# The first step in the capital

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## T

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### Self-Test Review Questions*

1. Should a consulting fee paid to a finance professor to evaluate a project be included in the analysis?

2. Should interest paid on debt solely to finance a project be included in the analy-sis?

3. Should lease revenues that are lost because property is used for a project be included in the analysis?

*1. No, the fee is a sunk cost and cannot be recover

ed even if the project is r ejected.

2. No.

3. Y es.

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### Terminal cash flow

Students often find the cal-culation of the initial cash flow confusing because there are so many pieces to keep track of. Keep your focus on the idea that you are simply trying to deter-mine how much cash will go out the door when the new asset is acquired. Pay particular attention to adjusting for taxes because this is where most errors are made.

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### Self-Test Review Question*

You are evaluating the purchase of a new plastic molding press. The sales represen-tative has quoted you a price of \$25,500. You contact the shipper and learn it will cost an additional \$1,500 to get it to your factory. It will cost \$750 to set it up for pro-duction. What is the net purchase price? What amount would you use as the basis for computing depreciation?

TABLE 11.1

### Calculation of Initial Cash Flow

- Initial purchase price of new asset - Installation/shipping cost of new asset = Net purchase price

+ Proceeds from sale of old asset +/- Tax on sale of old asset +/- Change in net working capital

= Initial cash flow

*Simply add the costs together: \$25,500+ \$1,500+ \$750= \$27,750. This is the amount that you would

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X A M P L E

### Computing Book Value

Suppose you bought a dump truck 2 years ago at a price of \$18,500. What is the current book value of the truck?

### Solution

You must first establish what life the asset will have for depreciation purposes. The IRS speci-fies asset classes and their associated lives. A sample of IRS asset classes is included in the chap-ter appendix. There we find that a truck is to be depreciated over 5 years.

We next need to sum the accumulated depreciation. Refer to the MACRS depreciation table in the appendix under the 5-year investment class. Depreciation is 20% the first year and 32% the second year, so total accumulated depreciation is 52% of the initial asset value, or \$9,620 (\$18,500!0.52=\$9,620). Apply Equation 11.1 to compute the book value:

Book value =Initial cost-Accumulated depreciation Book value=\$18,500-\$9,620=\$8,880

The book value of the truck is \$8,880 after 2 years.

### Self-Test Review Question*

Suppose the truck used in Example 11.1 was sold after 2 years for \$10,000. What would be the tax on the sale? Assume a 40% tax rate.

*Tax =(Sales price -Book value) !T ax rate, so Tax =(\$10,000 -\$8,880) !0.40 =\$448. Because the

car was sold for more than the book value, the firm owes a tax of \$448 on the sale. This is a cash outflow .

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X A M P L E

### Changes in Net Working Capital

As a result of a new machine, your production process has changed. This change requires that you keep \$12,000 worth of additional widgets on hand. Accounts payable are expected to increase by \$3,000 because you will rely on vendor financing as much as possible. What is the change in net working capital?

### Solution

The increase of \$12,000 in widgets means that you have to increase inventory. Because inventory is a current asset, this increase affects net working capital. Similarly, accounts payable are current liabilities that also affect net working capital. Using Equation 11.3 we get the following:

Change in net working capital=Change in current assets-Change in current liabilities Change in net working capital=\$12,000-\$3,000=\$9,000

Current assets go up by \$12,000. This increased need for assets is funded partly by an offset-ting increase in current liabilities of \$3,000. The change in the net working capital is \$9,000. This amount would be entered with a minus sign in the initial cash flow.

X A M P L E

### Initial Cash Flows: Comprehensive Example

Suppose that K-Mart is contemplating upgrading its computers at a cost of \$1 million to allow for increased inventory control systems. It will cost \$250,000 to install the computers. Assume the old computer system that originally cost \$500,000 has been in service for 3 years and has a MACRS depreciable life of 5 years. If the old system can be sold for \$200,000 and net work-ing capital decreases by \$40,000, what is the initial cash flow?

In a long, complex prob-lem it can be difficult to isolate the initial cash flows from the annual cash flows. The initial cash flows include items that occur only once and at the beginning of the project.

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### Solution

A tax of \$22,000 must be subtracted from the initial cash flow because the old machine was sold for a taxable gain, which required that additional taxes be paid.

The last line in the calculation of the initial cash flow is the change in net working capital. The problem states that net working capital decreases by \$40,000. A decrease in working cap-ital means that the firm holds less working capcap-ital than it did before. For example, the firm may hold less inventory with the new asset than it had to with the old asset. This reduction in net working capital is treated as a cash inflow and is given a positive sign, just as if the firm had received a check in the mail. By lowering the required net working capital, the firm frees up assets that can be used elsewhere. If the net working capital had increased, we would have subtracted rather than added it to the initial cash flow.

The initial cash flow for this new computer is \$1,032,000. It is substantially less than the initial net purchase price because the sale of the old machine resulted in a positive net cash flow and because net working capital decreased.

### deter-mine how the annual cash inflows are estimated.

Calculation of Initial Cash Flow

- Initial purchase price of new asset –\$1,000,000 - Installation/shipping cost of new asset –\$250,000

= Net purchase price –\$1,250,000

+ Proceeds from the sale of old asset +\$200,000 +/- Tax on sale of old asset (see below) –\$22,000 +/- Change in net working capital +\$40,000

= Initial cash flow –\$1,032,000

The initial purchase price and installation/shipping are added together to obtain the net pur-chase price of the asset. Offsetting this cost are the proceeds of selling the old computer for \$200,000. The tax on the sale of the old computer is figured as follows.

Accumulated depreciation = \$500,000 ×(0.20 + 0.32 + 0.19) = \$355,000 The depreciation percentages come from the MACRS table in the appendix to this chapter.

Continuing:

Book value = Initial cost-Accumulated depreciation Book value = \$500,000-\$355,000

Book value = \$145,000 and

Tax on sale = (Sales price-Book value) ×Tax rate Tax on sale = (\$200,000-\$145,000) ×0.40 Tax on sale = \$55,000 ×0.40=\$22,000

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X A M P L E

### Expansion Project

Logan’s Roadhouse Inc. owns a chain of restaurants that competes with Outback and Lone Star steakhouses. Its rapid growth earned it the ninth position on Business Week’s 1996 list of hottest growth companies. By offering smaller portions than the other restaurants, it can price meals so that the average customer check is \$11.25 instead of about \$16 at its competitors. If a new Logan’s restaurant will have revenues of \$2.5 million and revenue growth of 15% per year, and if the total expenses are 90% of revenues, what are the annual cash inflows over the next 5 years (2001–2005)? Assume straight-line depreciation over 39 years on an initial cost of \$2.73 mil-lion and a 40% marginal tax rate.

Many students are con-fused by the calculation of the incremental deprecia-tion. It may seem reason-able that because the old machine has been sold, there should not be any depreciation on it. Stay focused on the idea that we are computing changes that result from replacing the machine. One of the changes is in the deprecia-tion amount. If the new machine was not pur-chased, the old deprecia-tion amount would have continued.

TABLE 11.2

### Calculation of Annual Cash Flows

+ (New sales revenue – Old sales revenue)

- (New operating expenses – Old operating expenses) = Gross profit

- (New depreciation – Old depreciation) = Net profit before taxes

- Taxes

= Net profit after taxes

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### Solution

Because this is an expansion project, as opposed to a replacement project, no old revenues, expenses, or depreciation exist. This spreadsheet was prepared using formulas wherever pos-sible so that as estimates change, new cash flows can be computed easily. For example, the new revenues for the year 2002 are computed as the new revenues from 2001!1.15. Similarly, new expenses are computed as new revenues!0.9.

Because a restaurant is commercial property, it is straight-line depreciated over 39 years (see the appendix to this chapter):

\$2.73 million/39=\$70,000, or \$0.07 million

X A M P L E

### Replacement Project

As the manager of a movie theater, you were impressed at a local trade show with a new-generation popcorn machine. Despite being smaller than your old model, it pops corn faster. To help you decide whether you should buy the new machine, you collect the following information. The old machine generates revenues of \$50,000 per year. It costs \$10,000 to operate. Two years ago it cost \$15,000 and it is being depreciated over 3 years using MACRS. The new machine costs \$25,000 and will also be depreciated over 3 years. Revenues will increase to \$65,000 and costs will rise to \$11,000. Assume a 40% tax rate and compute the annual cash flows for the next 3 years.

### Solution

The revenues are found by subtracting the old revenues from the new projected revenues. Sim-ilarly, the expenses are found by subtracting the old expenses from the new expenses.

2001 2002 2003 2004 2005

New revenues – Old revenues \$2.500 \$2.875 \$3.306 \$3.802 \$4.373 New expenses – Old expenses 2.250 2.588 2.976 3.422 3.935

Gross profit 0.250 0.287 0.330 0.380 0.438 -(New depr. – Old depr.) 0.070 0.070 0.070 0.070 0.070 Net profit before tax 0.180 0.217 0.260 0.310 0.368

-Taxes (40%) 0.072 0.087 0.104 0.124 0.147

Net profit 0.108 0.130 0.156 0.186 0.221

+Depreciation 0.070 0.070 0.070 0.070 0.070

Net cash flow 0.178 0.200 0.226 0.256 0.291

Students tend to make mis-takes when computing depreciation. Study the appendix to this chapter and the calculation of depreciation in Example 11.5 carefully.

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The depreciation calculations require that you compute the depreciation on both the new and old machines and figure the difference. For the first year the new machine will be depre-ciated at 33% of its initial cost of \$25,000. Thus, the new depreciation for the first year will be \$8,250 (0.33!\$25,000=\$8,250). The depreciation for the old asset during its third year (2001) is \$2,250 (\$15,000!0.15=\$2,250). The depreciation during subsequent years is found the same way. Note that by the third year depreciation for the old asset is zero.

In 2001, a net profit results, so a tax of \$3.2 thousand (\$3,200) is due the IRS. We still can-not determine whether we should buy the popcorn machine. We must first compute the ter-minal cash flow.

### shows how to compute the terminal cash flow.

Popcorn Machine Analysis (thousands)

2001 2002 2003

New revenues – Old revenues \$65-\$50=\$15 \$65-\$50=\$15 \$65-\$50=\$15 New expenses – Old expenses \$11-\$10=\$1 \$11-\$10=\$1 \$11-\$10=\$1

Gross profit \$14 \$14 \$14 -(New depr. – Old depr.) \$8.25-\$2.25= \$11.25-\$1.05= \$3.75-0=

\$6.00 \$10.20 \$3.75

Net profit before tax \$8.00 \$3.80 \$10.25

-Taxes (40%) -\$3.20 -\$1.52 -\$4.10

Net profit \$4.80 \$2.28 \$6.15

+Depreciation \$6.00 \$10.20 \$3.75

Net cash flow \$10.80 \$12.48 \$9.90

TABLE 11.3

### Calculation of Terminal Cash Flow

+ (New sales revenue – Old sales revenue)

- (New operating expenses – Old operating expenses) = Gross profit

- (New depreciation – Old depreciation) = Net profit before taxes

- Taxes

= Net profit after taxes

+ (New depreciation – Old depreciation) = Operating cash inflows

+ Sale of new asset +/-Tax on sale of new asset +/-Change in net working capital

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X A M P L E

### Terminal Cash Flow

Return to the Logan’s Roadhouse example (Example 11.4). Suppose that the company plans to sell the restaurant to the manager after 5 years to be operated as a franchise. This frees up addi-tional capital to continue expansion. If the restaurant will sell for \$3 million, what is the ter-minal cash flow?

### Solution

The terminal cash flow is computed as follows:

The tax on the sale of the restaurant is computed later in this example.

The depreciation is computed as the number of years depreciation has been charged against the asset times the annual depreciation amount:

Accumulated depreciation=\$70,000!5=\$350,000

Note that this method is appropriate only where straight-line depreciation is used. For MACRS, the accumulated depreciation is found by summing the percentages off the MACRS table and multiplying this percentage by the initial value of the asset.

Continuing:

Book value=Initial cost-Accumulated depreciation Book value=\$2,730,000-\$350,000

Book value=\$2,380,000

and

Tax on sale=(Sales price-Book value)¥Tax rate Tax on sale=(\$3,000,000-\$2,380,000)¥0.40 Tax on sale=\$620,000¥0.40=\$248,000

The net terminal cash flow is \$3,043,000, which is composed of the \$291,000 cash flow from the year 2005 computations and \$2,752,000 additional cash flow due to terminating the project.

Calculation of Terminal Cash Flow

Net cash flow (year 2005 from solution to Example 11.4) +\$291,000 + Proceeds from the sale of new asset +\$3,000,000 +/- Tax on sale of new asset (see below) –\$248,000

+/- Change in net working capital 0

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X A M P L E

### Computing Cash Flows

Due to unexpectedly high demand, Pizzas-by-Mail finds that it may need a larger oven. The old oven cost \$20,000 new and has been in use for 1 year. It has a 3-year life for depreciation and can be sold today for \$12,000. The new oven costs \$30,000 but will require \$5,000 in remodeling to fit the restaurant. Shipping costs are \$1,000. The new oven also has a 3-year class life. The larger oven will require that an additional inventory of \$500 be held.

Revenues will increase \$5,000 (from \$25,000 per year to \$30,000 per year) and costs will increase \$2,000. Management expects to replace the larger oven after 5 years. It will have a sal-vage value of \$4,000. Assume a 40% tax rate and discount rate of 15% and compute the NPV.

### Solution

To compute the NPV we will need to first compute the cash flows that the new pizza oven will generate.

Computing the initial cash flow:

Accumulated depreciation=\$20,000!0.33=\$6,600

The depreciation percentages come from the MACRS table in the appendix to this chapter. Continuing:

Book value=Initial cost-Accumulated depreciation Book value=\$20,000-\$6,600

Book value=\$13,400

and

Tax on sale=(Sales price-Book value)!Tax rate Tax on sale=(\$12,000-\$13,400)!0.40

Tax on sale=\$-1,400!0.40=-\$560 (tax savings from the loss on sale)

We add \$560 in the cash flow estimate because we are reducing our taxes as a result of tak-ing a loss on the sale. Note that the sign is negative in the equation and positive in the table. We are subtracting a negative amount, so the result is a positive cash flow.

Calculation of Initial Cash Flow

-Initial purchase price of new asset –\$30,000 -Installation/shipping cost of new asset –\$6,000

=Net Purchase Price –\$36,000

+Proceeds from the sale of old asset +\$12,000 +/-Tax on sale of old asset (see below) +\$560 +/-Change in net working capital –\$500

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### Computing the Annual Cash Flows

This is an expansion project because a new oven is replacing an old oven. However, we do not need to subtract the old cash flows from the new because the figures given in the problem are already incremental.

Notice that the taxes have a positive sign in years 2000 and 2001, but they are negative in the other years. If the net profit before tax is positive, taxes are owed, so the sign is negative. If the net profit before tax is negative, a loss has occurred that can offset other income, so a tax savings results in a positive sign.

### Computing the Terminal Cash Flow

The first entry in this table is the last entry from the annual cash flow table. We append this figure with the additional cash flows that apply only to the final year. The larger oven is sold for its \$4,000 salvage value. Because it is fully depreciated, the sales amount is fully taxable. The increase in net working capital that was subtracted when we computed the initial cash flow is now added back. The terminal year cash flow is \$4,700.

### Computing NPV

Now that we have computed all of the relevant cash flows, we can compute the net present value:

Because the NPV is negative, Pizzas-by-Mail should keep its old oven.

NPV = \$2,952 1.15 + \$7,0 1.15 + \$3, 1.15 + \$2, 1.15 + \$4, 1.15 – \$ NPV = \$14,098.22 – \$ = \$ 2 3 4 5

1

### ( )

80 400 808 700 23 940 23 940 9 841 78 , , , .

Calculation of Terminal Cash Flow

Net cash flow (year 2003 from solution to annual cash flow table) +\$1,800 +Proceeds from the sale of new asset +\$4,000 +/-Tax on sale of new asset (see below) –\$1,600

+/-Change in net working capital +\$500

=Terminal cash flow +\$4,700

Pizza Oven Analysis

1999 2000 2001 2002 2003

New revenues-Old revenues \$5,000 \$5,000 \$5,000 \$5,000 \$5,000 New expenses-Old expenses \$2,000 \$2,000 \$2,000 \$2,000 \$2,000

Gross profit \$3,000 \$3,000 \$3,000 \$3,000 \$3,000 -(New depr.-Old depr.) \$2,880 \$13,200 \$4,000 \$2,520 0 Net profit before tax \$120 –\$10,200 –\$1,000 \$480 \$3,000 -Taxes (40%) –\$48 +\$4,080 +\$400 –\$192 –\$1,200

Net profit +\$72 –\$6,120 –\$600 +\$288 +\$1,800 +Depreciation \$2,880 \$13,200 \$4,000 \$2,520 0

Net cash flow \$2,952 \$7,080 \$3,400 \$2,808 \$1,800

Students often have trouble with the idea the sign on taxes can be positive. An easy way to be sure you get the sign right is to recog-nize that the signs on net profit before taxes and on taxes will always be oppo-site each other.

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X A M P L E

### Project Selection Through NPV Maximization

Department heads have submitted a number of proposed projects for management approval. Management has determined that only \$5 million can be spent on this year’s capital budget. Which of the projects listed in this table should be accepted?

### Solution

The following steps result in maximizing NPV: 1. Order the projects by PI.

2. Cumulate the NPV and cost.

Project Cost (millions) NPV (millions) PI

A \$1.50 \$0.20 1.13 B 1.50 0.30 1.20 C 2.00 0.10 1.05 D 2.50 0.25 1.10 E 0.75 0.15 1.20 F 0.50 0.10 1.20 Return/Cost (%) Total Investment (\$)

Investment opportunity schedule A

B

C

D

Marginal cost of capital schedule

FIGURE 11.1

Investment Opportunity Schedule

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3. Select projects until all available funds are committed.

4. Verify your choices by substituting alternatives and determining whether NPV increases. This has been done in the following table:

The “Total Cost” column is the cumulative cost of the projects listed. Similarly, the “Total NPV” column is the cumulative NPV of the projects accepted.

Our budget will allow us to accept projects B, E, F, and A. This will provide a total NPV of \$0.75 million. If we were to drop A and add D, we would exceed our budget. If we were to drop A and add C, we would still be within budget but total NPV would drop to \$0.65 million. Our first pass has maximized total NPV and hence shareholder wealth.

### approaches to dealing with this problem: the certainty equivalent method and the

Project Cost Total Cost NPV Total NPV PI

B \$1.50 \$1.50 \$0.30 \$0.30 1.20 E 0.75 2.25 0.15 0.45 1.20 F 0.50 2.75 0.10 0.55 1.20 A 1.50 4.25 0.20 0.75 1.13 D 2.50 6.75 0.25 1.00 1.10 C 2.00 8.75 0.10 1.10 1.05

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X A M P L E

### 11.9

Suppose that you are evaluating a project with a cost of \$1,000 and five annual cash inflows of \$325 each. The return on the market is 13%, the risk-free rate of interest is 6%, and the firm’s beta is 1. The project you are evaluating is very different from those usually undertaken by the firm. Another firm, which is exclusively in the business of doing projects like the one under consideration, has a beta of 2. Should you recommend that the firm accept the project? Assume that the firm is all equity financed.

### Solution

Before we can compute the NPV we need to compute the firm’s required return. We cannot use the firm’s beta because the risk of the project is not consistent with the risk of most

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projects done by the firm. Instead, we use the beta of the surrogate firm to compute the required return:

Ri=Rf+β(Rm-Rf)

Ri=0.06+2(0.13-0.06)

Ri=0.20

Now, using 20% as the discount rate, we can compute the NPV of the project:

NPV=\$325(PVIFA20%,5 yr)-\$1,000

NPV=\$325(2.9906)-\$1,000 NPV=-28.05

Because NPV is less than 0, we reject the project. If the firm’s beta of 1 had been used in the analysis, a positive NPV would have resulted (;\$143.10). In this case, adjusting for risk changed the decision about the project.

X A M P L E

### Chain Approach

Disney built Epcot Center in Florida partly to display the world as it may be in the future. How-ever, a recent editorialist noted that in one supposedly futuristic scene he spotted a rotary dial

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telephone. In 1996, Disney closed part of Epcot to remodel and update the displays. We can only speculate about the options the firm considered before beginning construction. Let us sup-pose that one option involved a \$10 million alteration to the exhibits that would allow quick and efficient updates as new technology became available. The flexibility of this option would postpone future updates for 10 years. The alternative is less costly, but requires a total recon-struction in 5 years. Assume for simplicity that both options initially cost \$10 million. The flex-ible option takes more space, so fewer visitors can be accommodated at one time. As a result, cash inflows are \$2.5 million per year. The alternative has cash inflows of \$3.75 million per year. Which option should Disney choose? Assume a cost of capital of 12%.

### Solution

Begin by computing the NPV for each option, ignoring the difference in lives:

NPVinflex=\$3.750(PVIFA5yr,12%)-\$10=\$3.518 million

NPVflex=\$2.5(PVIFA10 yr,12%)-\$10=\$4.123 million

Because the NPV of the long-term flexible project is greater than that of the short-term inflexible approach, we may be tempted to conclude that the long-term project should be accepted. Let us continue the analysis, however, by assuming that after 5 years the inflexible project will be repeated. The extended project is shown on the following time line:

After 5 years, an additional \$10 million must be invested to continue the cash inflows. We now compute the NPV of this extended project:

NPVinflex=\$3.75(PVIFA10 yr,12%)-\$10(PVIF5 yr,12%)-\$10

NPVinflex=\$21.188-\$5.674-\$10=\$5.514 million

The NPV of the shorter-term project done twice is greater than the NPV of the longer-term pro-ject done once. In this example, because Disney is assured of being able to redo the propro-ject at the end of the first 5 years, it should choose the short option.

### eas-ier in practice than it sounds and is best explained with an example.

3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75

–10 –10

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X A M P L E

### Project Evaluation: EAA

Use the numbers from the solution to Example 11.10 to compute the equal annual annuity (EAA) for each project.

### Solution

Step 1: Compute the NPV for each project. In the last example we found NPVflexto be \$4.123

million and NPVinflexto be \$3.518 million.

Step 2: Find the annuity that has the same present value as the NPV and the same number of periods as the project. The flexible project has a life of 10 years and an NPV of \$4.123 mil-lion. Using the firm’s cost of capital of 12% and the factors approach yields

NPV=EAA(PVIFA10 yr,12%)

\$4.123=EAA(5.6502) EAA=\$4.123/5.6502 EAA=\$0.7297 million

To find the EAA using a financial calculator, enter 4.123 as PV, 10 as N, 12% as I, and 0 as FV and compute PMT.

Review for a moment how this result is interpreted. An NPV of \$4.123 million is the same as having a 10-period annuity of \$0.729 million if the discount rate is 12%. We often convert annuities into present values. What we have done here is convert a present value back into an annuity.

Repeat this step for the other project:

\$3.518=EAA(PVIFA5 yr,12%)

\$3.518=EAA(3.6048) EAA=\$3.518/3.6048 EAA=\$0.9759 million

To find the EAA using a financial calculator, enter 3.518 as PV, 5 as N, 12% as I, and 0 as FV and compute PMT.

Step 3: We now assume that these annuities continue forever because the projects, or sim-ilar projects, could be repeated over and over. To find the value of a perpetuity, divide each annuity by the discount rate:

Projectflex=\$0.7297/0.12=\$6.0808 million

Projectinflex=\$0.9759/0.12=\$8.1325 million

We again find that the shorter-term inflexible project is preferred to the longer-term one.

### errors we have discussed with estimating cash flows are compounded when we assume

Since converting the EAA

to a perpetuity involves dividing both EAAs by the same value, the results are never changed by this step. It is only included to demonstrate that we are now comparing projects of equal (perpetual) length.

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### resound-ing failure, largely because of a design that made the keyboard difficult to use. The small

Many students who graduate with degrees in finance choose to continue their education by taking courses that lead to the Chartered Finan-cial Analyst certification. This certification is

very well respected. The CFA certification is often required by firms that employ people to analyze stocks. For exam-ple, Merrill Lynch employs CFAs to pick stocks that bro-kers will recommend to clients.

The Chartered Financial Analyst (CFA) certification dates back to 1963 when it was originally administered by an Association for Investment Management and Research (AIMR) predecessor. Since that time, the program has experienced great success, and in June 2001 AIMR expects to test as many as 80,000 candidates. The purpose of the CFA program is to act as a supplement to the education and work experience of individuals in the investment fields. The test focuses most strongly on the areas of portfolio management and financial analysis, but it also covers top-ics applicable to a wide range of investment specialists.

The CFA program is broken into three dis-tinct levels, each requiring an estimated 250 hours of individual exam preparation. Exam candidates are allowed to participate in only one exam per year, and the exams must be taken in chronolog-ical order.

The CFA Level I exam is completely multiple choice. Its primary focus is on the methods and theories of invest-ment valuation, portfolio manageinvest-ment, and ethics. The sec-ond exam, CFA Level II, is half essay and half “item-set” questions. Item-set questions are case study investigations with multiple-choice questions. This exam is primarily focused on asset valuation and ethics. The final level (CFA Level III) is structured like the Level II exam and concen-trates on portfolio management, asset allocation, and ethics. More details about the precise content of each exam can be found at the Web site listed below.

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### positive NPVs when sales are estimated to be 450 units. However, project 2 is much more

NPV Sales (\$) 200 400 600 800 –\$150 \$200 NPV of project 1 NPV of project 2 –\$100 0 –\$50 0 \$50 \$100 \$150 1,000 FIGURE 11.2 Sensitivity Analysis

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### Investment Class

Ownership

Year 3-Year 5-Year 7-Year 10-Year

1 33% 20% 14% 10% 2 45 32 25 18 3 15 19 17 14 4 7 12 13 12 5 11 9 9 6 6 9 7 7 9 7 8 4 7 9 7 10 6 _____ _____ _____ _____3 100% 100% 100% 100%

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### MACRS Asset Classes

Type of Asset Life

Manufacturing tools 3-year

Cars, light trucks, computers 5-year Industrial equipment, office furniture 7-year Heavy-duty types of equipment 10-year Residential rental property 27.5-year Nonresidential real property 3-year

The first step in the process of evaluating projects and invest-ment opportunities is to compute the cash flows that will be generated. The initial cash flow is the amount spent (net of salvage, net working capital, and taxes) on initiating the pro-ject. All shipping and installation costs are included. If an old machine is being replaced, the funds received from its sale can be used to offset a portion of the initial purchase price. If there is a tax gain or loss from the sale of the old asset, this also must be included in the analysis.

Once the initial cash flow has been computed, the annual cash flows are determined. These are found using a typical income statement format that adds noncash charges (depreciation) back at the end. The annual cash flows are best computed using an electronic spreadsheet so sensitivity analy-sis can be conducted on the results.

The terminal cash flow is computed for the final year of the project. It differs from the annual cash flow in that there may be salvage of the equipment used in the project or recap-ture of net working capital. Once all of the cash flows have been found, they can be put on a time line and analyzed using the capital budgeting techniques learned in Chapter 10.

Many firms face capital rationing. Capital rationing refers to limiting the number of projects that are accepted for one reason or another. Under capital rationing the firm selects the projects that will maximize its shareholders’ wealth. Share-holder wealth is maximized by accepting the group of projects that has the largest combined NPV possible. One way to sim-plify this is to first rank projects by their profitability index.

Accept those with the highest PI first and work down until the entire capital budget has been spent. There are times when this method does not yield the best possible selection of projects. Therefore, always check by substituting alternative projects to make sure some other mix is not marginally better.

Not all projects a firm evaluates have the same risk as the usual projects and investments in a firm’s portfolio. When this occurs, there are two ways to adjust the evaluation. First, the cash flows can be reduced to a level you are certain can be achieved and the risk-free rate of interest can be used as the discount rate. Alternatively, the discount rate can be increased to compensate for the increased risk. The beta of a surrogate firm that is primarily in the business of doing projects such as the one under consideration can be used to compute a new required return. This new required return can then be used to evaluate the cash flows.

A final adjustment to capital budgeting analysis is required for ranking projects with very different lives. A longer-term project has a longer period of time to accumulate earnings, so naturally it has a larger NPV than an equivalent, shorter-term project. To evaluate two projects with very dif-ferent lives, use either the replacement chain approach or the equal annual annuity approach. The replacement chain approach requires you to string together multiple cash flows until both projects are of equal length. The equal annual annuity approach requires you to find the annuity that has a value equivalent to the NPV. The sizes of the annual annuity payments are then compared.

References

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