In 2017, Intel announced plans to invest over $7 billion to produce 7-nanometer chips in its Chandler, Arizona, facility. How does a company such as Intel decide to go ahead with such a massive investment? We know the answer in principle. The company needs to forecast the project’s cash flows and discount them at the opportunity cost of capital to arrive at the project’s NPV. A project with a positive NPV increases shareholder value.
But those cash flow forecasts do not arrive on a silver platter. For example, Intel’s managers would have needed answers to several basic questions. How soon can the new plant be brought into operation? How many semiconductor chips are likely to be sold each year and at what price? How much does the firm need to invest in the new facilities, and what is the likely production cost? How long will the chips stay in production, and what happens to the plant and equipment at the end of that time?
These predictions need to be pulled together to produce a single set of cash-flow forecasts. That requires careful tracking of taxes; changes in working capital; inflation; and the end-of-project salvage values of plant, property, and equipment. The financial manager must also ferret out hidden cash flows and take care to reject accounting entries that look like cash flows but truly are not.
Our first task in this chapter is to look at how to develop a set of project cash flows. We set out several rules of good financial practice. Later in the chapter, we work through a realistic and comprehensive example of a capital investment analysis.
This is the first chapter in which we grapple with the complexities of taxes. Therefore, we have added a section that includes an overview of corporate income taxes and the dramatic recent changes in the U.S. tax code.
We conclude the chapter by looking at how the financial manager should apply the present value rule when choosing between investment in plant and equipment with different economic lives. For example, suppose you must decide between machine Y with a 5-year useful life and a similar machine Z with a 10-year life. The present value of Y’s lifetime investment and operating costs is naturally less than Z’s because Z will last twice as long. Does that necessarily make Y the better choice? Of course not. You will find that when you are faced with this type of problem, the trick is to transform the present value of the cash flow into an equivalent annual flow—that is, the total cash per year from buying and operating the asset.
6-1Applying the Net Present Value Rule
Many projects require a heavy initial outlay on new production facilities. But often the largest investments involve the acquisition of intangible assets. For example, U.S. banks invest huge sums annually in new information technology (IT) projects. Much of this expenditure goes to intangibles such as system design, programming, testing, and training. Think also of the huge expenditure by pharmaceutical companies on research and development (R&D). Merck, one of the largest pharmaceutical companies, spends more than $7 billion a year on R&D. The R&D cost of bringing one new prescription drug to market has been estimated at more than $2 billion.
Expenditures on intangible assets such as IT and R&D are investments just like expenditures on new plant and equipment. In each case, the company is spending money today in the expectation that it will generate a stream of future profits. Ideally, firms should apply the same criteria to all capital investments, regardless of whether they involve a tangible or intangible asset.
We have seen that an investment in any asset creates wealth if the discounted value of the future cash flows exceeds the up-front cost. Up to this point, however, we have glossed over the problem of what to discount. When you are faced with this problem, you should stick to five general rules:
1. Discount cash flows, not profits.
2. Discount incremental cash flows.
3. Treat inflation consistently.
4. Separate investment and financing decisions.
5. Forecast and deduct taxes.
We discuss each of these rules in turn.
Rule 1: Discount Cash Flows, Not Profits
The first and most important point: Net present value depends on the expected future cash flow. Cash flow is simply the difference between cash received and cash paid out. Many people nevertheless confuse cash flow with accounting income. Accounting income is intended to show how well the company is performing. Therefore, accountants start with “dollars in” and “dollars out,” but to obtain accounting income, they adjust these inputs in two principal ways.
Capital Expenses When calculating expenditures, the accountant deducts current expenses but does not deduct capital expenses. There is a good reason for this. If the firm lays out a large amount of money on a big capital project, you do not conclude that the firm is performing poorly, even though a lot of cash is going out the door. Therefore, instead of deducting capital expenditure as it occurs, the accountant depreciates the outlay over several years.
That makes sense when judging firm performance, but it will get you into trouble when working out net present value. For example, suppose that you are analyzing an investment proposal. It costs $2,000 and is expected to provide a cash flow of $1,500 in the first year and $500 in the second. If the accountant depreciates the capital expenditure straight line over the two years, accounting income is $500 in year 1 and −$500 in year 2:
|
Year 1 |
Year 2 |
|
|
Cash inflow |
+$1,500 |
+$ 500 |
|
Less depreciation |
− 1,000 |
− 1,000 |
|
Accounting income |
+$ 500 |
−$ 500 |
Suppose you were given this forecast income and naïvely discounted it at 10%. NPV would appear positive:
This has to be nonsense. The project is obviously a loser. You are laying out $2,000 today and simply getting it back later. At any positive discount rate the project has a negative NPV. The message is clear: When calculating NPV, state capital expenditures when they occur, not later when they show up as depreciation. To go from accounting income to cash flow, you need to add back depreciation (which is not a cash outflow) and subtract capital expenditure (which is a cash outflow).
Working Capital When measuring income, accountants try to show profit as it is earned, rather than when the company and its customers get around to paying their bills.
For example, consider a company that spends $60 to produce goods in period 1. It sells these goods in period 2 for $100, but its customers do not pay their bills until period 3. The following diagram shows the firm’s cash flows. In period 1 there is a cash outflow of $60. Then, when customers pay their bills in period 3, there is an inflow of $100.
It would be misleading to say that the firm was running at a loss in period 1 (when cash flow was negative) or that it was extremely profitable in period 3 (when cash flow was positive). Therefore, the accountant looks at when the sale was made (period 2 in our example) and gathers together all the revenues and expenses associated with that sale. In the case of our company, the accountant would show for period 2.
|
Revenue |
$100 |
|
Less cost of goods sold |
− 60 |
|
Income |
$ 40 |
Of course, the accountant cannot ignore the actual timing of the cash expenditures and payments. So the $60 cash outlay in the first period will be treated not as an expense but as an investment in inventories. Subsequently, in period 2, when the goods are taken out of inventory and sold, the accountant shows a $60 reduction in inventories.
The accountant also does not ignore the fact that the firm has to wait to collect on its bills. When the sale is made in period 2, the accountant will record accounts receivable of $100 to show that the company’s customers owe $100 in unpaid bills. Later, when the customers pay those bills in period 3, accounts receivable are reduced by that $100.
To go from the figure for income to the actual cash flows, you need to add back these changes in inventories and receivables:
|
Period |
|||
|
1 |
2 |
3 |
|
|
Accounting income |
0 |
+40 |
0 |
|
− Investment in inventories |
−60 |
+60 |
0 |
|
−Investment in receivables |
0 |
−100 |
+100 |
|
= Cash flow |
−60 |
0 |
+100 |
Net working capital (often referred to simply as working capital) is the difference between a company’s short-term assets and liabilities. Accounts receivable and inventories of raw materials, work in progress, and finished goods are the principal short-term assets. The principal short-term liabilities are accounts payable (bills that you have not paid) and taxes that have been incurred but not yet paid.1
Most projects entail an investment in working capital. Each period’s change in working capital should be recognized in your cash-flow forecasts.2 By the same token, when the project comes to an end, you can usually recover some of the investment. This results in a cash inflow. (In our simple example the company made an investment in working capital of $60 in period 1 and $40 in period 2. It made a disinvestment of $100 in period 3, when the customers paid their bills.)
Working capital is a common source of confusion in capital investment calculations. Here are the most common mistakes:
1. Forgetting about working capital entirely. We hope that you do not fall into that trap.
2. Forgetting that working capital may change during the life of the project. Imagine that you sell $100,000 of goods a year and customers pay on average six months late. You therefore have $50,000 of unpaid bills. Now you increase prices by 10%, so revenues increase to $110,000. If customers continue to pay six months late, unpaid bills increase to $55,000, and so you need to make an additional investment in working capital of $5,000.
3. Forgetting that working capital is recovered at the end of the project. When the project comes to an end, inventories are run down, any unpaid bills are (you hope) paid off, and you recover your investment in working capital. This generates a cash inflow.
Rule 2: Discount Incremental Cash Flows
The value of a project depends on all the additional cash flows that follow from project acceptance. Here are some things to watch for when you are deciding which cash flows to include.
Include All Incidental Effects It is important to consider a project’s effects on the remainder of the firm’s business. For example, suppose Sony proposes to launch PlayStation X, a new version of its videogame console. Demand for the new product will almost certainly cut into sales of Sony’s existing consoles. This incidental effect needs to be factored into the incremental cash flows. Of course, Sony may reason that it needs to go ahead with the new product because its existing product line is likely to come under increasing threat from competitors. So, even if it decides not to produce the new PlayStation, there is no guarantee that sales of the existing consoles will continue at their present level. Sooner or later, they will decline.
Sometimes a new project will help the firm’s existing business. Suppose that you are the financial manager of an airline that is considering opening a new short-haul route from Harrisburg, Pennsylvania, to Chicago’s O’Hare Airport. When considered in isolation, the new route may have a negative NPV. But once you allow for the additional business that the new route brings to your other traffic out of O’Hare, it may be a very worthwhile investment.
Do Not Confuse Average with Incremental Payoffs Most managers naturally hesitate to throw good money after bad. For example, they are reluctant to invest more money in a losing division. But occasionally you will encounter turnaround opportunities in which the incremental NPV from investing in a loser is strongly positive.
Conversely, it does not always make sense to throw good money after good. A division with an outstanding past profitability record may have run out of good opportunities. You would not pay a large sum for a 20-year-old horse, sentiment aside, regardless of how many races that horse had won or how many champions it had sired.
Here is another example illustrating the difference between average and incremental returns: Suppose that a railroad bridge is in urgent need of repair. With the bridge the railroad can continue to operate; without the bridge it can’t. In this case, the payoff from the repair work consists of all the benefits of operating the railroad. The incremental NPV of such an investment may be enormous. Of course, these benefits should be net of all other costs and all subsequent repairs; otherwise, the company may be misled into rebuilding an unprofitable railroad piece by piece.
Forecast Product Sales but also Recognize After-Sales Cash Flows Financial managers should forecast all incremental cash flows generated by an investment. Sometimes these incremental cash flows last for decades. When GE commits to the design and production of a new jet engine, the cash inflows come first from the sale of engines and then from service and spare parts. A jet engine will be in use for 30 years. Over that period revenues from service and spare parts will be roughly seven times the engine’s purchase price.
Many other manufacturing companies depend on the revenues that come after their products are sold. For example, the consulting firm Accenture estimates that services and parts typically account for about 25% of revenues and 50% of profits for auto companies.3
Include Opportunity Costs The cost of a resource may be relevant to the investment decision even when no cash changes hands. For example, suppose a new manufacturing operation uses land that could otherwise be sold for $100,000. This resource is not free: It has an opportunity cost, which is the cash it could generate for the company if the project were rejected and the resource were sold or put to some other productive use.
This example prompts us to warn you against judging projects on the basis of “before versus after.” The proper comparison is “with or without.” A manager comparing before versus after might not assign any value to the land because the firm owns it both before and after:
|
Before |
Take Project |
After |
Cash Flow, Before versus After |
|
Firm owns land |
→ |
Firm still owns land |
0 |
The proper comparison, with or without, is as follows:
|
With |
Take Project |
After |
Cash Flow, with Project |
|
Firm owns land |
→ |
Firm still owns land |
0 |
|
Without |
Do Not Take Project |
After |
Cash Flow, without Project |
|
→ |
Firm sells land for $100,000 |
$100,000 |
Comparing the two possible “afters,” we see that the firm gives up $100,000 by undertaking the project. This reasoning still holds if the land will not be sold but is worth $100,000 to the firm in some other use.
Sometimes opportunity costs may be very difficult to estimate; however, where the resource can be freely traded, its opportunity cost is simply equal to the market price. Consider a widely used aircraft such as the Boeing 737. Secondhand 737s are regularly traded, and their prices are quoted on the web. So, if an airline needs to know the opportunity cost of continuing to use one of its 737s, it just needs to look up the market price of a similar plane. The opportunity cost of using the plane is equal to the cost of buying an equivalent aircraft to replace it.
Forget Sunk Costs Sunk costs are like spilled milk: They are past and irreversible outflows. Because sunk costs are bygones, they cannot be affected by the decision to accept or reject the project, and so they should be ignored.
Take the case of the James Webb Space Telescope. It was originally supposed to launch in 2011 and cost $1.6 billion. But the project became progressively more expensive and further behind schedule. Latest estimates put the cost at $8.8 billion and a launch date of 2019. When Congress debated whether to cancel the program, supporters of the project argued that it would be foolish to abandon a project on which so much had already been spent. Others countered that it would be even more foolish to continue with a project that had proved so costly. Both groups were guilty of the sunk-cost fallacy; the money that had already been spent by NASA was irrecoverable and, therefore, irrelevant to the decision to terminate the project.
Beware of Allocated Overhead Costs We have already mentioned that the accountant’s objective is not always the same as the investment analyst’s. A case in point is the allocation of overhead costs. Overheads include such items as supervisory salaries, rent, heat, and light. These overheads may not be related to any particular project, but they have to be paid for somehow. Therefore, when the accountant assigns costs to the firm’s projects, a charge for overhead is usually made. Now our principle of incremental cash flows says that in investment appraisal we should include only the extra expenses that would result from the project. A project may generate extra overhead expenses; then again, it may not. We should be cautious about assuming that the accountant’s allocation of overheads represents the true extra expenses that would be incurred.
Remember Salvage Value When the project comes to an end, you may be able to sell the plant and equipment or redeploy the assets elsewhere in the business. If the equipment is sold, you must pay tax on the difference between the sale price and the book value of the asset. The salvage value (net of any taxes) represents a positive cash flow to the firm.
Some projects have significant shutdown costs, in which case the final cash flows may be negative. For example, the mining company, FCX, has earmarked $451 million to cover the future reclamation and closure costs of its New Mexico mines.
Rule 3: Treat Inflation Consistently
As we pointed out in Chapter 3, interest rates are usually quoted in nominal rather than real terms. For example, if you buy an 8% Treasury bond, the government promises to pay you $80 interest each year, but it does not promise what that $80 will buy. Investors take inflation into account when they decide what is an acceptable rate of interest.
If the discount rate is stated in nominal terms, then consistency requires that cash flows should also be estimated in nominal terms, taking account of trends in selling price, labor and materials costs, and so on. This calls for more than simply applying a single assumed inflation rate to all components of cash flow. Labor costs per hour of work, for example, normally increase at a faster rate than the consumer price index because of improvements in productivity. Tax savings from depreciation do not increase with inflation; they are constant in nominal terms because tax law in most countries allows only the original cost of assets to be depreciated.
Of course, there is nothing wrong with discounting real cash flows at a real discount rate. In fact, this is standard procedure in countries with high and volatile inflation. Here is a simple example showing that real and nominal discounting, properly applied, always give the same present value.
Suppose your firm usually forecasts cash flows in nominal terms and discounts at a 15% nominal rate. In this particular case, however, you are given project cash flows in real terms, that is, current dollars:
|
Real Cash Flows ($ thousands) |
|||
|
C0 |
1 |
C2 |
C3 |
|
−100 |
+35 |
+50 |
+30 |
It would be inconsistent to discount these real cash flows at the 15% nominal rate. You have two alternatives: Either restate the cash flows in nominal terms and discount at 15%, or restate the discount rate in real terms and use it to discount the real cash flows.
Assume that inflation is projected at 10% a year. Then the cash flow for year 1, which is $35,000 in current dollars, will be 35,000 × 1.10 = $38,500 in year-1 dollars. Similarly, the cash flow for year 2 will be 50,000 × (1.10)2 = $60,500 in year-2 dollars, and so on. If we discount these nominal cash flows at the 15% nominal discount rate, we have
Instead of converting the cash-flow forecasts into nominal terms, we could convert the discount rate into real terms by using the following relationship:
In our example, this gives
If we now discount the real cash flows by the real discount rate, we have an NPV of $5,500, just as before:
The message of all this is quite simple. Discount nominal cash flows at a nominal discount rate. Discount real cash flows at a real rate. Never mix real cash flows with nominal discount rates or nominal flows with real rates.
Rule 4: Separate Investment and Financing Decisions
Suppose you finance a project partly with debt. How should you treat the proceeds from the debt issue and the interest and principal payments on the debt? Answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and principal payments on the debt as cash outflows. Regardless of the actual financing, you should view the project as if it were all-equity-financed, treating all cash outflows required for the project as coming from stockholders and all cash inflows as going to them.
This procedure focuses exclusively on the project cash flows, not the cash flows associated with alternative financing schemes. It, therefore, allows you to separate the analysis of the investment decision from that of the financing decision. We explain how to recognize the effect of financing choices on project values in Chapter 19.
Rule 5: Remember to Deduct Taxes
Taxes are an expense just like wages and raw materials. Therefore, cash flows should be estimated on an after-tax basis. Subtract cash outflows for taxes from pretax cash flows and discount the net amount.
Some firms do not deduct tax payments. They try to offset this mistake by discounting the pretax cash flows at a rate that is higher than the cost of capital. Unfortunately, there is no reliable formula for making such adjustments to the discount rate.
Be careful to subtract cash taxes. Cash taxes paid are usually different from the taxes reported on the income statement provided to shareholders. For example, the shareholder accounts typically assume straight-line depreciation instead of the accelerated depreciation allowed by the U.S. tax code. We will highlight the differences between straight-line and accelerated depreciation later in this chapter.
The next section takes a broader look at corporate income taxes and the recent changes in the U.S. tax code.
6-2Corporate Income Taxes
Look at Table 6.1, which shows corporate income tax rates in 11 countries. These are the tax rates imposed by the national governments, but corporations may also need to pay tax to a regional government. For example, in Canada, the provincial governments levy an additional tax of between 11% and 16%. In the United States, states and some municipalities also impose an extra layer of corporate tax that averages around 4%. To complicate matters further, in many countries, the first tranche of income may be taxed at a lower rate, or special arrangements may apply to some types of business.
|
Country |
Corporate Tax Rate (%) |
|
Australia |
30 |
|
Brazil |
34 |
|
Canada |
15 |
|
China |
25 |
|
France |
33 |
|
Germany |
16 |
|
India |
30 |
|
Ireland |
13 |
|
Japan |
34 |
|
United Kingdom |
19 |
|
United States |
21 |
TABLE 6.1 National corporate tax rates
Source: PWC, Worldwide Tax Summaries: Corporate Taxes, 2017/2018, www.pwc.com/taxsummaries.
Tax rates change over time, sometimes dramatically. For example, the U.K. has cut its corporate tax rate from 30% in 1998 to 19% today. The U.S. reduced its rate from 35% to 21% starting in 2018. This rate reduction was one of several important changes in U.S. corporate income taxes. We summarize the changes now.
U.S. Corporate Income Tax Reform
The U.S. Tax Cuts and Jobs Act was passed in December 2017 and implemented immediately in 2018. Suddenly, the corporate tax rate dropped from 35% to 21%. But there were several other important changes.4
Depreciation Before 2018, when calculating taxable income, U.S. corporations were allowed to deduct an immediate bonus depreciation of 50% of the asset’s cost. The fraction of the investment not covered by this bonus depreciation was then depreciated over the following years using the modified accelerated cost recovery system (MACRS), a form of accelerated depreciation. (“Accelerated” means that depreciation is front-loaded: higher in the early years of an asset’s life but lower as the asset ages. Straight-line depreciation is the same in all years.) But the new tax law allows companies to take bonus depreciation sufficient to write off 100% of investment immediately—the ultimate in accelerated depreciation. With 100% bonus depreciation, the firm can treat investments in plant and equipment as immediate expenses.
Bonus depreciation is a temporary provision, however. It is scheduled for phase-out starting in 2023. By 2027, it will be gone. We will have to wait and see what depreciation schedules apply to investments not covered by 100% bonus depreciation. Perhaps it will be that old standby MACRS. We discuss MACRS and other forms of accelerated depreciation in the next section.
Investment in real estate does not qualify for bonus or accelerated depreciation. It is depreciated straight-line over periods of 15 years or more.
Amortization of Research Expenses U.S. companies can now could write off most outlays for R&D as immediate expenses. Starting in 2022, most R&D investments must be amortized (depreciated) over a five-year period. Many observers were puzzled by this change. If investments in plant and equipment now (2018–2022) qualify for immediate expensing, why must investments in R&D, which used to be expensed, be put on the balance sheet and amortized?
Tax Carry-Forwards When a corporation makes a profit, it pays tax. But what happens when it suffers a loss? In 2017 and earlier, U.S. corporations could carry back losses to recover taxes paid on the prior two years’ income. Starting in 2018, carry-backs are no longer allowed. But corporations can carry forward losses indefinitely, using the losses to offset up to 80% of future years’ income. Suppose, for example, that a manufacturer of gargle blasters loses $100,000 in 2018 but earns $100,000 in 2019 and 2020. It pays no tax in 2018, but carries forward the loss. In 2019, it uses $80,000 of the loss to offset income, paying tax of $4,200 (21% of $20,000). In 2020, it uses the remaining $20,000 carried forward, paying tax of $16,800 (21% of $80,000).
Limits on Interest Deductions U.S. tax law treats interest on debt as a tax-deductible expense. In Chapters 17 and 18, we will show that the resulting interest tax shields favor debt over equity financing. But interest deductions are now (2018–2021) limited to 30% of taxable income before depreciation and amortization, though unused deductions can be carried forward and used in later years. From 2022 on, interest deductions are limited to 30% of taxable income after depreciation and amortization. (There are exceptions for small businesses, car dealerships, farmers, and some other taxpayers.) In other words, the limit from 2018–2021 is 30% of taxable EBITDA (earnings before interest, taxes, depreciation, and amortization); from 2022, it is 30% of taxable EBIT (earnings before interest and taxes). EBIT is smaller than EBITDA, so the restriction on interest deductions is tighter post-2021.
It appears that most large U.S. corporations will be safely below the 30% limits. But those corporations that do hit the limits may have to rethink their valuation methods and financing strategies. We cover these issues in Chapters 18, 19, and 25.
Territorial versus Worldwide Taxation Most countries have territorial corporate income taxes: They tax income earned in their own countries but not outside their borders. The United States switched over to a territorial system in 2018.
Before the switch, the United States taxed U.S. corporations’ worldwide income, which had some unfortunate consequences. To see why it mattered, think of a U.S. and a Canadian company, both operating in the United States and in Canada before the U.S. tax reform. Both companies paid U.S. taxes at 35% on their U.S. income and Canadian taxes at 15% on their Canadian income. But the U.S company owed an additional 20% in U.S. taxes when its Canadian income was repatriated. Thus, the U.S. company’s total tax rate on its Canadian profits added up to 35%, far in excess of the 15% rate paid by the Canadian company on its Canadian profits.
The U.S. company could defer payment of the 20% additional U.S. tax by refusing to bring its Canadian profits home. That is exactly what U.S. corporations did. As we will see in Chapter 30, Apple, Microsoft, Alphabet, and several large pharmaceutical companies stored up mountains of cash in low-tax foreign jurisdictions. Once the U.S. switched to a territorial tax in 2018, these companies had no incentive to make their cash mountains higher. They were, however, subject to a one-time tax of 15.5% on overseas profits accumulated through the end of 2017. For example, Apple announced that it would pay a tax of $38 billion to repatriate cumulative foreign profits of $252 billion.
U.S. taxation of worldwide income also affected mergers and acquisitions. Suppose the U.S. company in our example bought the Canadian company before 2018, when the United States moved to the territorial system. The Canadian company’s home operations would then be owned by the U.S. company and subject to the U.S. worldwide tax. But if the Canadian company bought the U.S. company, the profits from the Canadian operations that the U.S. company used to own would escape the worldwide tax. Only the Canadian tax of 15% is paid. If there were a merger, it was clearly better for the Canadian company to be the buyer.
Thus, worldwide taxation rewarded foreign acquisitions of U.S. companies. Some U.S. companies arranged inversions, which were takeovers designed so that the foreign party was treated as the buyer. For example, Pfizer’s proposed 2016 merger with the smaller Irish company Allergen was designed to move the combined company’s headquarters to Ireland, where the corporate tax rate was only 13%. The deal was abandoned after stubborn resistance by the U.S. Treasury. But if the Pfizer-Allergen deal resurfaced today, there would be no tax motive to move the headquarters to Ireland because the United States no longer taxes Pfizer’s foreign profits.
6-3Example—IM&C’s Fertilizer Project
The Three Elements of Project Cash Flows
You can think of an investment project’s cash flow as composed of three elements:
Capital Investment To get a project off the ground, a company typically makes an up-front investment in plant, equipment, research, start-up costs, and diverse other outlays. This expenditure is a negative cash flow—negative because cash goes out the door.
When the project comes to an end, the company can either sell the plant and equipment or redeploy it elsewhere in its business. This salvage value (net of any taxes if the plant and equipment is sold) is a positive cash flow. However, remember our earlier comment that final cash flows can be negative if there are significant shutdown costs.
Operating Cash Flow Operating cash flow consists of the net increase in sales revenue brought about by the new project less outlays for production, marketing, distribution, and other incremental costs. Incremental taxes are likewise subtracted.
Operating cash flow = revenues − expenses − taxes
Many investments do not produce any additional revenues; they are simply designed to reduce the costs of the company’s existing operations. Such projects also contribute to the firm’s operating cash flow. The after-tax cost saving is a positive addition to the cash flow.
Don’t forget that the depreciation charge is not a cash flow. It affects the tax that the company pays, but the company does not send anyone a check for depreciation, and it should not be deducted when calculating operating cash flow.
Investment in Working Capital When a company builds up inventories of raw materials or finished products, this investment in inventories requires cash. Cash is also absorbed when customers are slow to pay their bills; in this case the firm makes an investment in accounts receivable. On the other hand, cash is preserved when the firm can delay paying its bills. Accounts payable are in a way a source of financing.
Investment in working capital, just like investment in plant and equipment, represents a negative cash flow. On the other hand, later in the project’s life, as inventories are sold and accounts receivable are collected, working capital is reduced and the firm enjoys a positive cash flow.
Forecasting the Fertilizer Project’s Cash Flows
As the newly appointed financial manager of International Mulch and Compost Company (IM&C), you are about to analyze a proposal for marketing guano as a garden fertilizer. (IM&C’s planned advertising campaign features a rustic gentleman who steps out of a vegetable patch singing, “All my troubles have guano way.”)5
Table 6.2 shows the forecasted cash flows from the project. All the entries in the table are nominal. In other words, the forecasts that you have been given take into account the likely effect of inflation on revenues and costs. We assume initially that for tax purposes the company uses straight-line depreciation. In other words, when it calculates each year’s taxable income, it deducts one-sixth of the initial investment.
TABLE 6.2 Calculating the cash flows and net present value of IM&C’s guano project assuming straight-line depreciation ($ thousands)
a The asset has been entirely depreciated for tax purposes and the entire sales price is subject to tax.
b Start-up costs in years 0 and 1, and general and administrative costs in years 1–6.
c Depreciation is calculated straight line on the initial investment of $12 million.
d A negative tax payment means a cash inflow, assuming that IM&C can use the tax loss on the guano project to shield income from the rest of its business.
BEYOND THE PAGE
Try It! The guano spreadsheets
mhhe.com/brealey13e
The calculation in panel B of profit after tax is similar to the calculation in IM&C’s financial statements. There is one important difference. When calculating the depreciation figure in the published income statement, IM&C may choose to depreciate the plant and equipment to its likely salvage value. By contrast, IRS rules for calculating the company’s tax liability always assume that the plant and equipment has a salvage value of zero.
Capital Investment Rows 1 through 4 of Table 6.2 show the cash flows from the investment in fixed assets. The project requires an investment of $12 million in plant and machinery. IM&C expects to sell the equipment in year 7 for $1.949 million. Any difference between this figure and the book value of the equipment is a taxable gain. By year 7, IM&C has fully depreciated the equipment, so the company will be taxed on a capital gain of $1.949 million. If the tax rate is 21%, the company will pay tax of .21 × 1.949 = $0.409 million, and the net cash flow from the sale of equipment will be 1.949 – 0.409 = $1.540 million. This is shown in rows 2 and 3 of the table.
Operating Cash Flow Panel B of Table 6.2 show the calculation of the operating cash flow from the guano project. Operating cash flow consists of revenues from the sale of guano less the cash expenses of production and any taxes. Taxes are calculated on profits net of depreciation. Thus, if the tax rate is 21%,
Tax = .21 × (sales − cash expenses − depreciation)
We assume in this first-pass table that the company uses straight-line depreciation. This means that, if the depreciable life of the equipment is six years, IM&C can deduct from profits one-sixth of the initial $12 million investment. Thus, row 8 shows that straight-line depreciation in each year is
Annual depreciation = (1/6 × 12.0) = $2.0 million
Pretax profits and taxes are shown in rows 9 and 10. For example, in year 2
Pretax profit = 12.887 – (7.729 + 1.210) − 2.000 = $1.948 million
Tax = .21 × 1.948 = $0.409 million
Once we have calculated taxes, it is a simple matter to calculate operating cash flow. Thus,
Operating cash flow in year 2 = revenues − cash expenses − taxes
= 12.887 − (7.729 + 1.210) − 0.409 = $3.539 million6
Notice that, when calculating operating cash flow, we ignored the possibility that the project may be partly financed by debt. Following our earlier Rule 4, we did not deduct any debt proceeds from the original investment, and we did not deduct interest payments from the cash inflows. Standard practice forecasts cash flows as if the project is all-equity financed. Any additional value resulting from financing decisions is considered separately.
Investment in Working Capital You can see from Table 6.2 that working capital increases in the early and middle years of the project. Why is this? There are several possible reasons:
1. Sales recorded on the income statement overstate actual cash receipts from guano shipments because sales are increasing and customers are slow to pay their bills. Therefore, accounts receivable increase.
2. It takes several months for processed guano to age properly. Thus, as projected sales increase, larger inventories have to be held in the aging sheds.
3. An offsetting effect occurs if payments for materials and services used in guano production are delayed. In this case accounts payable will increase.
Thus, the additional investment in working capital can be calculated as:
There is an alternative to worrying about changes in working capital. You can estimate cash flow directly by counting the dollars coming in from customers and deducting the dollars going out to suppliers. You would also deduct all cash spent on production, including cash spent for goods held in inventory. In other words,
1. If you replace each year’s sales with that year’s cash payments received from customers, you don’t have to worry about accounts receivable.
2. If you replace cost of goods sold with cash payments for labor, materials, and other costs of production, you don’t have to keep track of inventory or accounts payable.
However, you would still have to construct a projected income statement to estimate taxes.
Project Valuation Rows 16 to 19 of Table 6.2 show the calculation of project NPV. Row 16 shows the total cash flow from IM&C’s project as the sum of the capital investment, operating cash flow, and investment in working capital. IM&C estimates the opportunity cost of capital for projects of this type as 20%.
Remember that to calculate the present value of a cash flow in year t you can either divide the cash flow by (1 + r)t or you can multiply by a discount factor that is equal to 1/(1 + r)t. Row 17 shows the discount factors for a 20% discount rate, and Row 18 multiplies the discount factor by the cash flow to give each flow’s present value. When all the cash flows are discounted and added up, the project is seen to offer a net present value of $3.806 million.
Accelerated Depreciation and First-Year Expensing
Depreciation is a noncash expense; it is important only because it reduces taxable income. It provides an annual tax shield equal to the product of depreciation and the marginal tax rate. In the case of IM&C:
Annual tax shield = depreciation × tax rate = 2,000 × .21 = 420.0, or $420,000.
The present value of these tax shields ($420,000 for six years) is $1,397,000 at a 20% discount rate.
In Table 6.2 we assumed that IM&C was required to use straight-line depreciation, which allowed it to write off a fixed proportion of the initial investment each year. This is the most common method of depreciation, but some countries, including the United States, permit firms to depreciate their investments more rapidly.
There are several different methods of accelerated depreciation. For example, firms may be allowed to use the double-declining-balance method. Suppose that IM&C is permitted to use double-declining-balance depreciation. In this case, it can deduct not one-sixth, but 2 × 1/6 = 1/3 of the remaining book value of the investment in each year.7 Therefore, in year 1, it deducts depreciation of 12/3 = $4 million, and the written-down value of the equipment falls to 12 – 4 = $8 million. In year 2, IM&C deducts depreciation of 8/3 = $2.7 million, and the written-down value is further reduced to $8 – 2.7 = $5.3 million. In year 5, IM&C observes that depreciation would be higher if it could switch to straight-line depreciation and write off the balance of $2.4 million over the remaining two years of the equipment’s life. If this is permitted, IM&C’s depreciation allowance each year would be as follows:
The present value of the tax shields with double-declining-balance depreciation is $1.608 million, $212,000 million higher than if IM&C was restricted to straight-line depreciation.
From 1986 to the end of 2017, U.S. companies used a slight variation of the double-declining balance method, called the modified accelerated cost recovery system (MACRS).8 But the 2017 Tax Cuts and Jobs Act offered companies bonus depreciation sufficient to write off 100% of their investment expenditures in the year that they come on line. Table 6.3 recalculates the NPV of the guano project, assuming that the full $12 million investment can be depreciated immediately.
BEYOND THE PAGE
MACRS depreciation system
mhhe.com/brealey13e
We initially assumed that the guano project could be depreciated straight-line over six years. This resulted in an NPV of $3.806 million. We then calculated that if IM&C could use the double-declining-balance method, NPV would increase by $212,000 to $4.018 million. Finally, Table 6.3 shows that full first-year expensing introduced in the 2017 tax reform would increase NPV further to $4.929 million.
TABLE 6.3 IM&C’s guano project. Revised analysis with immediate expensing of investment expenditures.
Final Comments on Taxes
Two final comments. First, note that all of the guano project’s $12 million capital investment is in plant and equipment, which, under current U.S. tax law, can be expensed immediately. But suppose the project also requires an up-front R&D outlay of $500,000. Under the Tax Cuts and Jobs Act, R&D expenditures after 2021 cannot be expensed but must be written off over five years.
Second, all large U.S. corporations keep two separate sets of books, one for stockholders and one for the Internal Revenue Service (IRS). It is common to use straight-line depreciation on the stockholder books and accelerated depreciation on the tax books. The IRS doesn’t object to this, and it makes the firm’s reported earnings higher than if accelerated depreciation were used everywhere. There are many other differences between tax books and shareholder books.9
The financial analyst must be careful to remember which set of books he or she is looking at. In capital budgeting only the tax books are relevant, but to an outside analyst only the shareholder books are available.
Project Analysis
Let us review. Earlier in this section, you embarked on an analysis of IM&C’s guano project. You drew up a series of cash-flow forecasts assuming straight-line depreciation. Then you remembered accelerated depreciation and recalculated cash flows and NPV. Finally, you recognized that under the Tax Cuts and Jobs Act, IM&C could write off the capital expenditure in the year that it was incurred.
You were lucky to get away with just three NPV calculations. In real situations, it often takes several tries to purge all inconsistencies and mistakes. Then you may want to analyze some alternatives. For example, should you go for a larger or smaller project? Would it be better to market the fertilizer through wholesalers or directly to the consumer? Should you build 90,000-square-foot aging sheds for the guano in northern South Dakota rather than the planned 100,000-square-foot sheds in southern North Dakota? In each case, your choice should be the one offering the highest NPV. Sometimes the alternatives are not immediately obvious. For example, perhaps the plan calls for two costly, high-speed packing lines. But, if demand for guano is seasonal, it may pay to install just one high-speed line to cope with the base demand and two slower but cheaper lines simply to cope with the summer rush. You won’t know the answer until you have compared NPVs.
You will also need to ask some “what if clear” questions. How would NPV be affected if inflation rages out of control? What if technical problems delay start-up? What if gardeners prefer chemical fertilizers to your natural product? Managers employ a variety of techniques to develop a better understanding of how such unpleasant surprises could damage NPV. For example, they might undertake a sensitivity analysis, in which they look at how far the project could be knocked off course by bad news about one of the variables. Or they might construct different scenarios and estimate the effect of each on NPV. Another technique, known as break-even analysis, is to explore how far sales could fall short of forecast before the project goes into the red.
In Chapter 10, we practice using each of these “what if clear” techniques. You will find that project analysis is much more than one or two NPV calculations.10
Calculating NPV in Other Countries and Currencies
Our guano project was undertaken in the United States by a U.S. company. But the principles of capital investment are the same worldwide. For example, suppose that you are the financial manager of the German company, K.G.R. Ökologische Naturdüngemittel GmbH (KGR), that is faced with a similar opportunity to make a €10 million investment in Germany. What changes?
1. KGR must also produce a set of cash-flow forecasts, but in this case the project cash flows are stated in euros, the eurozone currency.
2. In developing these forecasts, the company needs to recognize that prices and costs will be influenced by the German inflation rate.
3. Profits from KGR’s project are liable to the German rate of corporate tax, which is currently 15.8% plus a large municipal trade tax.
4. KGR must use the German system of depreciation allowances. In common with many other countries, Germany requires firms to use the straight-line system. KGR, therefore, writes off one-sixth of the capital outlay each year.
5. Finally, KGR discounts the project’s euro cash flows at the German cost of capital measured in euros.
Now suppose you are the financial manager of a U.S. company considering the same investment in Germany. You would go through exactly the same steps as KGR. You would not have to worry about U.S. taxes on your company’s German profits because the United States now has a territorial corporate income tax. You would probably convert the project NPV from euros to U.S. dollars, however, and you might use a different cost of capital. We discuss cross-border capital investment decisions in Chapter 27.
6-4Using the NPV Rule to Choose among Projects
Almost all real-world investment decisions entail either-or choices. Such choices are said to be mutually exclusive. We came across an example of mutually exclusive investments in Chapter 2. There we looked at whether it was better to build an office block for immediate sale or to rent it out and sell it at the end of two years. To decide between these alternatives, we calculated the NPV of each and chose the one with the higher NPV.
That is the correct procedure as long as the choice between the two projects does not affect any future decisions that you might wish to make. But sometimes the choices that you make today will have an impact on future opportunities. When that is so, choosing between competing projects is trickier. Here are four important, but often challenging, problems:
· The investment timing problem. Should you invest now or wait and think about it again next year? (Here, today’s investment is competing with possible future investments.)
· The choice between long- and short-lived equipment. Should the company save money today by choosing cheaper machinery that will not last as long? (Here, today’s decision would accelerate a later investment in machine replacement.)
· The replacement problem. When should existing machinery be replaced? (Using it another year could delay investment in more modern equipment.)
· The cost of excess capacity. What is the cost of using equipment that is temporarily not being used? (Increasing use of the equipment may bring forward the date at which additional capacity is required.)
We will look at each of these problems in turn.
Problem 1: The Investment Timing Decision
The fact that a project has a positive NPV does not mean that it is best undertaken now. It might be even more valuable if undertaken in the future. The question of optimal timing is not difficult when the cash flows are certain. You must first examine alternative start dates (t) for the investment and calculate the net future value at each of these dates. Then, to find which of the alternatives would add most to the firm’s current value, you must discount these net future values back to the present:
For example, suppose you own a large tract of inaccessible timber. To harvest it, you need to invest a substantial amount in access roads and other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices may rise as you wait, and the trees will keep growing, although at a gradually decreasing rate.
Let us suppose that the net present value of the harvest at different future dates is as follows:
As you can see, the longer you defer cutting the timber, the more money you will make. However, your concern is with the date that maximizes the net present value of your investment, that is, its contribution to the value of your firm today. You therefore need to discount the net future value of the harvest back to the present. Suppose the appropriate discount rate is 10%. Then, if you harvest the timber in year 1, it has a net present value of $58,500:
The net present value for other harvest dates is as follows:
The optimal point to harvest the timber is year 4 because this is the point that maximizes NPV.
Notice that before year 4, the net future value of the timber increases by more than 10% a year: The gain in value is greater than the cost of the capital tied up in the project. After year 4, the gain in value is still positive but less than the required return. So delaying the harvest further just reduces shareholder wealth.11
The investment timing problem is much more complicated when you are unsure about future cash flows. We return to the problem of investment timing under uncertainty in Chapters 10 and 22.
BEYOND THE PAGE
Investment timing decisions
mhhe.com/brealey13e
Problem 2: The Choice between Long- and Short-Lived Equipment
An advertising agency needs to choose between two digital presses. Let’s call them machines A and B. The two machines are designed differently but have identical capacity and do exactly the same job. Machine A costs $15,000 and will last three years. It costs $5,000 per year to run. Machine B is an “economy” model, costing only $10,000, but it will last only two years and costs $6,000 per year to run.
The only way to choose between these two machines is on the basis of cost. The present value of each machine’s cost is as follows:
Should the agency take machine B, the one with the lower present value of costs? Not necessarily. All we have shown is that machine B offers two years of service for a lower total cost than three years of service from machine A. But is the annual cost of using B lower than that of A?
Suppose the financial manager agrees to buy machine A and pay for its operating costs out of her budget. She then charges the annual amount for use of the machine. There will be three equal payments starting in year 1. The financial manager has to make sure that the present value of these payments equals the present value of the costs of each machine.
BEYOND THE PAGE
Equivalent annual costs
mhhe.com/brealey13e
When the discount rate is 6%, the payment stream with such a present value turns out to be $10,610 a year. In other words, the cost of buying and operating machine A over its three-year life is equivalent to an annual charge of $10,610 a year for three years.
We calculated this equivalent annual cost by finding the three-year annuity with the same present value as A’s lifetime costs.
At a 6% cost of capital, the annuity factor is 2.673 for three years, so
A similar calculation for machine B gives an equivalent annual cost of $11,450:
Machine A is better because its equivalent annual cost is less ($10,610 versus $11,450 for machine B).
Equivalent Annual Cash Flow, Inflation, and Technological Change When we calculated the equivalent annual costs of machines A and B, we implicitly assumed that inflation is zero. But, in practice, the cost of buying and operating the machines is likely to rise with inflation. If so, the nominal costs of operating the machines will rise, while the real costs will be constant. Therefore, when you compare the equivalent annual costs of two machines, we strongly recommend doing the calculations in real terms. Do not calculate equivalent annual cash flows as level nominal annuities. This procedure can give incorrect rankings of true equivalent annual flows at high inflation rates. See Challenge Problem 37 at the end of this chapter for an example.12
There will also be circumstances in which even the real cash flows of buying and operating the two machines are not expected to be constant. For example, suppose that thanks to technological improvements, new machines cost 20% less each year in real terms to buy and operate. In this case, future owners of brand-new, lower-cost machines will be able to cut their (real) rental cost by 20%, and owners of old machines will be forced to match this reduction. Thus, we now need to ask: If the real level of rents declines by 20% a year, how much will it cost to rent each machine?
If the real rent for year 1 is rent1, then the real rent for year 2 is rent2 = 0.8 × rent1. Rent3 is 0.8 × rent2, or 0.64 × rent1. The owner of each machine must set the real rents sufficiently high to recover the present value of the costs. If the real cost of capital is 6%:
For machine B:
The merits of the two machines are now reversed. Once we recognize that technology is expected to reduce the real costs of new machines, then it pays to buy the shorter-lived machine B rather than become locked into an aging technology with machine A in year 3.
You can imagine other complications. Perhaps machine C will arrive in year 1 with an even lower equivalent annual cost. You would then need to consider scrapping or selling machine B at year 1 (more on this decision follows). The financial manager could not choose between machines A and B in year 0 without taking a detailed look at what each machine could be replaced with.
Comparing equivalent annual cash flows should never be a mechanical exercise; always think about the assumptions that are implicit in the comparison. Finally, remember why equivalent annual cash flows are necessary in the first place. It is because A and B will be replaced at different future dates. The choice between them therefore affects future investment decisions. If subsequent decisions are not affected by the initial choice (e.g., because neither machine will be replaced), then we do not need to take future decisions into account.13
Equivalent Annual Cash Flow and Taxes We have not mentioned taxes. But you surely realized that machine A and B’s lifetime costs should be calculated after-tax, recognizing that operating costs are tax-deductible and that capital investment generates depreciation tax shields.
Problem 3: When to Replace an Old Machine
Our earlier comparison of machines A and B took the life of each machine as fixed. In practice, the point at which equipment is replaced reflects economics, not physical collapse. We must decide when to replace. The machine will rarely decide for us.
Here is a common problem. You are operating an elderly machine that is expected to produce a net cash inflow of $4,000 in the coming year and $4,000 next year. After that it will give up the ghost. You can replace it now with a new machine, which costs $15,000 but is much more efficient and will provide a cash inflow of $8,000 a year for three years. You want to know whether you should replace your equipment now or wait a year.
We can calculate the NPV of the new machine and also its equivalent annual cash flow—that is, the three-year annuity that has the same net present value:
In other words, the cash flows of the new machine are equivalent to an annuity of $2,387 per year. So we can equally well ask at what point we would want to replace our old machine with a new one producing $2,387 a year. When the question is put this way, the answer is obvious. As long as your old machine can generate a cash flow of $4,000 a year, who wants to put in its place a new one that generates only $2,387 a year?
It is a simple matter to incorporate salvage values into this calculation. Suppose that the current salvage value is $8,000 and next year’s value is $7,000. Let us see where you come out next year if you wait and then sell. On one hand, you gain $7,000, but you lose today’s salvage value plus a year’s return on that money. That is 8,000 × 1.06 = $8,480. Your net loss is 8,480 – 7,000 = $1,480, which only partly offsets the operating gain. You should not replace yet.
Remember that the logic of such comparisons requires that the new machine be the best of the available alternatives and that it in turn be replaced at the optimal point.
Problem 4: Cost of Excess Capacity
Any firm with a centralized information system (computer servers, storage, software, and telecommunication links) encounters many proposals for using it. Recently installed systems tend to have excess capacity, and since the immediate marginal costs of using them seem to be negligible, management often encourages new uses. Sooner or later, however, the load on a system increases to the point at which management must either terminate the uses it originally encouraged or invest in another system several years earlier than it had planned. Such problems can be avoided if a proper charge is made for the use of spare capacity.
Suppose we have a new investment project that requires heavy use of an existing information system. The effect of adopting the project is to bring the purchase date of a new, more capable system forward from year 4 to year 3. This new system has a life of five years, and at a discount rate of 6%, the present value of the cost of buying and operating it is $500,000.
We begin by converting the $500,000 present value of the cost of the new system to an equivalent annual cost of $118,700 for each of five years.14 Of course, when the new system in turn wears out, we will replace it with another. So we face the prospect of future information-system expenses of $118,700 a year. If we undertake the new project, the series of expenses begins in year 4; if we do not undertake it, the series begins in year 5. The new project, therefore, results in an additional cost of $118,700 in year 4. This has a present value of 118,700/ (1.06)4, or about $94,000. This cost is properly charged against the new project.
When we recognize it, the NPV of the project may prove to be negative. If so, we still need to check whether it is worthwhile undertaking the project now and abandoning it later, when the excess capacity of the present system disappears.
SUMMARY
By now present value calculations should be a matter of routine. However, forecasting project cash flows will never be routine. Here is a checklist that will help you to avoid mistakes:
1. Discount cash flows, not profits.
a. Remember that depreciation is not a cash flow (though it affects tax payments).
b. Remember to track investment in working capital. As sales increase, the firm will probably make additional investments in working capital, and as the project comes to an end, it will recover those investments.
c. Beware of allocated overhead charges. These may not reflect the incremental costs of the project.
2. Estimate the project’s incremental cash flows—that is, the difference between the cash flows with the project and those without the project.
a. Include all indirect effects of the project, such as its impact on the sales of the firm’s other products.
b. Forget sunk costs.
c. Include opportunity costs, such as the value of land that you would otherwise sell.
3. Treat inflation consistently.
a. If cash flows are forecasted in nominal terms, use a nominal discount rate.
b. Discount real cash flows at a real rate.
4. Forecast cash flows as if the project is all-equity-financed. Thus, project cash flows should exclude debt interest or the cost of repaying any loans. This enables you to separate the investment from the financing decision.
5. Concentrate on cash flows after taxes. Stay alert for differences between tax depreciation and depreciation used in reports to shareholders.
The U.S. Tax Cuts and Jobs Act of 2017 changed corporate income taxes in several important ways:
1. The tax rate was cut from 35% to 21%.
2. Most investments in plant and equipment can be expensed—that is, completely depreciated—in their first year of operation. This expensing provision will phase out starting in 2023.
3. Starting in 2022, most investments in research and development (R&D) must be amortized (depreciated) over a five-year period.
4. Losses can no longer be carried back to recover past taxes. But losses can be carried forward to offset up to 80% of future income.
5. Interest expense exceeding 30% of taxable income is no longer tax deductible.
6. The United States moved to a territorial tax system. It no longer attempts to tax U.S. corporations’ worldwide income.
The principles of valuing capital investments are the same worldwide, but inputs and assumptions vary by country and currency. For example, cash flows from a project in Germany would be in euros, not dollars, and would be forecasted after German taxes.
When we assessed the guano project, we transformed the series of future cash flows into a single measure of their present value. Sometimes it is useful to reverse this calculation and to convert the present value into a stream of annual cash flows. For example, when choosing between two machines with unequal lives, you need to compare equivalent annual cash flows. Remember, though, to calculate equivalent annual cash flows in real terms and adjust for technological change if necessary.
FURTHER READING
For a valuable summary of tax rules in different countries, see
PWC, Worldwide Tax Summaries, Corporate Taxes 2017/18,www.pwc.com/taxsummaries.
PROBLEM SETS
Select problems are available in McGraw-Hill’s Connect. Please see the preface for more information.
1. Cash flows* Which of the following should be treated as incremental cash flows when deciding whether to invest in a new manufacturing plant? The site is already owned by the company, but existing buildings would need to be demolished.
a. The market value of the site and existing buildings.
b. Demolition costs and site clearance.
c. The cost of a new access road put in last year.
d. Lost earnings on other products due to executive time spent on the new facility.
e. A proportion of the cost of leasing the president’s jet airplane.
f. Future depreciation of the new plant.
g. The reduction in the corporation’s tax bill resulting from tax depreciation of the new plant.
h. The initial investment in inventories of raw materials.
i. Money already spent on engineering design of the new plant.
2. Cash flows Reliable Electric, a major Ruritanian producer of electrical products, is considering a proposal to manufacture a new type of industrial electric motor that would replace most of its existing product line. A research breakthrough has given Reliable a two-year lead on its competitors. The project proposal is summarized in Table 6.4.
a. Read the notes to the table carefully. Which entries make sense? Which do not? Why or why not?
b. What additional information would you need to construct a version of Table 6.4 that makes sense?
Construct such a table and recalculate NPV. Make additional assumptions as necessary.
TABLE 6.4 Cash flows and present value of Reliable Electric’s proposed investment ($ thousands). See Problem 2.
Notes:
1. Capital expenditure: $8 million for new machinery and $2.4 million for a warehouse extension. The full cost of the extension has been charged to this project, although only about half of the space is currently needed. Since the new machinery will be housed in an existing factory building, no charge has been made for land and building.
2. Research and development: $1.82 million spent in 2017. This figure was corrected for 10% inflation from the time of expenditure to date. Thus 1.82 × 1.1 = $2 million.
3. Working capital: Initial investment in inventories.
4. Revenue: These figures assume sales of 2,000 motors in 2019, 4,000 in 2020, and 10,000 per year from 2021 through 2028. The initial unit price of $4,000 is forecasted to remain constant in real terms.
5. Operating costs: These include all direct and indirect costs. Indirect costs (heat, light, power, fringe benefits, etc.) are assumed to be 200% of direct labor costs. Operating costs per unit are forecasted to remain constant in real terms at $2,000.
6. Overhead: Marketing and administrative costs, assumed equal to 10% of revenue.
7. Depreciation: Straight-line for 10 years.
8. Interest: Charged on capital expenditure and working capital at Reliable’s current borrowing rate of 15%.
9. Income: Revenue less the sum of research and development, operating costs, overhead, depreciation, and interest.
10. Tax: 30% of income. However, income is negative in 2018. This loss is carried forward and deducted from taxable income in 2020.
11. Net cash flow: Assumed equal to income less tax.
12. Net present value: NPV of net cash flow at a 15% discount rate.
3. Cash flows* True or false?
a. Project cash flows should take account of interest paid on any borrowing undertaken to finance the project.
b. In the United States, income reported to the tax authorities must equal income reported to shareholders.
c. Accelerated depreciation reduces near-term project cash flows and therefore reduces project NPV.
4. Cash flows In 1898, Simon North announced plans to construct a funeral home on land he owned and rented out as a storage area for railway carts. (A local newspaper commended Mr. North for not putting the cart before the hearse.) Rental income from the site barely covered real estate taxes, but the site was valued at $45,000. However, Mr. North had refused several offers for the land and planned to continue renting it out if, for some reason, the funeral home was not built. Therefore, he did not include the value of the land as an outlay in his NPV analysis of the funeral home. Was this the correct procedure? Explain.
5. Real and nominal flows Mr. Art Deco will be paid $100,000 one year hence. This is a nominal flow, which he discounts at an 8% nominal discount rate:
The inflation rate is 4%.
Calculate the PV of Mr. Deco’s payment using the equivalent real cash flow and real discount rate. (You should get exactly the same answer as he did.)
6. Real and nominal flows Restate the net cash flows in Table 6.2 in real terms. Discount the restated cash flows at a real discount rate. Assume a 20% nominal rate and 10% expected inflation. NPV should be unchanged at +3,806, or $3,806,000.
7. Real and nominal flows Guandong Machinery is evaluating a new project to produce encapsulators. The initial investment in plant and equipment is RMB 500,000.15 Sales of encapsulators in year 1 are forecasted at RMB 200,000 and costs at RMB 100,000. Both are expected to increase by 10% a year in line with inflation. Profits are taxed at 25%. Working capital in each year consists of inventories of raw materials and is forecasted at 20% of sales in the following year. The project will last five years and the equipment at the end of this period will have no further value. For tax purposes the equipment can be depreciated straight-line over these five years. If the nominal discount rate is 15%, show that the net present value of the project is the same whether calculated using real cash flows or nominal flows.
8. Working capital Each of the following statements is true. Use an example to explain why they are consistent.
a. When a company introduces a new product, or expands production of an existing product, investment in net working capital is usually an important cash outflow.
b. Forecasting changes in net working capital is not necessary if the timing of all cash inflows and outflows is carefully specified.
9. Working capital* The following table tracks the main components of working capital over the life of a four-year project.
Calculate net working capital and the cash inflows and outflows due to investment in working capital.
10. Project NPV* Better Mousetrap’s research laboratories have developed a new trap. The project requires an initial investment in plant and equipment of $6 million. This investment will be depreciated straight-line over five years to a value of zero, but when the project comes to an end at the end of five years, the equipment will, in fact, be sold for $500,000. The firm believes that working capital at each date must be maintained at 10% of next year’s forecasted sales starting immediately. Production costs are estimated at 25% of revenues. (There are no marketing expenses.) Sales forecasts are given in the following table. The firm pays tax at 25% and the required return on the project is 12%. What is the NPV?
11. Project NPV A widget manufacturer currently produces 200,000 units a year. It buys widget lids from an outside supplier at a price of $2 a lid. The plant manager believes that it would be cheaper to make these lids rather than buy them. Direct production costs are estimated to be only $1.50 a lid. The necessary machinery would cost $150,000 and would last 10 years. This investment could be written off immediately for tax purposes. The plant manager estimates that the operation would require additional working capital of $30,000 but argues that this sum can be ignored since it is recoverable at the end of the 10 years. If the company pays tax at a rate of 21% and the opportunity cost of capital is 15%, would you support the plant manager’s proposal? State clearly any additional assumptions that you need to make.
12. Project NPV Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $35,000. The object is to save on horse transporter rentals. Marsha had been renting a transporter every other week for $200 per day plus $1.00 per mile. Most of the trips are 80 or 100 miles in total. Marsha usually gives the driver, Joe Laminitis, a $40 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.45 per mile. Insurance costs for Marsha’s transporter are $1,200 per year.
The transporter will probably be worth $15,000 (in real terms) after eight years, when Marsha’s horse Spike, will be ready to retire. Is the transporter a positive-NPV investment? Assume a nominal discount rate of 9% and a 3% forecasted inflation rate. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored.
13. Project NPV United Pigpen is considering a proposal to manufacture high-protein hog feed. The project would make use of an existing warehouse, which is currently rented out to a neighboring firm. The next year’s rental charge on the warehouse is $100,000, and thereafter the rent is expected to grow in line with inflation at 4% a year. In addition to using the warehouse, the proposal envisages an investment in plant and equipment of $1.2 million. This could be depreciated for tax purposes over 10 years. However, Pigpen expects to terminate the project at the end of eight years and to resell the plant and equipment in year 8 for $400,000. Finally, the project requires an initial investment in working capital of $350,000. Thereafter, working capital is forecasted to be 10% of sales in each of years 1 through 7. Year 1 sales of hog feed are expected to be $4.2 million, and thereafter sales are forecasted to grow by 5% a year, slightly faster than the inflation rate. Manufacturing costs are expected to be 90% of sales, and profits are subject to tax at 25%. The cost of capital is 12%. What is the NPV of Pigpen’s project?
14. Project NPV Imperial Motors is considering producing its popular Rooster model in China. This will involve an initial investment of RMB 4 billion. The plant will start production after one year. It is expected to last for five years and have a salvage value at the end of this period of RMB 500 million in real terms. The plant will produce 100,000 cars a year. The firm anticipates that in the first year, it will be able to sell each car for RMB 65,000, and thereafter the price is expected to increase by 4% a year. Raw materials for each car are forecasted to cost RMB 18,000 in the first year, and these costs are predicted to increase by 3% annually. Total labor costs for the plant are expected to be RMB 1.1 billion in the first year and thereafter will increase by 7% a year. The land on which the plant is built can be rented for five years at a fixed cost of RMB 300 million a year payable at the beginning of each year. Imperial’s discount rate for this type of project is 12% (nominal). The expected rate of inflation is 5%. The plant can be depreciated straight-line over the five-year period, and profits will be taxed at 25%. Assume all cash flows occur at the end of each year except where otherwise stated. What is the NPV of the project plant?
15. Project NPV and IRR A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,000 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Company B pays corporate taxes at a rate of 21% and can claim 100% bonus depreciation on the investment. Suppose the opportunity cost of capital is 8%. Ignore inflation.
a. Calculate project NPV for each company.
b. What is the IRR of the after-tax cash flows for each company? Why are the IRRs for A and B the same?
16. Project analysis Go to the Excel spreadsheet versions of Table 6.2 and answer the following questions.
a. New engineering estimates raise the possibility that capital investment will be more than $12 million, perhaps as much as $15 million. On the other hand, you believe that the 20% cost of capital is unrealistically high and that the true cost of capital is about 11%. Is the project still attractive under these alternative assumptions?
b. Continue with the assumed $15 million capital investment and the 11% cost of capital. What if sales, cost of goods sold, and net working capital are all 10% higher in each year? Recalculate NPV. (Note: Enter the revised sales, cost, and working-capital forecasts in the spreadsheet for Table 6.2.)
17. Taxes and project NPV In the International Mulch and Compost example (Section 6-3), we assumed that early losses on the project could be used to offset taxable profits elsewhere in the corporation. Suppose that the losses had to be carried forward and offset against future taxable profits from the project. How would the project NPV change? What is the value of the company’s ability to use the tax deductions immediately?
18. Depreciation and project NPV Suppose that Sudbury Mechanical Drifters is proposing to invest $10 million in a new factory. It can depreciate this investment straight-line over 10 years. The tax rate is 40%, and the discount rate is 10%.
a. What is the present value of Sudbury’s depreciation tax shields?
b. Suppose that the government allows companies to use double-declining-balance depreciation with the option to switch at any point to straight-line. Now what is the present value of the depreciation tax shields?
c. What would be the present value of the tax shield if the government allowed Sudbury to write-off the factory immediately?
19. Depreciation and project NPV Ms. T. Potts, the treasurer of Ideal China, has a problem. The company has just ordered a new kiln for $400,000. Of this sum, $50,000 is described by the supplier as an installation cost. Ms. Potts does not know whether the company will need to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $50,000 straight-line over five years. How will the tax authority’s decision affect the after-tax cost of the kiln? The tax rate is 25%, and the opportunity cost of capital is 5%.
20. Equivalent annual cash flow When appraising mutually exclusive investments in plant and equipment, financial managers calculate the investments’ equivalent annual cash flows and rank the investments on this basis. Why is this necessary? Why not just compare the investments’ NPVs? Explain briefly.
21. Equivalent annual cash flow* Air conditioning for a college dormitory will cost $1.5 million to install and $200,000 per year to operate at current prices. The system should last 25 years. The real cost of capital is 5%, and the college pays no taxes. What is the equivalent annual cost?
22. Equivalent annual cash flow In 2022, the California Air Resources Board (CARB) started planning its “Phase 3” requirements for reformulated gasoline (RFG). RFG is gasoline blended to tight specifications designed to reduce pollution from motor vehicles. CARB consulted with refiners, environmentalists, and other interested parties to design these specifications. As the outline for the Phase 3 requirements emerged, refiners realized that substantial capital investments would be required to upgrade California refineries. Assume a refiner is contemplating an investment of $400 million to upgrade its California plant. The investment lasts for 25 years and does not change raw material and operating costs. The real (inflation-adjusted) cost of capital is 7%. How much extra revenue would be needed each year to recover that cost?
23. Equivalent annual cash flow Look at Problem 22 where you calculated the equivalent annual cost of producing reformulated gasoline in California. Capital investment was $400 million. Suppose this amount can be depreciated immediately for tax purposes. The marginal tax rate, including California taxes, is 25%, the cost of capital is 7%, and there is no inflation. The refinery improvements have an economic life of 25 years.
a. Calculate the after-tax equivalent annual cost.
b. How much extra would retail gasoline customers have to pay to cover this equivalent annual cost? (Note: Extra income from higher retail prices would be taxed.)
24. Equivalent annual cash flow Deutsche Transport can lease a truck for four years at a cost of €30,000 annually. It can instead buy a truck at a cost of €80,000, with annual maintenance expenses of €10,000. The truck will be sold at the end of four years for €20,000. Ignore taxes.
a. What is the equivalent annual cost of buying and maintaining the truck if the discount rate is 10%?
b. Which is the better option: leasing or buying?
25. Investment timing You can purchase an optical scanner today for $400. The scanner provides benefits worth $60 a year. The expected life of the scanner is 10 years. Scanners are expected to decrease in price by 20% per year. Suppose the discount rate is 10%.
1. Should you purchase the scanner today or wait to purchase?
2. When is the best purchase time?
26. Mutually exclusive investments and project lives The Borstal Company has to choose between two machines that do the same job but have different lives. The two machines have the following costs:
|
Year |
Machine A |
Machine B |
|
0 |
$40,000 |
$50,000 |
|
1 |
10,000 |
8,000 |
|
2 |
10,000 |
8,000 |
|
3 |
10,000 + replace |
8,000 |
|
4 |
8,000 + replace |
27. These costs are expressed in real terms.
a. Suppose you are Borstal’s financial manager. If you had to buy one or the other machine and rent it to the production manager for that machine’s economic life, what annual rental payment would you have to charge? Assume a 6% real discount rate and ignore taxes.
b. Which machine should Borstal buy?
c. Usually the rental payments you derived in part (a) are just hypothetical—a way of calculating and interpreting equivalent annual cost. Suppose you actually do buy one of the machines and rent it to the production manager. How much would you actually have to charge in each future year if there is steady 8% per year inflation? [Note: The rental payments calculated in part (a) are real cash flows. You would have to mark up those payments to cover inflation.]
28. Mutually exclusive investments and project lives Look again at your calculations for Problem 26. Suppose that technological change is expected to reduce costs by 10% per year. There will be new machines in year 1 that cost 10% less to buy and operate than A and B. In year 2, there will be a second crop of new machines incorporating a further 10% reduction, and so on. How does this change the equivalent annual costs of machines A and B?
29. Mutually exclusive investments and project lives. Econo-Cool air conditioners cost $300 to purchase, result in electricity bills of $150 per year, and last for five years. Luxury Air models cost $500, result in electricity bills of $100 per year, and last for eight years. The discount rate is 21%.
a. What is the equivalent annual cost of the Econo-Cool model?
b. What is the equivalent annual cost of the Luxury Air model?
c. Which model is more cost-effective?
d. Now you remember that the inflation rate is expected to be 10% per year for the foreseeable future. Redo parts (a) and (b).
30. Mutually exclusive investments and project lives* As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $50,000. Its operating costs are $20,000 a year, but at the end of five years, the machine will require a $20,000 overhaul (which is tax deductible). Thereafter, operating costs will be $30,000 until the machine is finally sold in year 10 for $5,000. The older machine could be sold today for $25,000. If it is kept, it will need an immediate $20,000 (tax-deductible) overhaul. Thereafter, operating costs will be $30,000 a year until the machine is finally sold in year 5 for $5,000. Both machines are fully depreciated for tax purposes. The company pays tax at 21%. Cash flows have been forecasted in real terms. The real cost of capital is 12%. Which machine should United Automation sell? Explain the assumptions underlying your answer.
31. Mutually exclusive investments and project lives Machines A and B are mutually exclusive and are expected to produce the following real cash flows:
The real opportunity cost of capital is 10%.
a. Calculate the NPV of each machine.
b. Calculate the equivalent annual cash flow from each machine.
c. Which machine should you buy?
32. Replacement decisions Machine C was purchased five years ago for $200,000 and produces an annual real cash flow of $80,000. It has no salvage value but is expected to last another five years. The company can replace machine C with machine B (see Problem 30) either now or at the end of five years. Which should it do?
33. Replacement decisions Hayden Inc. has a number of copiers that were bought four years ago for $20,000. Currently maintenance costs $2,000 a year, but the maintenance agreement expires at the end of two years, and thereafter, the annual maintenance charge will rise to $8,000. The machines have a current resale value of $8,000, but at the end of year 2, their value will have fallen to $3,500. By the end of year 6, the machines will be valueless and would be scrapped. Hayden is considering replacing the copiers with new machines that would do essentially the same job. These machines cost $25,000, and the company can take out an eight-year maintenance contract for $1,000 a year. The machines would have no value by the end of the eight years and would be scrapped. Both machines are depreciated using seven-year straight-line depreciation, and the tax rate is 39%. Assume for simplicity that the inflation rate is zero. The real cost of capital is 7%. When should Hayden replace its copiers?
34. Replacement decisions. You are operating an old machine that is expected to produce a cash inflow of $5,000 in each of the next three years before it fails. You can replace it now with a new machine that costs $20,000 but is much more efficient and will provide a cash flow of $10,000 a year for four years. Should you replace your equipment now? The discount rate is 15%.
35. Replacement decisions. A forklift will last for only two more years. It costs $5,000 a year to maintain. For $20,000 you can buy a new forklift that can last for 10 years and should require maintenance costs of only $2,000 a year.
a. If the discount rate is 4% per year, should you replace the forklift?
b. What if the discount rate is 12% per year?
36. The cost of excess capacity The president’s executive jet is not fully utilized. You judge that its use by other officers would increase direct operating costs by only $20,000 a year and would save $100,000 a year in airline bills. On the other hand, you believe that with the increased use the company will need to replace the jet at the end of three years rather than four. A new jet costs $1.1 million and (at its current low rate of use) has a life of six years. Assume that the company does not pay taxes. All cash flows are forecasted in real terms. The real opportunity cost of capital is 8%. Should you try to persuade the president to allow other officers to use the plane?
CHALLENGE
36. Effective tax rates One measure of the effective tax rate is the difference between the IRRs of pretax and after-tax cash flows, divided by the pretax IRR. Consider, for example, an investment I generating a perpetual stream of pretax cash flows C. The pretax IRR is C/I, and the after-tax IRR is C(1 – TC)/I, where TC is the statutory tax rate. The effective rate, call it TE, is
In this case, the effective rate equals the statutory rate.
a. Calculate the effective tax rate for the guano project in Section 6-3.
b. How does the effective rate depend on the tax depreciation schedule? On the inflation rate?
c. Consider a project where all of the up-front investment is treated as an expense for tax purposes. Does this definition of the effective tax rate make sense for such a project?
37. Equivalent annual costs We warned that equivalent annual costs should be calculated in real terms. We did not fully explain why. This problem will show you.
Look back to the cash flows for machines A and B (in “The Choice between Long- and Short-Lived Equipment”). The present values of purchase and operating costs are 28.37 (over three years for A) and 21.00 (over two years for B). The real discount rate is 6% and the inflation rate is 5%.
a. Calculate the three- and two-year level nominal annuities which have present values of 28.37 and 21.00. Explain why these annuities are not realistic estimates of equivalent annual costs. (Hint: In real life machinery rentals increase with inflation.)
b. Suppose the inflation rate increases to 25%. The real interest rate stays at 6%. Recalculate the level nominal annuities. Note that the ranking of machines A and B appears to change. Why?
MINI-CASE 
New Economy Transport (A)
The New Economy Transport Company (NETCO) was formed in 1959 to carry cargo and passengers between ports in the Pacific Northwest and Alaska. By 2018, its fleet had grown to four vessels, including a small dry-cargo vessel, the Vital Spark.
The Vital Spark is 25 years old and badly in need of an overhaul. Peter Handy, the finance director, has just been presented with a proposal that would require the following expenditures:
|
Overhaul engine and generators |
$340,000 |
|
Replace radar and other electronic equipment |
75,000 |
|
Repairs to hull and superstructure |
310,000 |
|
Painting and other repairs |
95,000 |
|
$820,000 |
Mr. Handy believes that all these outlays could be written off immediately for tax purposes.
NETCO’s chief engineer, McPhail, estimates the postoverhaul operating costs as follows:
|
Fuel |
$ 450,000 |
|
Labor and benefits |
480,000 |
|
Maintenance |
141,000 |
|
Other |
110,000 |
|
$1,181,000 |
These costs generally increase with inflation, which is forecasted at 2.5% a year.
The Vital Spark is carried on NETCO’s books at a net depreciated value of only $100,000, but could probably be sold “as is,” along with an extensive inventory of spare parts, for $200,000. The book value of the spare parts inventory is $40,000. Sale of the Vital Spark would generate an immediate tax liability on the difference between sale price and book value.
The chief engineer also suggests installation of a brand-new engine and control system, which would cost an extra $600,000.16 This additional equipment would not substantially improve the Vital Spark’s performance, but would result in the following reduced annual fuel, labor, and maintenance costs:
|
Fuel |
$ 400,000 |
|
Labor and benefits |
405,000 |
|
Maintenance |
105,000 |
|
Other |
110,000 |
|
$1,020,000 |
Overhaul of the Vital Spark would take it out of service for several months. The overhauled vessel would resume commercial service next year. Based on past experience, Mr. Handy believes that it would generate revenues of about $1.4 million next year, increasing with inflation thereafter.
But the Vital Spark cannot continue forever. Even if overhauled, its useful life is probably no more than 10 years, 12 years at the most. Its salvage value when finally taken out of service will be trivial.
NETCO is a conservatively financed firm in a mature business. It normally evaluates capital investments using an 11% cost of capital. This is a nominal, not a real, rate. NETCO’s tax rate is 21%.
QUESTION
1. Calculate the NPV of the proposed overhaul of the Vital Spark, with and without the new engine and control system. To do the calculation, you will have to prepare a spreadsheet table showing all costs after taxes over the vessel’s remaining economic life. Take special care with your assumptions about depreciation tax shields and inflation.
New Economy Transport (B)
There is no question that the Vital Spark needs an overhaul soon. However, Mr. Handy feels it unwise to proceed without also considering the purchase of a new vessel. Cohn and Doyle Inc., a Wisconsin shipyard, has approached NETCO with a design incorporating a Kort nozzle, extensively automated navigation and power control systems, and much more comfortable accommodations for the crew. Estimated annual operating costs of the new vessel are:
|
Fuel |
$380,000 |
|
Labor and benefits |
330,000 |
|
Maintenance |
70,000 |
|
Other |
105,000 |
|
$885,000 |
The crew would require additional training to handle the new vessel’s more complex and sophisticated equipment. Training would probably cost $50,000 next year.
The estimated operating costs for the new vessel assume that it would be operated in the same way as the Vital Spark. However, the new vessel should be able to handle a larger load on some routes, which could generate additional revenues, net of additional out-of-pocket costs, of as much as $100,000 per year. Moreover, a new vessel would have a useful service life of 20 years or more.
Cohn and Doyle offered the new vessel for a fixed price of $3,000,000, payable half immediately and half on delivery next year.
Mr. Handy stepped out on the foredeck of the Vital Spark as she chugged down the Cook Inlet. “A rusty old tub,” he muttered, “but she’s never let us down. I’ll bet we could keep her going until next year while Cohn and Doyle are building her replacement. We could use up the spare parts to keep her going. We might even be able to sell or scrap her for book value when her replacement arrives.
“But how do I compare the NPV of a new ship with the old Vital Spark? Sure, I could run a 20-year NPV spreadsheet, but I don’t have a clue how the replacement will be used by the end of that time. Maybe I could compare the overall cost of overhauling and operating the Vital Spark to the cost of buying and operating the proposed replacement.”
QUESTIONS
1. Calculate and compare the equivalent annual costs of (a) overhauling and operating the Vital Spark for 12 more years, and (b) buying and operating the proposed replacement vessel for 20 years. What should Mr. Handy do if the replacement’s annual costs are the same or lower?
2. Suppose the replacement’s equivalent annual costs are higher than the Vital Spark’s. What additional information should Mr. Handy seek in this case?
1If you delay paying your bills, your investment in net working capital is reduced. When you finally pay up, it is increased.
2Holdings of cash and marketable securities are also short-term assets and debt due within a year is a short-term liability. These are not relevant to your capital budgeting calculations.
3Accenture, “Refocusing on the After-Sales Market,” 2010.
4 The Tax Cuts and Jobs Act is much more extensive and complicated than the changes that we outline here. For example, we say nothing about changes in personal income taxes. We are not offering comprehensive tax advice, just noting the most important changes for corporate finance.
5Sorry.
6There are several alternative ways to calculate operating cash flow. For example, you can add depreciation back to the after-tax profit:
Operating cash flow = after-tax profit + depreciation
Thus, in year 2 of the guano project:
Operating cash flow = 1.539 + 2.000 = $3.539 million
Another alternative is to calculate after-tax profit assuming no depreciation, and then to add back the tax saving provided by the depreciation allowance:
Operating cash flow = (revenues − expenses) × (1 − tax rate) + (depreciation × tax rate)
Thus, in year 2 of the guano project:
Operating cash flow = (12.887 − 7.729 − 1.210) × (1 − .21) + (2.000 × .21) = $3.539 million.
7IM&C’s new plant and equipment has a life of six years. Therefore, with double-declining-balance, it can depreciate each year 2 × (1/6) = 1/3 of the asset’s written-down value. If, for example, IM&C was allowed only 150% declining balance, it would be able to depreciate each year 1.5 × (1/6) = 1/4 of the written-down value.
8The only difference between MACRS and our example of double-declining-balance is that MACRS assumes that the investment is made halfway through the year and, therefore, receives only half the allowance in the first year.
9This separation of tax accounts from shareholder accounts is not found worldwide. In Japan, for example, taxes reported to shareholders must equal taxes paid to the government; ditto for France and many other European countries.
10In the meantime, you might like to get ahead of the game by viewing the spreadsheets for the guano project and seeing how NPV would change with a shortfall in sales or an unexpected rise in costs.
11Our timber-cutting example conveys the right idea about investment timing, but it misses an important practical point: The sooner you cut the first crop of trees, the sooner the second crop can start growing. Thus, the value of the second crop depends on when you cut the first. This more complex and realistic problem can be solved in one of two ways:
1. Find the cutting dates that maximize the present value of a series of harvests, taking into account the different growth rates of young and old trees.
2. Repeat our calculations, counting the future market value of cut-over land as part of the payoff to the first harvest. The value of cut-over land includes the present value of all subsequent harvests.
The second solution is far simpler if you can figure out what cut-over land will be worth.
12If you actually rent out the machine to the plant manager, or anyone else, be careful to specify that the rental payments be “indexed” to inflation. If inflation runs on at 5% per year and rental payments do not increase proportionally, then the real value of the rental payments must decline and will not cover the full cost of buying and operating the machine.
13However, if neither machine will be replaced, then we have to consider the extra revenue generated by machine A in its third year, when it will be operating but B will not.
14The present value of $118,700 a year for five years discounted at 6% is $500,000.
15 The renminbi (RMB) is the Chinese currency.
16 This additional outlay would also qualify for an immediate 100% bonus depreciation.