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6.1

 How to Compute Cash Flows

We discussed how to use accounting statements to estimate cash flows in Chapter 2. There we showed a simple approach that gave a reasonable approximation in most cases and a more complete approach. The simple approach just added depreciation expense back to net income to find an estimate of cash flow. This approach is usually fairly close to the exact value because depreciation is usually the primary account that causes net income and cash flow to differ.

The more complete approach begins with net income and subtracts increases in assets and adds increases in liabilities. Note that depreciation expense will be included in changes in fixed assets or property, plant, and equipment (PP&E), so is not treated separately as it was in the simple approach. If you are not comfortable with translating accounting data into cash flows, be sure to review the more detailed description of the process in Chapter 2.

The appropriate cash flows for evaluating a corporate investment decision are incremental after-tax cash flows. We will explain this definition in some detail as the chapter progresses. For now, let's look at the logic underlying each portion of this expression.

Incremental: This is similar to the concept of marginal in microeconomics. Economists make decisions by comparing marginal costs and marginal revenues. Recall that a product's marginal cost is the cost of making one more unit of the product. If the marginal cost is less than the marginal revenue (the price the unit will be sold for), then the company produces and sells that additional unit of production. Production continues as long as marginal cost is below marginal revenue. In finance we have adopted the concept underlying marginal analysis to evaluate corporate investment proposals. We compare the additional cash flow that the proposed project or product will generate to the additional costs that the investment requires.

After-tax: When we evaluate a project proposal, we do so from the perspective of the owners of the company. If the company is publicly traded, this means we evaluate from the shareholders' perspective. Owners receive their return from after-tax dollars. That is, shareholders have a claim on after-tax profits. These are often referred to as residual cash flows because they are left after all other obligations have been paid. We will see that taxes can have a large effect on cash flows, so they cannot be ignored.

Cash flows: As we discussed at the very beginning of this chapter (and in Chapter 2), it is cash that allows a company to pay its obligations—wages to employees, bills from suppliers, taxes, etc.—and remain financially viable.

Incremental Cash Flows

The use of incremental cash flows builds on the concept of marginal costs and revenues in economics. In corporate finance we don't deal with individual units of production, but rather with investments in assets and other expenditures (training, marketing, R&D, etc.) to make new products or services, to expand production of existing product lines, or to reduce costs. In these situations we are dealing with a set of expenditures, sometimes totaling millions or even billions of dollars. The underlying concept is the same as in economics: If additional revenues exceed additional costs, then the investment should be pursued.

To make revenues and outlays (cash inflows and outflows) comparable, we apply the present value tools from Chapter 4 to translate all cash flows into today's dollars. If the present value of cash inflows exceeds the present value of costs, then the investment is said to have a positive net present value, and so it is wealth-creating and should be accepted. You will learn more about actually computing a net present value in Chapter 7. In this chapter we focus on the most important input in the net present value computation: cash flows.

The With-and-Without Principle

To determine incremental cash flows, we imagine the company with and without the proposed investment. The cash flows that the company generates without the proposed investment act as a baseline against which to identify changes in cash flows. We subtract the cash flows without the project from the company's cash flows if the project is accepted. This difference is the incremental cash flow from the proposed project.

You might ask how the with-and-without approach differs from just measuring the proposed product's revenue and costs. If you add up all the costs of designing, producing, marketing, and distributing a new product, there is a good chance that some of the costs will not be incremental. Examples include sunk costs, allocation of overhead, and cannibalism of sales.

Sunk Costs

Consider research and development costs for a product. Before a proposal can be submitted for funding, money has to be spent designing the product. It might seem like these costs should be included in the proposal. But including them is incorrect. They are sunk costs. It doesn't matter whether or not the new product is pursued; these funds have been spent and cannot be recovered. In respect to these R&D expenditures, the company is no different with or without the project; in either case the money has been spent. Another common type of sunk cost is marketing research.

Basically, anything that is spent prior to the proposal being submitted and analyzed cannot be recovered, so it is a sunk cost.

Sunk Costs

Allocation of Overhead

Managerial accounting classes typically dedicate several weeks to the allocation of overhead costs. There are several approaches for doing this. If you thought that cost accounting was challenging, we have good news for you: In finance we do not allocate overhead. If a cost is truly overhead and fixed, then the with-and-without principle will not identify it as incremental. Whether or not the proposed project is accepted, the company will incur the cost.

Let's look at some examples. Sometimes factory floor space is allocated by square feet or square meters utilized by a project. Almost always, the rent or lease expense for this area has to be paid whether or not the new project is accepted. Applying the with-and-without concept means that if rent or lease payments do not change, no floor space cost is incremental to the project. We discuss a possible exception to this rule under opportunity costs below.

Salaried managers may have some portion of their time allocated to a new project, but unless there are new cash outlays associated with hiring a replacement to complete other assigned tasks the managers no longer have time to complete, there is no allocation of salaries to the new project. Only if salary expenses with the project were greater than without it would there be any incremental cost.

To summarize, we only look at changes in cash flows, so anything that is truly fixed, and by definition doesn't change, is not incremental and therefore is not a relevant cash flow for corporate investment analysis purposes.

Cannibalism of Sales

Often new products are related to a company's existing products. This makes sense because companies develop expertise in certain markets, certain types of production, certain types of distribution, and so on. This is an application of the core competency idea that is a central thesis of management. Examples abound. Boeing makes passenger jets; Campbell makes soup; McDonald's sells fast food via franchises; John Deere makes farm equipment.

When a company introduces a new product, it is likely related to existing product lines. Thus, it may compete with existing products. Consider the Campbell Soup Company and its chicken soup line. Is Campbell's Chicken & Stars very different from Chicken Alphabet soup or Chicken Noodle soup or Chicken NoodleO's or Chicken with Mini Noodles or Homestyle Chicken Noodle soup or Chunky Classic Chicken Noodle soup? When a new chicken noodle soup variant is introduced, it is very likely that some of its sales will come from the existing chicken noodle variants that Campbell is already selling. If so, how should the revenues (and thus the cash inflows) from the new product be calculated?

Using the with-and-without principle we would compare the revenues after the new soup is introduced to the sales before and use this difference. The difference is the incremental revenue from the new product.

Bloomberg/Getty Images

The Campbell Soup Company produces a variety of chicken soups.

Computing incremental revenues can be complicated. Let's go back about 20 years to the time when doctors began warning about people having too much sodium (or salt) in their diets. It was thought that too much salt could result in higher blood pressure and possibly other health problems. At that time people starting shifting their purchases toward low-sodium versions of products. If the Campbell Soup Company introduced a low-sodium chicken noodle soup in response to a competitor doing so (although Campbell Soup is so huge that it may not have any significant competitors), we would compute incremental cash inflows differently.

The without baseline would be Campbell Soup's sales without the low-sodium variety. The sales would presumably be lower because health-conscious consumers would shift to the competitor's low-sodium soup. If Campbell Soup introduces a low-sodium variety and prevents sales from being lost, those recovered sales should be included as incremental revenue in the cash flows for the low-sodium-soup analysis. This is a subtle distinction: When a company introduces a defensive product, it needs to consider the revenues protected (i.e., not lost to competitors) in addition to new revenues when determining incremental cash inflows or benefits associated with the product.

After-Tax Cash Flows

Because we take the perspective of owners when analyzing corporate investment proposals, and because owners are paid from after-tax dollars, we need to consider taxes when determining the appropriate cash flows for investment analysis.

Taxes affect investment cash flows in several ways. Companies pay tax on their income. Income is computed as revenues for the period minus tax-deductible expenses for that period. An important expense when evaluating an investment proposal is depreciation expense. Most large investments involve the purchase of long-lived equipment, which will have its cost depreciated over time via depreciation expense.

Try Demonstration Problem 6.1 to assess your skill at estimating cash flows.

Demonstration Problem 6.1: Cash Flow Estimation

You and several other entrepreneurial recent college graduates are considering organizing a series of bluegrass music festivals. You have found a group of bands and musicians who will commit to come and perform over a 3-day period each July for the next 5 years. You have found an old outdoor amphitheater, but it requires some remodeling and new equipment before it can be used. Before you commit to this series of five bluegrass festivals, use the following information to estimate the cash flow from the festivals.

a. The musicians, as a group, want a guarantee of $25,000 per year plus $1 per ticket sold. In addition, the musicians need housing. The total housing expense will be $4,500.

b. Refurbishing and equipping the pavilion will generate a depreciation expense of $6,500 per year for 5 years.

c. Insurance, security, equipment rental, lighting, and audio services will total about $8,500 per year. Printing, advertising, telephone use, postage, and other expenses related to the festival are estimated to total $7,500 per year.

d. With effective advertising, a member of the group, who is a marketing professional, believes the festival will draw people from throughout the region. Tentatively, an average ticket price of $10 is being considered.

e. Based on similar events elsewhere, she estimates total ticket sales over the 3 days will be about 6,500 the first year, growing to 8,000 in years 2 and 3, and to 9,000 in years 4 and 5.

f. The appropriate tax rate for this project is 28%.

Solution

			Revenues
Year	1	2	3	4	5
Tickets	6,500	8,000	8,000	9,000	9,000
Revenue at $10/ticket	$65,000	$80,000	$80,000	$90,000	$90,000
			Expenses
Year	1	2	3	4	5
Musicians' fee	$25,000	$25,000	$25,000	$25,000	$25,000
Musicians' gate receipts	6,000	8,000	8,000	9,000	9,000
Musicians' housing	4,500	4,500	4,500	4,500	4,500
Depreciation	6,500	6,500	6,500	6,500	6,500
Insurance, etc.	20,500	20,500	20,500	20,500	20,500
Total expenses	$62,500	$64,500	$64,500	$65,500	$65,500
		Taxes, Profits, and Cash Flow
Year	1	2	3	4	5
Profit	$2,000	$15,500	$15,500	$24,500	$24,500
Tax	560	4,340	4,340	6,860	6,860
Net profit	1,440	11,160	11,160	17,640	17,640
Cash flow	7,940	17,660	17,660	24,140	24,140

The Depreciation Tax Shield

The income statement in Table 6.1 includes a line for depreciation expense. This expense reduces taxable income, so reduces the amount of taxes paid. In Table 6.2 depreciation expense is removed, so taxable income and taxes go up.

Table 6.1: Income statement with depreciation expense
Income Statement for the Year 2012
Revenue	1,000,000
COGS	487,500
Gross margin	512,500
Depreciation expense	200,000
Taxable income	312,500
Taxes (32%)	100,000
Net income	212,500
Add back depreciation	200,000
Cash flow	412,500

Table 6.2: Income statement without depreciation expense
Income Statement for the Year 2012
Revenue	1,000,000
COGS	487,500
Gross margin	512,500
Depreciation expense	0
Taxable income	512,500
Taxes	164,000
Net income	348,500
Add back depreciation	0
Cash flow	348,500

In Table 6.1 depreciation expense reduced taxable income by $200,000. Because of this tax shield, taxes decreased by $64,000, from $164,000 (in Table 6.1 without depreciation expense) to $100,000 in Table 6.2. The tax shield effect can be estimated directly from

(6.1)

Tax Savings = Depreciation Expense × Tax Rate

Substituting in the values we are given gives us

Tax Savings	= $200,000 × 0.32
	= $64,000

In Tables 6.1 and 6.2 notice how the presence of depreciation expense affects cash flow. Cash flow in Table 6.1, estimated by adding depreciation expense to net income, is $412,500. When depreciation expense is removed, as shown in Table 6.2, cash flow decreases to $348,500. This $64,000 fall in cash flow arises because of the loss of the depreciation tax shield. The change in cash flow is exactly equal to the tax savings estimated with Equation (6.1).

While there are tax savings and cash flow increases in years when depreciation expense is recognized, you need to think about the cash flow implications over an asset's entire life. When the asset is purchased, a large outlay is made. Think of this as a negative cash flow or an outflow of cash. Over the depreciable life of the asset, the tax savings from depreciation expense generate positive cash flows. Figure 6.1 shows the timeline of cash flows associated with the purchase and depreciation of a long-lived asset.

Figure 6.1: Timeline of cash flows associated with a long-lived asset

Pat Byrnes/The New Yorker Collection/www.cartoonbank.com

In Figure 6.1 a company purchases a machine (or some other asset) for $1,200,000. The company recognizes $200,000 of depreciation expense each year for the wear and tear (or the consumption) of the machine for the next 6 years. Assuming a tax rate of 32%, the $200,000 of depreciation expense reduces taxable income by $200,000 and thereby reduces taxes by $64,000. It is the $64,000 annual tax savings that we recognize as a cash flow. While these tax savings are great, you need to remember that they exist only because the company spent $1,200,000 on the machine initially. The tax shields are not free.

Ignoring the time value of money for a moment, we see that the sum of the tax shield cash flows is $384,000 (= 6 × $64,000), not $1,200,000. The sum of the tax shields is less than the amount spent because, though over the 6-year asset life taxable income is reduced by $1,200,000 ($200,000 per year), this only reduces taxes, and creates cash flows, by $64,000 per year. Notice that $1,200,000 × 0.32 = $384,000. If the time value of money is considered, then the present value of the depreciation tax shields is less than $384,000. Sometimes government economic stimulus policies accelerate depreciation, even allowing companies to take all of the depreciation in the first year. This increases the value of the tax shields in terms of their present value.

Tax Deductible Expenses

For companies, almost all business expenses are tax deductible; that is, they are subtracted from revenue and reduce taxable income. We can calculate after-tax cost using

(6.2)

After-Tax Cost = Cost × (1 – Tax Rate)

The after-tax cost of a deductible expense for a $2,000 outlay and a 35% tax rate is then given by

After-Tax Cost	= $2,000 × (1 – 0.35)
	= $1,300

The company writes a check to the supplier for $2,000, but after the cost reduces taxable income, the company realizes a tax savings of $700, making the after-tax cost of the $2,000 just $1,300.

For both depreciation and deductible expenses, the tax savings are greater the higher the tax rate. This also means that the savings decrease with a drop in the tax rate. A company with losses, which would pay no taxes, would see little immediate benefit from either depreciation or tax-deductibility of expenses. If the losses are temporary, the company might receive value via tax-loss carry forwards (which enable firms to deduct the losses from 1 year from future profits in order to lower taxes in future years) or other provisions of the tax code.

This approach [(dollars × (1 – Tax Rate)] can also be applied to cash inflows, so

(6.3)

After-Tax Earnings = Earnings × (1 – Tax Rate)

For example, if you earn an extra $5,000 and your tax rate is 22%, then your after-tax earnings will be $3,900 as

After-Tax Earnings	= Earnings × (1 – Tax Rate)
	= $5,000 × (1 – 0.22)
	= $3,900

Your 22% tax rate means you pay $1,100 on $5,000 of additional earning, leaving $3,900 after-tax income.

Recapture of Depreciation, Gains, and Losses

As companies upgrade equipment and change their product mix (and thereby the machines required for production), they sell some assets. If an asset is sold for its current book value (usually, original cost less accumulated depreciation), then there are no tax consequences. However, if the sales price differs from the current book value, then we need to consider taxes.

If the sales price falls between the original cost and the current book value, then the company depreciated the asset too quickly. This extra depreciation is recaptured by the tax authorities in the form of tax at the company's ordinary tax rate. Since the company reduced its taxes too much, it has to return some of those savings. Here is an example: A construction company bought a bulldozer 3 years ago for $150,000. It depreciated the bulldozer using the straight-line method at $30,000 per year, assuming a 5-year life. The current book value is $60,000 ($150,000 – 3 × $30,000). It decides to replace the machine, so it sells it for $75,000. The sales price of the used machine ($75,000) exceeds the current book value ($60,000). The company depreciated the bulldozer $15,000 too much, so it must pay taxes on that excessive depreciation. Assuming the tax rate is 35%, the company would have a tax bill of $5,250 (= 0.35 × $15,000). The after-tax income from the sale of the used bulldozer would be $75,000 – $5,250 = $69,750.

There isn't anything wrong (i.e., it isn't illegal) for the sales price of an asset to differ from the asset's book value. Market values fluctuate, and depreciation is just a guess about the loss of economic value of a machine or factory. When the sales price is finally known, then there is a settling up.

If the sales price is less than the current book value, then the company has a loss (or didn't depreciate fast enough) and receives tax relief equal to the tax shield if it had depreciated the asset to the sales price. Using the bulldozer example above, suppose the sales price of the used machine was $40,000. The current book value is $60,000, as above. Therefore the company deserves $20,000 of extra depreciation, which would reduce its taxes by $7,000 (= 0.35 × $20,000). The after-tax income from the sale of the used bulldozer would be $40,000 (from the sale) + $7,000 (from tax savings) = $47,000.

The last possibility is that the asset is sold for more than its original price. This situation is probably rare for equipment, but it is actually common in real estate transactions and for other assets that typically appreciate in value, such as antique cars.

Suppose that in 1957 a company bought its CEO a Ford Thunderbird to use as a company car. The price of the car in 1957 was $3,408. Over the years repairs added about $3,000 to this cost, resulting in a total investment of $6,408. This is called the cost basis. For information about these tax issues, see the IRS item in the Web Resources section at the end of the chapter. Today, according to several websites, the car would sell for between $30,000 and $60,000. Suppose the company had depreciated the car to zero over 6 years many years ago (presumably by 1963 or 1964) but today sold it for $40,000. It would have to recapture $6,408 of depreciation. The gain beyond $6,408 would be a long-term capital gain taxed at the preferential 15% long-term gain rate. The first $6,408 would be taxed at the company's ordinary rate of 35%. The remaining amount, the capital gain of $40,000 – $6,408 = $33,592, would be taxed at 15%. The after-tax cash flow from selling this classic roadster would be

After-Tax Cash Flow	= $40,000 – $6,408 × 0.35 – $33,592 × 0.15
	= $40,000 – $2,242.80 – $5,038.80
	= $32,718.40

As an interesting aside, consider the following: In 1957 Ford hand-built 12 supercharged racing Thunderbirds. One came to auction in 2009 with an estimated price of $300,000 to $350,000! Ford also made 222 factory-built supercharged Thunderbirds in 1957. They sell for well over $100,000 today.

Figure 6.2 summarizes the tax issues of selling a piece of equipment. If the sales price is below the current book value (in the yellow area), then there is a loss. If the sales price is in the green area, then depreciation needs to be recaptured. If the sales price is higher than the original cost (or current cost basis), then there will be recapture of depreciation and a capital gain.

Figure 6.2: Losses, recapture, and gains from the sale of an asset

We have presented a somewhat simplified version of these tax issues. There are some potential complications when selling more than one asset in a fiscal year, and when selling to a related party. If this topic interests you, be sure to look at the IRS tax document in the Web Resources at the end of the chapter.

.2

 Categories of Cash Flows

When we analyze proposed investments, it is handy to categorize cash flows into three types. By creating a checklist for each type, we can help to assure that nothing has been left out of the analysis. The three categories of cash flows are

· initial investment,

· operating cash flows, and

· terminal cash flows.

Initial Investment

For the purposes of analysis we assume that the initial investment occurs today, at time t = 0. This ensures that the expenditures associated with the initial investment are in today's dollars or are present values that need no further discounting. All other cash flows will be discounted using present value techniques to time t = 0, so that cash flows can be compared.

The initial investment always includes the purchase of new equipment or facilities or some other large outlay. Remember that we estimate these cash flows so that they can be used in an analysis of whether or not an investment should be made. If there is no significant outlay for equipment or facilities, then there is no investment to examine.

If the proposed investment is to replace existing equipment, then the initial investment will usually include proceeds from the sale of the old equipment, with appropriate tax adjustments.

Any additional (uncompleted and not contracted by time t = 0) R&D or marketing research would also be included, as would training for employees and specific installation costs for equipment or machinery. Costs for R&D and/or marketing research that have already been paid are not included, as they are sunk costs.

Part of the initial investment that is often overlooked is working capital. To produce and sell merchandise, a company needs raw materials from suppliers (which generate accounts payable), to maintain inventory (which adds to the inventory account), and often it must offer credit to customers (which creates accounts receivable). Using the with-and-without concept, changes in these working capital accounts become part of the incremental cash flows for the project. At the start of the project the investment will include some level of inventory and accounts receivable less the amount of spontaneous financing provided by suppliers through accounts payable. As the sales of the product increase, additional working capital investment may be required to support higher sales levels.

Operating Cash Flows: New Revenue or Profit

The goal of a new product introduction or other corporate investment is to increase shareholder wealth. In the introduction to this chapter we said that this means increasing cash flows available for owners or residual cash flows. As discussed in Chapter 2 and above, cash flows are approximated by net income plus depreciation expense, or more exactly as net income plus changes in assets and liabilities.

We will show two different ways to get the approximate cash flows, and then later consider changes in working capital (the main source of changes in assets and liabilities for most projects). The two approaches differ by the information with which they begin: EBT (earnings before taxes) or EBDT (earnings before depreciation and taxes).

Approach 1: The EBT Approach

If you know the change in earnings before taxes (taxable income), then you can find the after-tax operating cash flows by creating the very bottom of an income statement and adding depreciation expense to net income. This approach is also excellent if you are creating pro forma or projected income statements for the proposed project. An example shows this slightly extended version. See A Closer Look: Is EBITDA a Measure of Cash Flow? for an in-depth discussion of using earnings before interest, taxes, depreciation, and amortization (EBITDA) as a measure of cash flows.

A Closer Look: Is EBITDA a Measure of Cash Flow?

Some financial analysts specialize in evaluating whether firms can borrow more money. In the 1980s these debt analysts began using EBITDA as an indicator of a company's ability to repay its debt. EBITDA quickly became the favorite tool of debt analysts, particularly those studying high-yield or junk bonds. We know from our discussion of transforming accounting profits into cash flow that one method is to add depreciation (and amortization) to net income. EBITDA does this. It also adds back taxes and interest payments. Because interest is paid before taxes, EBITDA is a reasonable estimate of the cash available to make those interest payments. If EBITDA is sufficiently high (approximately two or three times the total debt service payments), analysts feel comfortable recommending that the company borrow more money.

Over time, other analysts started using EBITDA as an estimate of cash flow. Equity analysts estimate the value, today and in the near future, of shares of stock. Depending on their valuation, the analysts issue recommendations to buy, hold, or sell the stock. Many stock price valuation models use estimates of future cash flows available to stockholders to form a current share price. Some equity analysts and companies themselves began using EBITDA to argue for higher share prices. By definition, the EBITDA must be larger than cash flow estimates that add depreciation to net income, so that the valuation can support a higher stock value. Soon investment analysts began criticizing the use of EBITDA as a universally appropriate measure of cash flow. Their argument, in a nutshell, was that the measure of cash flow appropriate for one use might not be appropriate for other uses. While EBITDA may be an appropriate measure for lenders, it is not appropriate for stockholders. Stockholders care about the cash paid for interest and taxes. Equity investors are interested in after-tax cash flows. In fact, equity investors are interested in cash flows after all payments have been made. These residual (or remaining) cash flows are available to investors, so they are the best measure of an investment's value to stockholders. As this brief discussion makes clear, there is not a single measure of cash flow that is always appropriate. The measure of cash flow needs to fit the job it is being applied to.

As an example, consider that a new product will generate sales of $20,000 per year. COGS (direct costs) will be $14,000 and there will be $1,500 of depreciation expense. The company's tax rate is 30%. Find the annual after-tax cash flows for this product.

First, subtracting COGS from sales gives us the gross margin:

	Sales	$20,000
	COGS	–$14,000
	Gross margin	$6,000

Then subtract depreciation to get the taxable income:

	Gross margin	$6,000
	Depreciation expense	–$1,500
	Taxable income	$4,500

A tax rate of 30% means $1,350 must be paid in taxes, so that the net income will be

	Taxable income	$4,500
	Tax (30%)	–$1,350
	Net income	$3,150

Adding back depreciation gives the after-tax cash flow:

	Net income	$3,150
	Add back depreciation	+$1,500
	After-tax cash flow	$4,650

Demonstration Problem 6.2: Cash Flow Estimation

Lincoln Composite Materials produces aerospace parts from fiberglass, Kevlar™, and other plastics. Last year Lincoln had a net income of $2,746,347 on sales of $68 million. The depreciation expense was $710,558 and taxes were $976,994. Use this information to provide a rough estimate of Lincoln's cash flow.

Solution

Cash Flow	= Net Income + Depreciation
	= $2,746,347 + $710,558 = $3,456,905

Approach 2: The Tax Shield Approach

Suppose instead of the entire income statement, you are given just three pieces of information: The change in EBDT will be $6,000 per year; the tax rate is 30%; and annual depreciation expense is $1,500 per year. We compute the after-tax value of the EBDT (or net operating income) using Equation 6.3 and add the value of the depreciation tax shield.

After-tax value of EBDT

= ($6,000) × (1 – .30) = $6,000 × 0.7 = $4,200

Value of the depreciation tax shield

= Depreciation Expense × Tax Rate = $1,500 × 0.3 = $450

Add these for an after-tax cash flow

= $4,200 + $450 = $4,650

This is identical to the after-tax cash flow from the EBT method.

Using the Two Approaches

A common error made by beginning students is to mix these two approaches. For example, some people add the value of the depreciation tax shield ($450) to net income instead of depreciation expense ($1,500). Be careful that you choose one method and stick with it throughout the entire cash flow estimation process.

Changes in Working Capital

As sales of a product rise, companies typically purchase more inventory, and when sales fall, firms buy less inventory. Accounts receivable automatically adjusts as the volume of sales has a large influence on credit sales. For example, for a firm whose sales are typically 80% on credit and 20% cash, an increase of sales of $100,000 will result in an increase of $80,000 in accounts receivable.

Financing Costs

Financing costs, such as interest, are not included in cash flow estimates. We will show in Chapter 7 that financing costs are included in the discount rate. Therefore, including them in cash flows would be double-counting these costs. In most cases in corporate finance we separate financing and the investment decisions; that is, we determine the company's financing mix, then use that decision in our investment analysis. An exception to this rule is project finance, where certain large projects might have their own financing and therefore their own financing costs.

Terminal Cash Flows

A few unique cash flows occur at the termination of a product's life. These are called terminal cash flows. At the end of a project we assume that equipment is sold, possibly for minimal scrap value. There are sometimes cleanup or closure costs. These are most common in natural resource extraction situations in which mine sites have to be reclaimed. A much more common cash flow associated with the end of a project is the recovery of working capital.

Salvage Value

Salvage value follows the same process as the sale of an asset. If the sales price is less than the current book value (which is usually quite small or zero), then there is a loss. If the sales price is between the current book value and the original cost (or cost basis), then depreciation must be recaptured at the ordinary tax rate. If the sales price is greater than the original cost (or cost basis), then depreciation must be recaptured at the ordinary tax rate and the gain may be taxed at the long-term capital gains rate.

Table 6.3: Tax consequences for the sale of machinery
Book value	Sales price	Taxable gain/loss on sale
$5,000	$8,000	$3,000 (gain)
$5,000	$5,000	$0
$5,000	$1,000	$4,000 (loss)

Consider the example in Table 6.3. Here a piece of machinery has been depreciated to the point that its book value is $5,000. This example illustrates the gain or loss from three hypothetical sales prices. This gain (or loss) will be added to (or subtracted from) a firm's taxable income and will result in higher taxes if there was a gain from sale, or lower taxes if the equipment was sold at a loss.

Cleanup or Reclamation

These costs will be tax deductible, so they should be treated as an expense in the last year of the project's anticipated life.

Recovery of Working Capital

As a product line winds down, there is reduced need for inventory and raw materials, so accounts payable and inventory accounts shrink. Similarly, as sales decrease, the investment in accounts receivable shrinks. The company sees a decrease in working capital and those investments flow back into the company as cash. If this seems confusing, consider the last few months of a product's sales before the product is discontinued. Revenue and profits are earned, but there is no cash expenditure on producing more items. For example, there is no need to purchase more inventory for the discontinued product. The recovery of working capital occurs as the profits from these final sales are retained with no further outlay being made.

Sometimes all of the working capital is not recovered. Older inventory may not be sellable, maybe because of spoilage or being an outdated version of the product. This is frequently the case with older electronics that have short product life cycles. In order to sell the last units of inventory, a company may have to sell at a discount, which would mean less working capital is recovered than expected.