30 percent. What are the relevant cash flows? How do they change if the market price of the machine is $600,000 instead? The relevant cash flows include the sale price of the machine, as well as the tax on the capital gain: 1,000,000 0.3(1,000,000 800,000) = $940,000 When the market price of the machine is changed to $600,000, the relevant cash flows include the sale price and tax saving on capital loss: 6,000,000 + 0.3(800,000 600,000) = $6,060,000 30
11.7 Cash flows from operations: What are variable costs and fixed costs? What are some examples of each? How are these costs estimated in forecasting operating expenses? Variable costs vary directly with unit sales. Fixed costs do not vary with unit sales. For an example of each, see the video game player scenario on page 379. Variable costs are those associated with purchasing the components for the player, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses. 11.8 Investment cash flows: Six Twelve is considering opening up a new convenience store in downtown New York City. The expected annual revenue is $800,000. To estimate the increase in working capital, analysts estimate the ratio of cash and cash equivalents to revenue to be 0.03, and the ratio of receivables to revenue to be 0.05 in the same industry. What are the incremental cash flows related to working capital when the store is opened? Cash flow related to working capital in year 0 = $(800,000)*(0.03 + 0.05) = $(64,000) 11.9 Investment cash flows: Keswick Supply Company wants to set up a division providing copy and fax business. Customers will be given 20 days to pay for such services. The annual revenue of the division is estimated to be $25,000. What is the incremental cash flow associated with accounts receivable? 31
The customers are expected to take 20 days to pay, and the average accounts receivable balance will be (20days/365days/year)*100%*25,000 = 5.48%*25,000 = $1,370. Alternatively, the average daily credit sale is $25,000 / 365 = $68.49, and it takes 20 days, on average, to collect the sale. Therefore, 20 x $68.49 = $1,369.86, or about $1,370. 11.10 Expected cash flows: Define expected cash flows and explain why this concept is important in evaluating projects. Expected cash flows are probability-weighted averages of the future cash flows generated by a project under alternative scenarios. In the real business world there are a lot of uncertainties. Future cash flows may vary across different states of the world. It is not possible to estimate a unique number of cash flow for all states. We can estimate the expected cash flows across different states and use that as an estimation of future cash flows. The cash flows that are discounted in an NPV analysis are the expected incremental cash flows the project will produce. 11.11 Projects with different lives: Explain the concept of equivalent annual cost and how it is used to compare projects with different lives. 32
The equivalent annual cost (EAC) is the annualized cost of an investment stated in nominal dollars. In other words, it is the annual payment from an annuity with a life equal to that of a project that has the same NPV as the project. Since it is a measure of the annual cost or cash inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects. 11.12 Replace an existing asset: Explain how we decide the optimal time to replace an existing asset with a new one. The optimal time to replace an existing asset with a new one is if the benefits of replacing the machine exceed the costs. INTERMEDIATE 11.13 Nominal versus real cash flows: You are buying a sofa. You will pay $200 today and make three consecutive annual payments of $300 in the future. The real rate of return is 10 percent, and the expected inflation rate is 4 percent. What is the actual price of the sofa? We can calculate it in two different ways: (1) Use nominal dollars and nominal rate of return: Nominal rate of return = (1 + 10%)*(1 + 4%)-1 = 14.4% 33
Price = 200 + 300 / (1 + 14.4%) + 300/(1 + 14.4%) 2 + 300 / (1 + 14.4%) 3 = 891.84 (2) Use real dollars and a real rate of return: Real annual payments are: 300 / (1 + 4%) = 288.46, 300 / (1 + 4%) 2 = 277.37, and 300 / (1 + 4%) 3 = 266.70 Price = 200 + 288.46/(1 + 10%) + 277.37/(1 + 10.4%) 2 +266.7 / (1+10.4%) 3 =891.84 Note that we get identical results as long as we are consistent in using nominal or real cash flows and corresponding discount rates. 11.14 Nominal versus real cash flows: You are graduating in two years. You want to invest your current savings of $5,000 in bonds for the down payment on a new car when you graduate and start to work. You can invest the money in either Bond A, a two-year bond with a 3 percent annual interest rate, or Bond B, an inflation-indexed two-year bond paying 1 percent real interest above the inflation rate (assume this bond makes annual interest payments). The inflation rate over the next two years is expected to be 1.5 percent. Assume that both bonds are default free and have the same market price. Which one should you invest in? The nominal interest rate is 3 percent for bond A, and (1 + 1%)*(1 +1.5%) 1 = 2.52% for the inflation-indexed bond B. You should invest in bond A. 34
11.15 Marginal and average tax rates: Given the U.S. Corporate Tax Rate Schedule in Exhibit 11.5, what is the marginal tax rate and average tax rate of a corporation that generates a taxable income of $12 million in 2007? The marginal tax rate is 35 percent. The total tax payable is 3,400,000 + (12,000,000-10,000,000)*35% = $4,100,000 Therefore the average tax rate = 4,100,000 / 12,000,000 = 34.2% 11.16 Investment cash flows: Healthy Potions, Inc., is considering investing in a new production line of eye drops. Other than investing in the equipment, the company needs to increase its cash and cash equivalents by $10,000, increase the level of inventory by $30,000, increase accounts receivable by $25,000, and increase accounts payable by $5,000 at the beginning of the investment. Healthy Potions will recover these changes in working capital at the end of the project 10 years later. Assume the appropriate discount rate to be 12 percent. What are the relevant cash flows given the above information? The relevant cash flow related to working capital at the beginning of the project is: $(10,000)-$30,000-$25,000 + $5,000 = $(60,000) The present value of relevant cash flow related to working capital at the end of the project is: 60,000 / (1 + 12%) 10 = $19,318.39 35
11.17 Cash flows from operations: Given the soaring price of gasoline, Ford is considering introducing a new production line of gas-electric hybrid sedans. The expected annual sales number of such hybrid cars is 30,000; the price is $22,000 per car. Variable costs of production amount to $10,000 per car. The fixed overhead including salary of top executives is $80 million per year. However, the introduction of the hybrid sedan will decrease Ford s sales of regular sedans by 10,000 cars per year; the regular sedans have a unit price of $20,000 and unit variable cost of $12,000, and fixed costs of $250,000 per year. Depreciation costs of the production plant are $50,000 per year. The marginal tax rate is 40 percent. What is the incremental annual cash flow from operations? Step One: Revenue: $22,000 x 30,000 machines =$660,000,000 Step Two: Op Exp: $10,000 x 30,000 machines = $300,000,000, plus lost net revenue from regular sedans = ($20,000 $12,000) x 10,000 = $80,000,000; total Op Exp = $380,000,000 Step Three: D&A: $50,000 Step Four: Plug information into the text book template as below. ΔNR 660,000,000 - ΔOpEx -380,000,000 = ΔEBITDA 280,000,000 - ΔD&A -50,000 = ΔEBIT 279,950,000 x (1-t) 0.60 = ΔNOPAT 167,970,000 + ΔD&A 50,000 = ΔCFO 168,020,000 - ΔCapEx 0 - ΔAWC 0 = ΔFCF 168,020,000 36
Alternatively, the incremental annual cash flow from operations is: ((22,000-10,000)*30,000-(20,000-12,000)*10,000)*(1-0.4) + 50,000*0.4 = 168,020,000 Note that the fixed costs are not included in the incremental cash flows calculations, since they exist regardless of the hybrid sedan investment. 11.18 FCF and NPV for a project: Archers Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12 million. The investment will consist of $2 million for land and $10 million for trucks and other equipments. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years at a price of $5 million, $2 million above book value. The farm is expected to produce revenue of $2 million each year, and annual cash flow from operates equals $1.8 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment. Cash flow of investment in year 0 is: $(12,000,000) PV of annual investment year 1 to 10 is found using the present value factor for an annuity: Payment * ( 1 {1 / (1 + i) n }) / i) $(1,000,000)( 1 {1 / (1.1) 10 }) / 0.1) = $(6,144,567.11) PV of sales and tax on capital gain in year 10 is: (5,000,000-[2,000,000*0.35]) / (1.1) 10 = 1,657,836.15 Therefore, PV of investment cash flows = $(16,486,730.97) 37
The company should not buy the farm. 11.19 Projects with different lives: You are starting a family pizza restaurant and need to buy a motorcycle for delivery orders. You have two models in mind. Model A costs $9,000 and is expected to run for 6 years; model B is more expensive, with a price of $14,000 and an expected life of 10 years. The annual maintenance costs are $800 for model A and $700 for model B. Assume that the opportunity cost of capital is 10 percent. Which one should you buy? You need first calculate the NPV of costs for each of the motorcycles: NPV A = 9,000 + 800*(((1.1) 6-1) / ((1.1) 6 *0.1)) = 12,484.21 NPV B = 14,000 + 700*(((1.1) 10-1) / ((1.1) 10 *0.1)) = 18,301.20 Then you need to calculate the EAC of each model: EAC A = 12,484.21*10%*((1.1) 6 ) / ((1.1) 6-1) = 2,866.47 EAC B = 18,301.20*10%*((1.1) 10 ) / ((1.1) 10-1) = 2,978.44 Therefore you should buy model A. 11.20 When to harvest an asset: Predator LLC, a leveraged buyout specialist, recently bought a company and want to decide the optimal time to sell it. The partner in charge of this investment has estimated the after-tax cash flows at different times as follows: $700,000 if sold one year later; $1,000,000 if sold two years later; $1,200,000 if sold three years later; and 38
$1,300,000 if sold four years later. The opportunity cost of capital is 12 percent. When should Predator sell the company? Why? The NPV of each choice is: NPV 1 = 700,000 / (1.12) 1 = 625,000 NPV 2 = 1,000,000 / (1.12) 2 = 797,194 NPV 3 = 1,200,000 / (1.12) 3 = 854,136 NPV 4 = 1,300,000 / (1.12) 4 =826,174 Therefore you should sell the company three years later. 11.21 Replace an existing asset: Bell Mountain Vineyards is considering updating its current accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. Bell Mountain s opportunity cost of capital is 10 percent, and the costs and values of future savings choices are as follows: Year Cost Value of Future Savings (at time of purchase) 0 $5,000 $7,000 1 4,500 7,000 2 4,000 7,000 3 3,600 7,000 4 3,300 7,000 5 3,100 7,000 39
When should Bell Mountain buy the new accounting system? The NPV of each choice is: NPV 0 = 2,000 NPV 1 = 2,500 / (1.1) 1 = 2,275 NPV 2 = 3,000 / (1.1) 2 = 2,479 NPV 3 = 3,400 /(1.1) 3 =2,554 NPV 4 = 3,700 / (1.1) 4 = 2,527 NPV 5 = 3,900 / (1.1) 5 = 2,422 Therefore the company should buy it in year 3. 11.22 Replace an existing asset: You have a 1993 Nissan that is expected to run for another three years, but you are considering buying a new Hyundai in a few years. You will donate the old Nissan to Goodwill when you buy the new car. The annual maintenance cost is $1,500 per year for the old Nissan and $200 for the new Hyundai. The price of your favorite Hyundai model is $18,000; it is expected to run for 15 years. Your opportunity cost of capital is 3 percent. Ignore taxes. When should you buy the new Hyundai? NPV of cost of the new car is: NPV Hyundai = 18,000 + 200*(((1.03) 15-1) / ((1.03) 15 *0.03)) = 20,387.59 EAC of the new car is: 40
EAC Hyundai = 20,387.59*0.03*((1.03) 15 ) / ((1.03) 15-1) = 1,707.8 > 1,500 Therefore, you should drive the 1993 Nissan for three more years and then buy a new Hyundai. 11.23 Replace an existing asset: Assume that you are considering replacing your old Nissan with a new Hyundai, as in the previous problem. However, the annual maintenance cost of the old Nissan increases as time goes by. It is $1,200 in the first year, $1,500 in the second year, and $1,800 in the third year. When should you replace it with the new Hyundai in this case? The EAC of the Hyundai remains at $1,707.8, as calculated in the previous problem. Compare this amount with the annual maintenance costs of the Nissan and you will see that in year 2 it is cheaper to drive the Nissan, but in year 3 it is cheaper to drive the Hyundai. Therefore, the optimal time to replace the old car is at the end of year 2. 11.24 When to harvest an existing asset: Anaconda Manufacturing Company currently own a mine that is known to contain a known amount of gold. Since Anaconda does not have any goldmining expertise, the company plans to sell the entire mine and base the selling price on a fixed multiple of the spot price for gold at the time of the sale. Analysts at Anaconda have forecast the price spot for gold and have determined that the price will increase by 14 percent, 12 percent, 9 percent, and 6 percent during the next one, two, three, and four years, respectively. If Anaconda s opportunity cost of capital is 10 percent, what is the optimal time for Anaconda to sell the mine? 41