Comparative Analysis

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Capital Budgeting Decisions

LEARNING OBJECTIVES After studying Chapter 13, you should be able to: LO13-1 Determine the payback period for an

investment. LO13-2 Evaluate the acceptability of an

investment project using the net present value method.

LO13-3 Evaluate the acceptability of an investment project using the internal rate of return method.

LO13-4 Evaluate an investment project that has uncertain cash flows.

LO13-5 Rank investment projects in order of preference.

LO13-6 Compute the simple rate of return for an investment.

LO13-7 (Appendix 13A) Understand present value concepts and the use of present value tables.

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M

LO13-8 (Appendix 13C) Include income taxes in a net present value analysis.

Commercial Delivery Fleets Adopt Electric Trucks

Staples, Frito-Lay, and AT&T have begun purchasing electric delivery trucks even though they cost $30,000 more than diesel delivery trucks. Staples is willing to make the more expensive up-front investment because it expects each electric truck to incur lower operating costs. For example, it estimates that electric trucks will save $2,450 per year in maintenance costs and $6,500 per year in fuel costs. It also expects to replace each electric truck’s brakes every four or five years instead of every one or two years with diesel trucks. In total, Staples expects each electric delivery truck to save $60,000 over its 10-year useful life. Source: Mike Ramsey, “As Electric Vehicles Arrive, Firms See Payback in Trucks,” The Wall Street Journal, December 8, 2010, pp. B1–B2.

anagers often consider decisions that involve an investment today in the hope of realizing future profits. For example, Yum! Brands, Inc., makes an investment when it opens a new Pizza Hut restaurant. L. L. Bean makes an investment when it installs a new computer to handle customer billing. Ford makes an investment when it redesigns a

vehicle such as the F-150 pickup truck. Merck & Co. invests in medical research. Amazon.com makes an investment when it redesigns its website. All of these investments require spending now with the expectation of additional future net cash inflows.

The term capital budgeting is used to describe how managers plan significant investments in projects that have long-term implications such as the purchase of new equipment or the introduction of new products. Most companies have many more potential projects than can actually be funded. Hence, managers must carefully select those projects that promise the greatest future return. How well managers make these capital budgeting decisions is a critical factor in the long-run financial

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health of the organization. This chapter discusses four methods for making capital budgeting decisions—the payback method, the net present value method, the internal rate of return method, and the simple rate of return method.

Capital Budgeting—An Overview Typical Capital Budgeting Decisions Any decision that involves a cash outlay now in order to obtain a future return is a capital budgeting decision. Typical capital budgeting decisions include:

1. Cost reduction decisions. Should new equipment be purchased to reduce costs? 2. Expansion decisions. Should a new plant, warehouse, or other facility be acquired to increase

capacity and sales? 3. Equipment selection decisions. Which of several available machines should be purchased? 4. Lease or buy decisions. Should new equipment be leased or purchased? 5. Equipment replacement decisions. Should old equipment be replaced now or later? Capital budgeting decisions fall into two broad categories—screening decisions and preference

decisions. Screening decisions relate to whether a proposed project is acceptable—whether it passes a preset hurdle. For example, a company may have a policy of accepting projects only if they provide a return of at least 20% on the investment. The required rate of return is the minimum rate of return a project must yield to be acceptable. Preference decisions, by contrast, relate to selecting from among several acceptable alternatives. To illustrate, a company may be considering several different machines to replace an existing machine on the assembly line. The choice of which machine to purchase is a preference decision. Cash Flows versus Net Operating Income The first three capital budgeting methods discussed in the chapter—the payback method, the net present value method, and internal rate of return method—all focus on analyzing the cash flows associated with capital investment projects, whereas the simple rate of return method focuses on incremental net operating income. To better prepare you to apply the payback, net present value, and internal rate of return methods, we’d like to define the most common types of cash outflows and cash inflows that accompany capital investment projects. Typical Cash Outflows Most projects have at least three types of cash outflows. First, they often require an immediate cash outflow in the form of an initial investment in equipment, other assets, and installation costs. Any salvage value realized from the sale of old equipment can be recognized as a reduction in the initial investment or as a cash inflow. Second, some projects require a company to expand its working capital.

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Working capital is current assets (e.g., cash, accounts receivable, and inventory) less current liabilities. When a company takes on a new project, the balances in the current asset accounts often increase. For example, opening a new Nordstrom’s department store requires additional cash in sales registers and more inventory. These additional working capital needs are treated as part of the initial investment in a project. Third, many projects require periodic outlays for r%pairs and ma intenance and additional operating costs. Typical Cash Inflows Most projects also have at least three types of cash inflows. First, a project will normally increase revenues or reduce costs. Either way, the amount involved should be treated as a cash inflow for capital budgeting purposes. Notice that from a cash flow standpoint, a reduction in costs is equivalent to an increase in revenues. Second, cash inflows are also frequently realized from selli. g equipment for its salvage value when a project ends, although the company may actually have to pay to dispose of some low-value or hazardous items. Third, any working capital that was tied up in the project can be released for use elsewhere at the end of the project and should be treated as a cash inflow at that time. Working capital is released, for example, when a company sells off its inventory or collects its accounts receivable. The Time Value of Money Beyond defining a capital project’s cash outflows and inflows, it is also important to consider when those cash flows occur. For example, if someone offered to give you $1,000 dollars today that you could save toward your eventual retirement or $1,000 dollars a year from now that you could save toward your future retirement, which alternative would you choose? In all likelihood, you would choose to receive $1,000 today because you could invest it and have more than $1,000 dollars a year from now. This simple example illustrates an important capital budgeting concept known as the time value of money. The time value of money recognizes that a dollar today is worth more than a dollar a year from now if for no other reason than you could put the dollar in a bank today and have more than a dollar a year from now. Because of the time value of money, capital investments that promise earlier cash flows are preferable to those that promise later cash flows.

Although the payback method focuses on cash flows, it does not recognize the time value of money. In other words, it treats a dollar received today as being of equal value to a dollar received at any point in the future. Conversely, the net present value and internal rate of return methods not only focus on cash flows, but they also recognize the time value of those cash flows. These two methods use a technique called discounting cash flows to translate the value of future cash flows to their lesser present value. If you are not familiar with the concept of discounting cash flows and the use of present value tables, you should read Appendix 13A: The Concept of Present Value, at the end of the chapter, before studying the net present value and internal rate of return methods.

IN BUSINESS INVESTING IN A VINEYARD: A CASH FLOWS PERSPECTIVE

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When Michael Evans was contemplating moving to Buenos Aires, Argentina, to start a company called the Vines of Mendoza, he had to estimate the project’s initial cash outlays and compare them to its future net cash inflows. The initial cash outlays included $2.9 million to buy 1,046 acres of land and to construct a tasting room, $300,000 for a well and irrigation system, $30,000 for underground power lines, and $285,000 for 250,000 grape plants. The annual operating costs included $1,500 per acre for pruning, mowing, and irrigation and $114 per acre for harvesting.

In terms of future cash inflows, Evans hopes to sell his acreage to buyers who want to grow their own grapes and make their own wine while avoiding the work involved with doing so. He intends to charge buyers a one- time fee of $55,000 per planted acre. The buyers would also reimburse Evans for his annual operating costs per acre plus a 25% markup. In a good year, buyers should be able to get 250 cases of wine from their acre of grapevines. Source: Helen Coster, “Planting Roots,” Forbes, March 1, 2010, pp. 42–44.

The Payback Method LO13-1 Determine the payback period for an investment.

The payback method of evaluating capital budgeting projects focuses on the payback period. The payback period is the length of time that it takes for a project to recover its initial cost from the net cash inflows that it generates. This period is sometimes referred to as “the time that it takes for an investment to pay for itself.” The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment.

The payback period is expressed in years. When the annual net cash inflow is the same every year, the following formula can be used to compute the payback period:

To illustrate the payback method, consider the following data:

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Example A: York Company needs a new milling machine. The company is considering two machines: machine A and machine B. Machine A costs $15,000, has a useful life of ten years, and will reduce operating costs by $5,000 per year. Machine B costs only $12,000, will also reduce operating costs by $5,000 per year, but has a useful life of only five years. Required: Which machine should be purchased according to the payback method?

According to the payback calculations, York Company should purchase machine B because it has a shorter payback period than machine A. Evaluation of the Payback Method The payback method is not a true measure of the profitability of an investment. Rather, it simply tells a manager how many years are required to recover the original investment. Unfortunately, a shorter payback period does not always mean that one investment is more desirable than another.

To illustrate, refer back to Example A on the previous page. Machine B has a shorter payback period than machine A, but it has a useful life of only 5 years rather than 10 years for machine A. Machine B would have to be purchased twice—once immediately and then again after the fifth year—to provide the same service as just one machine A. Under these circumstances, machine A would probably be a better investment than machine B, even though machine B has a shorter payback period. Unfortunately, the payback method ignores all cash flows that occur after the payback period.

A further criticism of the payback method is that it does not consider the time value of money. A cash inflow to be received several years in the future is weighed the same as a cash inflow received right now. To illustrate, assume that for an investment of $8,000 you can purchase either of the two following streams of cash inflows:

Which stream of cash inflows would you prefer to receive in return for your $8,000 investment? Each stream has a payback period of 4.0 years. Therefore, if payback alone is used to make the decision, the streams would be considered equally desirable. However, from a time value of money perspective, stream 2 is much more desirable than stream 1.

On the other hand, under certain conditions the payback method can be very useful. For one thing, it can help identify which investment proposals are in the “ballpark.” That is, it can be used as

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a screening tool to help answer the question, “Should I consider this proposal further?” If a proposal doesn’t provide a payback within some specified period, then there may be no need to consider it further. In addition, the payback period is often important to new companies that are “cash poor.” When a company is cash poor, a project with a short payback period but a low rate of return might be preferred over another project with a high rate of return but a long payback period. The reason is that the company may simply need a faster return of its cash investment. And final,y, the payback method is sometimes used in industries where products become obsolete very rapidly—such as consumer electronics. Because products may last only a year or two, the payback period on investments must be very short.

IN BUSINESS THE ECONOMICS OF HYBRID VEHICLES The table below shows the price premiums (after tax credits) that customers must pay to buy four types of hybrid vehicles. It also depicts the annual gas savings that customers realize by driving a hybrid version of the vehicle instead of a standard model of the same vehicle (assuming the vehicles are driven 15,000 miles per year and gas costs $2.79 a gallon). Dividing the price premium by the annual gas savings yields the payback period when purchasing the hybrid version of the vehicle.

The above payback figures highlight the dilemma faced by customers who want to make environmentally friendly purchases, but are constrained by limited financial resources. Source: Mike Spector, “The Economics of Hybrids,” The Wall Street Journal, October 29, 2007, pp. R5–R6.

An Extended Example of Payback As shown by formula (1) on page 586, the payback period is computed by dividing the investment in a project by the project’s annual net cash inflows. If new equipment is replacing old equipment, then any salvage value to be received when disposing of the old equipment should be deducted from the cost of the new equipment, and only the incremental investment should be used in the payback computation. In addition, any depreciation deducted in arriving at the project’s net operating income must be added back to obtain the project’s expected annual net cash inflow. To illustrate, consider the following data:

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Example B: Goodtime Fun Centers, Inc., operates amusement parks. Some of the vending machines in one of its parks provide very little revenue, so the company is considering removing the machines and installing equipment to dispense soft ice cream. The equipment would cost $80,000 and have an eight-year useful life with no salvage value. Incremental annual revenues and costs associated with the sale of ice cream would be as follows:

The vending machines can be sold for a $5,000 scrap value. The company will not purchase equipment unless it has a payback period of three years or less. Does the ice cream dispenser pass this hurdle?

Exhibit 13-1 computes the payback period for the ice cream dispenser. Several things should be noted. First, depreciation is added back to net operating income to obtain the annual net cash inflow from the new equipment. Depreciation is not a cash outlay; thus, it must be added back to adjust net operating income to a cash basis. Second, the payback computation deducts the salvage value of the old machines from the cost of the new equipment so that only the incremental investment is used in computing the payback period.

Because the proposed equipment has a payback period of less than three years, the company’s payback requirement has been met. Payback and Uneven Cash Flows When the cash flows associated with an investment project change from year to year, the simple payback formula that we outlined earlier cannot be used. Instead, the payoff period can be computed as follows (assuming that cash inflows occur evenly throughout the year): Payback period = Number of years up to the year in which the investment is paid off + (Unrecovered investment at the beginning of the year in which the investment is paid off ÷ Cash inflow in the period in which the investment is paid off). To illustrate how to apply this formula, consider the following data:

EXHIBIT 13-1 Computation of the Payback Period

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What is the payback period on this investment? The answer is 5.5 years, computed as follows: 5 + ($1,500 ÷ $3,000) = 5.5 years. In essence, we are tracking the unrecovered investment year by year as shown in Exhibit 13-2. By the middle of the sixth year, sufficient cash inflows will have been realized to recover the entire investment of $6,000 ($4,000 + $2,000).

EXHIBIT 13-2 Payback and Uneven Cash Flows

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The Net Present Value Method LO13-2 Evaluate the acceptability of an investment project using the net present value method.

As previously mentioned, the net present value method and the internal rate of return method use discounted cash flows to analyze capital budgeting decisions. The net present value method is discussed in this section followed by a discussion of the internal rate of return method. The Net Present Value Method Illustrated The net present value method compares the present value of a project’s cash inflows to the present value of its cash outflows. The difference between the present value of these cash flows, called the net present value, determines whether or not a project is an acceptable investment.

When performing net present value analysis, managers usually make two important assumptions. First, they assume that all cash flows other than the initial investment occur at the end of periods. This assumption is somewhat unrealistic because cash flows typically occur throughout a period rather than just at its end; however, it simplifies the computations considerably. Second, managers assume that all cash flows generated by an investment project are immediately reinvested at a rate of return equal to the rate used to

discount the future cash flows, also known as the discount rate. If this condition is not met, the net present value computations will not be accurate.

To illustrate net present analysis, consider the following data:

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Example C: Harper Company is contemplating the purchase of a machine capable of performing some operations that are now performed manually. The machine will cost $50,000, and it will last for five years. At the end of the five-year period, the machine will be sold for its salvage value of $5,000. Use of the machine will reduce labor costs by $18,000 per year. Harper Company requires a minimum pretax return of 18% on all investment projects.1

Should the machine be purchased? Harper Company must determine whether a cash investment now of $50,000 can be justified if it will result in an $18,000 reduction in cost in each of the next five years. It may appear that the answer is obvious because the total cost savings is $90,000 ($18,000 per year × 5 years). However, the company can earn an 18% return by investing its money elsewhere. It is not enough that the cost reductions cover just the original cost of the machine; they must also yield a return of at least 18% or the company would be better off investing the money elsewhere.

To determine whether the investment is desirable, the stream of annual $18,000 cost savings and the machine’s salvage value of $5,000 should be discounted to their present values and then compared to the cost of the new machine. Exhibit 13-3 demonstrates a four-step approach for performing these computations. First, it calculates the present value of the initial investment by multiplying $50,000 by 1.000, the present value factor for any cash flow that occurs immediately. Second, it calculates the present value of the annual cost savings by multiplying $18,000 by 3.127, the present value factor of a five-year annuity at the discount rate of 18%, to obtain $56,286. Third, it calculates the present value of the machine’s salvage value by multiplying $5,000 by 0.437, the present value factor of a single sum to be received in five years at the discount rate of 18%, to obtain $2,185. Finally, cells B8 through D8 are added together to derive the net present value of $8,471.2

Exhibit 13-4 demonstrates an alternative approach for performing these same calculations. This alternative approach also begins by calculating the present value of the initial investment by multiplying $50,000 by 1.000, the present value factor for any cash flow that occurs immediately. However, rather than calculating the present value of the annual cost savings using a discount factor of 3.127 from Exhibit 13B-2, it discounts the annual cost savings in Years 1–5 and the machine’s salvage value in Year 5 to their present values using the discount factors from Exhibit 13B-1. For example, the $18,000 cost savings in Year 3 is multiplied by the discount factor of 0.609 to derive this future cash flow’s present value of $10,962. As another example, the $23,000 of total cash flows in Year 5 is multiplied by the discount factor of 0.437 to determine these future cash flows’ present value of $10,051. The present values in cells B8 through G8 are then added together to compute the project’s net present value of $8,471.

EXHIBIT 13-3 Net Present Value Analysis Using Discount Factors from Exhibits 13B-1 and 13B-2 in Appendix 13B

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EXHIBIT 13-4 Net Present Value Analysis Using Discount Factors from Exhibit 13B-1 in Appendix 13B

The methods described in Exhibits 13-3 and 13-4 are mathematically equivalent—they both produced a net present value of $8,471. The only difference between these two exhibits relates to the discounting of the annual labor cost savings. In Exhibit 13-3, the labor cost savings are discounted to their present value using the annuity factor of 3.127, whereas in Exhibit 13-4, these cost savings are discounted using five separate factors that sum to 3.127 (0.847 + 0.718 + 0.609 + 0.516 + 0.437 = 3.127). In other words, the calculations are equivalent.

While you should feel free to use either of these methods when performing net present value calculations, from this point forward we’ll be emphasizing the approach used in Exhibit 13-4 for two reasons. First, most managers use an approach similar to Exhibit 13-4 when performing net present value calculations. They use Microsoft Excel to summarize each year’s cash flows in a separate column and then they discount each year’s cash flows to their present values using the factors shown in Exhibit 13B-1. Second, many students believe that the approach shown in Exhibit 13-4 is easier to understand than competing methods when the net present value computations become increasingly complex.

Once you have computed a net present value using either of the approaches that we just demonstrated, you’ll need to interpret your findings. For example, because Harper Company’s proposed project has a positive net present value of $8,471, it implies that the company should purchase the new machine. A positive net present value indicates that the project’s return exceeds the discount rate. A negative net present value indicates that the project’s return is less than the discount rate. Therefore, if the company’s minimum required rate of return is used as the discount rate, a project with a positive net present value has a return that exceeds the minimum required rate of return and is acceptable. Conversely, a project with a negative net present value has a return that is less than the minimum required rate of return and is unacceptable. In sum:

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To improve your understanding of the minimum required rate of return, it bears emphasizing that a company’s cost of capital is usually regarded as its minimum required rate of return. The cost of capital is the average rate of return that the company must pay to its long-term creditors and its shareholders for the use of their funds. If a project’s rate of return is less than the cost of capital, the company does not earn enough to compensate its creditors and shareholders. Therefore, any project with a rate of return less than the cost of capital should be rejected.

The cost of capital serves as a screening device. When the cost of capital is used as the discount rate in net present value analysis, any project with a negative net present value does not cover the company’s cost of capital and should be discarded as unacceptable. Recovery of the Original Investment The net present value method automatically provides for return of the original investment. Whenever the net present value of a project is positive, the project will recover the original cost of the investment plus sufficient excess cash inflows to compensate the organization for tying up funds in the project. To demonstrate this point, consider the following situation:

Example D: Carver Hospital is considering the purchase of an attachment for its X-ray machine that will cost $3,169. The attachment will be usable for four years, after which time it will have no salvage value. It will increase net cash inflows by $1,000 per year in the X-ray department. The hospital’s board of directors requires a rate of return of at least 10% on such investments.

A net present value analysis of the desirability of purchasing the X-ray attachment is presented in Exhibit 13-5. Notice that the attachment has exactly a 10% return on the original investment because the net present value is zero at a 10% discount rate.

Each annual $1,000 cash inflow arising from use of the attachment is made up of two parts. One part represents a recovery of a portion of the original $3,169 paid for the attachment, and the other part represents a return on this investment. The breakdown of each year’s $1,000 cash inflow between recovery of investment and return on investment is shown in Exhibit 13-6.

The first year’s $1,000 cash inflow consists of a return on investment of $317 (a 10% return on the $3,169 original investment), plus a $683 return of that investment. Because the amount of the

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unrecovered investment decreases each year, the dollar amount of the return on investment also decreases each year. By the end of the fourth year, all $3,169 of the original investment has been recovered.

EXHIBIT 13-5 Carver Hospital—Net Present Value Analysis of X-Ray Attachment

EXHIBIT 13-6 Carver Hospital—Breakdown of Annual Cash Inflows

IN BUSINESS COOLING SERVERS NATURALLY

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Google consumes more than 2 terawatt hours of electricity per year, which is greater than the annual electricity consumption of 200,000 American homes. A large part of Google’s electricity consumption relates to running and cooling its huge number of servers. In an effort to lower its electricity bill, Google invested €200 million to build a server storage facility in the Baltic Sea coastal community of Hamina, Finland. Hamina’s low electricity rates coupled with its persistently low ambient air temperatures will lower Google’s annual electricity bills considerably. Shortly after Google’s facility opened in Hamina, Facebook opened a five-acre data center in Luleå, Sweden, where the average temperature is 35 degrees Fahrenheit. Source: Sven Grunberg and Niclas Rolander, “For Data Center, Google Goes for the Cold,” The Wall Street Journal, September 12, 2011, p. B10.

An Extended Example of the Net Present Value Method Example E provides an extended example of how the net present value method is used to analyze a proposed project. This example helps tie together and reinforce many of the ideas discussed thus far.

Example E: Under a special licensing arrangement, Swinyard Corporation has an opportunity to market a new product for a five-year period. The product would be purchased from the manufacturer, with Swinyard responsible for promotion and distribution costs. The licensing arrangement could be renewed at the end of the five-year period. After careful study, Swinyard estimated the following costs and revenues for the new product:

At the end of the five-year period, if Swinyard decides not to renew the licensing arrangement the working capital would be released for investment elsewhere. Swinyard uses a 14% discount rate. Would you recommend that the new product be introduced?

EXHIBIT 13-7 The Net Present Value Method—An Extended Example

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This example involves a variety of cash inflows and cash outflows. The solution is given in Exhibit 13-7.

Notice how the working capital is handled in this exhibit. It is counted as a cash outflow at the beginning of the project and as a cash inflow when it is released at the end of the project. Also notice how the sales revenues, cost of goods sold, and out-of-pocket costs are handled. Out-of-pocket costs are actual cash outlays for salaries, advertising, and other operating expenses.

Because the net present value of the proposal is positive, the new product is acceptable.

IN BUSINESS ECONOMIC WOES SHRINK CAPITAL BUDGETS When the health of the economy is uncertain, capital spending declines. Rite Aid CEO Mary Sammons cut her company’s capital budget by $50 million due to uncertain economic conditions. PetroHawk Energy responded to a weak economy by slashing its $1.5 billion capital budget by one-third. Estee Lauder tightened its belt by challenging managers to defend what they must have and define what they can give up. YUMa Brands (owner of Pizza Hut, KFC, and Taco Bell) navigated the difficult economy by abandoning projects that “might come true” in favor of a “must have” capital budgeting mentality. Source: Matthew Boyle, “The Budget Knives Come Out,” BusinessWeek, October 13, 2008, p. 30.

The Internal Rate of Return Method LO13-3 Evaluate the acceptability of an investment project using the internal rate of return method.

The internal rate of return is the rate of return of an investment project over its useful life. The internal rate of return is computed by finding the discount rate that equates the present value of a project’s cash outflows with the present value of its cash inflows. In other words, the internal rate of return is the discount rate that results in a net present value of zero.

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The Internal Rate of Return Method Illustrated To illustrate the internal rate of return method, consider the following data:

Example F: Glendale School District is considering the purchase of a large tractor-pulled lawn mower. At present, the lawn is mowed using a small hand-pushed gas mower. The large, tractor-pulled mower will cost $21,630 and will have a useful life of 5 years. It will have a negligible scrap value, which can be ignored. The tractor-pulled mower would do the job faster than the old mower, resulting in labor savings of $6,000 per year.

To compute the internal rate of return of the new mower, we must find the discount rate that will result in a zero net present value. How do we do this? The simplest and most direct approach when the net cash inflow is the same every year is to divide the investment in the project by the expected annual net cash inflow. This computation yields a factor from which the internal rate of return can be determined. The formula is as follows:

The factor derived from formula (2) is then located in the present value tables to see what rate of return it represents. Using formula (2) and the data for the Glendale School District’s proposed project, we get:

Thus, the discount factor that will equate a series of $6,000 cash inflows with a present investment of $21,630 is 3.605. Now we need to find this factor in Exhibit 13B-2 in Appendix 13B to see what rate of return it represents. We should use the 5-period line in Exhibit 13B-2 because the cash flows for the project continue for 5 years. If we scan along the 5-period line, we find that a factor of 3.605 represents a 12% rate of return. Therefore, the internal rate of return of the mower project is 12%. We can verify this by computing the project’s net present value using a 12% discount rate as shown in Exhibit 13-8.

Notice that the net present value in Exhibit 13-8 is zero, confirming that the project’s internal rate of return equals 12%. However, you’ll also notice that the discount factors used in Exhibit 13-8 come from Exhibit 13B-1 in Appendix 13B, whereas the discount factor cited above (3.605) comes from Exhibit 13B-2 in Appendix 13B. Although these approaches to discounting cash flows appear to differ from one another, they are actually mathematically equivalent. To prove this fact, notice that the sum of the discount factors used in Exhibit 13-8 equals 3.605 (0.893 + 0.797 + 0.712 + 0.636 + 0.567 = 3.605). The five discount factors in Exhibit 13-8 are being used to discount five annual cash flows of $6,000 per year to their present value of $21,630, whereas the discount factor of 3.605 discounts the entire five-year annuity stream to its present value of $21,630.

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Once the Glendale School District computes the project’s internal rate of return of 12%, it would accept or reject the project by comparing this percentage to the school district’s minimum required rate of return. If the internal rate of return is equal to or greater than the required rate of return, then the project is acceptable. If the internal rate of return is less than the required rate of return, then the project is rejected. For example, if we assume that Glendale’s minimum required rate of return is 15%, then the school district would reject this project because the 12% internal rate of return does not clear the 15% hurdle rate.

EXHIBIT 13-8 Evaluation of the Mower Using a 12% Discount Rate

Comparison of the Net Present Value and Internal Rate of Return Methods This section compares the net present value and internal rate of return methods in three ways. First, both methods use the cost of capital to screen out undesirable investment projects. When the internal rate of return method is used, the cost of capital is used as the hurdle rate that a project must clear for acceptance. If the internal rate of return of a project is not high enough to clear the cost of capital hurdle, then the project is ordinarily rejected. When the net present value method is used, the cost of capital is the discount rate used to compute the net present value of a proposed project. Any project yielding a negative net present value is rejected unless other factors are significant enough to warrant its acceptance.

Second, the net present value method is often simpler to use than the internal rate of return method, particularly when a project does not have identical cash flows every year. For example, if a project has some salvage value at the end of its life in addition to its annual cash inflows, the internal rate of return method requires a trial-and-error process to find the rate of return that will result in a net present value of zero. While computer software can be used to perform this trial-and-error process in seconds, it is still a little more complex than using spreadsheet software to perform net present value analysis.

Third, the internal rate of return method makes a questionable assumption. Both methods assume that cash flows generated by a project during its useful life are immediately reinvested elsewhere. However, the two methods make different assumptions concerning the rate of return that is earned on

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those cash flows. The net present value method assumes the rate of return is the discount rate, whereas the internal rate of return method assumes the rate of return earned on cash flows is the internal rate of return on the project. Specifically, if the internal rate of return of the project is high, this assumption may not be realistic. It is generally more realistic to assume that cash inflows can be reinvested at a rate of return equal to the discount rate—particularly if the discount rate is the company’s cost of capital or an opportunity rate of return. For example, if the discount rate is the company’s cost of capital, this rate of return can be actually realized by paying off the company’s creditors and buying back the company’s stock with cash flows from the project. In short, when the net present value method and the internal rate of return method do not agree concerning the attractiveness of a project, it is best to go with the net present value method. Of the two methods, it makes the more realistic assumption about the rate of return that can be earned on cash flows from the project.

Expanding the Net Present Value Method So far, all of our examples have involved an evaluation of a single investment project. In the following section we use the total-cost approach to explain how the net present value method can be used to evaluate two alternative projects.

The total-cost approach is the most flexible method for comparing competing projects. To illustrate the mechanics of the approach, consider the following data:

Example G: Harper Ferry Company operates a high-speed passenger ferry service across the Mississippi River. One of its ferryboats is in poor condition. This ferry can be renovated at an immediate cost of $200,000. Further repairs and an overhaul of the motor will be needed three years from now at a cost of $80,000. In all, the ferry will be usable for 5 years if this work is done. At the end of 5 years, the ferry will have to be scrapped at a salvage value of $60,000. The scrap value of the ferry right now is $70,000. It will cost $300,000 each year to operate the ferry, and revenues will total $400,000 annually.

EXHIBIT 13-9 The Total-Cost Approach to Project Selection

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As an alternative, Harper Ferry Company can purchase a new ferryboat at a cost of $360,000. The new ferry will have a life of 5 years, but it will require some repairs costing $30,000 at the end of 3 years. At the end of 5 years, the ferry will have a scrap value of $60,000. It will cost $210,000 each year to operate the ferry, and revenues will total $400,000 annually.

Harper Ferry Company requires a return of at least 14% on all investment projects. Should the company purchase the new ferry or renovate the old ferry? Exhibit 13-9 shows the

solution using the total-cost approach. Two points should be noted from the exhibit. First, all cash inflows and all cash outflows are

included in the solution under each alternative. No effort has been made to isolate those cash flows that are relevant to the decision and those that are not relevant. The inclusion of all cash flows associated with each alternative gives the approach its name—the total-cost approach.

Second, notice that a net present value is computed for each alternative. This is a strength of the total-cost approach because an unlimited number of alternatives can be compared side by side to determine the best option. For example, another alternative for Harper Ferry Company would be to get out of the ferry business entirely. If management desired, the net present value of this alternative could be computed to compare with the alternatives shown in Exhibit 13-9. Still other alternatives might be available to the company. In the case at hand, given only two alternatives, the data indicate that the net present value in favor of buying the new ferry is $252,630.3

Least-Cost Decisions

Some decisions do not involve any revenues. For example, a company may be trying to decide whether to buy or lease an executive jet. The choice would be made on the basis of which alternative—buying or leasing—would be least costly. In situations such as these, where no revenues are involved, the most desirable alternative is the one with the least total cost from a present value

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perspective. Hence, these are known as least-cost decisions. To illustrate a least-cost decision, consider the following data:

IN BUSINESS HOME CONSTRUCTION GOES GREEN—OR DOES IT?

Many homebuyers like the idea of building environmentally friendly homes until they get the bill. Specpan, an Indianapolis research firm, estimates a “green” home costs 10%–19% more than a comparable conventional home. For example, installing solar-electric glass-faced tiles on a roof costs $15,000 per 100 square feet compared to $1,200 per 100 square feet for standard fiber-cement tiles. Environmentally friendly interior paint costs $35–$42 per gallon compared to $20–$32 per gallon for standard latex paint. To further complicate this least-cost decision, the average homeowner lives in a house only seven years before moving. Within this time frame, many green investments appear to be financially unattractive. Nonetheless, the American Institute of Architects reports that 63% of their clients expressed an interest in renewable flooring materials such as cork and bamboo, up from 53% a year earlier. Source: June Fletcher, “The Price of Going Green,” The Wall Street Journal, February 29, 2008, p. W8.

Example H: Val-Tek Company is considering replacing an old threading machine with a new threading machine that would substantially reduce annual operating costs. Selected data relating to the old and new machines are presented below:

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Val-Tek Company uses a 10% discount rate. Exhibit 13-10 analyzes the alternatives using the total-cost approach. Because this is a least-cost

decision, the present values are negative for both alternatives. However, the present value of the alternative of buying the new machine is $109,440 higher than the other alternative. Therefore, buying the new machine is the less costly alternative.

EXHIBIT 13-10 Least-Cost Decision: A Net Present Value Analysis

Uncertain Cash Flows LO13-4 Evaluate an investment project that has uncertain cash flows.

Thus far, we have assumed that all future cash flows are known with certainty. However, future cash flows are often uncertain or difficult to estimate. A number of techniques are available for handling this complication. Some of these techniques are quite technical—involving computer simulations or advanced mathematical skills—and are beyond the scope of this book. However, we can provide some very useful information to without getting too technical. An Example

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As an example of difficult-to-estimate future cash flows, consider the case of investments in automated equipment. The up-front costs of automated equipment and the tangible benefits, such as reductions in operating costs and waste, tend to be relatively easy to estimate. However, the intangible benefits, such as greater reliability, greater speed, and higher quality, are more difficult to quantify in terms of future cash flows. These intangible benefits certainly impact future cash flows—particularly in terms of increased sales and perhaps higher selling prices—but the cash flow effects are difficult to estimate. What can be done?

A fairly simple procedure can be followed when the intangible benefits are likely to be significant. Suppose, for example, that a company with a 12% discount rate is considering purchasing automated equipment that would have a 10-year useful life. Also suppose that a discounted cash flow analysis of just the tangible costs and benefits shows a negative net present value of $226,000. Clearly, if the intangible benefits are large enough, they could turn this negative net present value into a positive net present value. In this case, the amount of additional cash flow per year from the intangible benefits that would be needed to make the project financially attractive can be computed as follows:

Thus, if the intangible benefits of the automated equipment are worth at least $40,000 a year to the company, then the automated equipment should be purchased. If, in the judgment of management, these intangible benefits are not worth $40,000 a year, then the automated equipment should not be purchased.

This technique can be used in other situations in which future cash flows are difficult to estimate. For example, this technique can be used when the salvage value is difficult to estimate. To illustrate, suppose that all of the cash flows from an inve