Chapter 26 Capital Investment Decisions

Chapter 26 Capital Investment Decisions
© 2016 Pearson Education, Inc.

Learning Objectives Describe the importance of capital investments and the capital budgeting process Use the payback and the accounting rate of return methods to make capital investment decisions © 2016 Pearson Education, Inc.

Learning Objectives Use the time value of money to compute the present values of lump sums and annuities Use discounted cash flow methods to make capital investment decisions © 2016 Pearson Education, Inc.

What Is Capital Budgeting?
Capital asset: An operational asset used for a long period of time. Capital investment: The acquisition of a capital asset. Capital budgeting: The process of planning to invest in long-term assets in a way that returns the most profitability to the company. The focus of this chapter is on how companies make capital investment decisions. The process of making capital investment decisions is often referred to as capital budgeting, which is planning for investments in long-term assets in a way that returns the most profitability to the company. Capital budgeting is critical to the business because these investments affect operations for many years and usually require large sums of cash. Previously, when you learned how to complete the master budget, we discussed the budgeting objectives: to develop strategy, plan, act, and control. The same objectives apply to capital budgeting, but the planning process is more involved due to the long-term nature of the assets. Exhibit 26-1 illustrates the capital budgeting process. © 2016 Pearson Education, Inc.

The Capital Budgeting Process
The first step in the capital budgeting process is to develop strategies. These are the long-term goals of the business, such as expanding international operations or being a value leader in one market while diversifying into other markets. This step is the same for short-term, intermediate, and long-term budgeting. After companies develop strategies, the next steps are to plan and budget for specific actions to achieve those goals. The second step in the capital budgeting process is the planning process, which has three substeps. The first is to identify potential capital investments—for example, new technology and equipment that may make the company more efficient, competitive, and/or profitable. After identifying potential capital investments, the second substep is to analyze the investments using one or more capital budgeting methods. The fourth step in the capital budgeting process is control. In the short-term operational budgeting process, the control step is called variance analysis. After acquiring and using the capital assets, companies compare the actual results from the investments to the projected results. The comparisons are called post-audits, and they help companies determine whether the investments are going as planned and deserve continued support or whether they should abandon the project and dispose of the assets. Notice in Exhibit 26-1 that the control step loops back to the first step: develop strategies. The post-audits help mangers learn from their decisions and make adjustments as needed. The adjustments are then considered when developing new strategies. © 2016 Pearson Education, Inc.

Capital rationing: The process of ranking and choosing among alternative capital investments based on the availability of funds. Post-audit: The comparison of the actual results of capital investments to the projected results. The analysis of capital investments sometimes involves a two-stage process. In the first stage, managers screen the potential capital investments using one or both of the methods that do not incorporate the time value of money: payback and accounting rate of return. These simple methods quickly weed out undesirable investments. Potential capital investments that pass Stage 1 go on to a second stage of analysis. In the second stage, managers further analyze the potential investments using the net present value and/or internal rate of return methods. Because these methods consider the time value of money, they provide more accurate information about the potential investment’s profitability. Some companies can pursue all of the potential investments that meet or exceed their decision criteria. However, because of limited resources, most companies must engage in capital rationing, which is the third substep in the planning process. Capital rationing is the process of ranking and choosing among alternative capital investments based on the availability of funds. Managers must determine if and when to make specific capital investments, so capital rationing occurs when the company has limited cash available to invest in long-term assets. In the fourth substep, companies compare the actual results from investments to the projected results. A post-audit is the comparison of the actual results of capital investments to the projected results. © 2016 Pearson Education, Inc.

Four popular methods of analyzing potential capital investments are: Payback Accounting rate of return (ARR) Net present value (NPV) Internal rate of return (IRR) Step two in the capital budgeting process involves analyzing the investments using one or more capital budgeting methods. In this chapter, we discuss four popular methods of analyzing potential capital investments: payback, accounting rate of return, net present value, and internal rate of return. The first two methods, payback and accounting rate of return, are fairly quick and easy, and they work well for capital investments that have a relatively short life span, such as computer equipment and software that may have a useful life of only three to five years. Payback and accounting rate of return are also used to screen potential investments from those that are less desirable. Payback provides management with valuable information on how fast the cash invested will be recouped. The accounting rate of return shows the effect of the investment on the company’s accrual-based income. However, these two methods are inadequate if the capital investments have a longer life span because these methods do not consider the time value of money. The last two methods, net present value and internal rate of return, factor in the time value of money, so they are more appropriate for longer-term capital investments. Management often uses a combination of methods to make final capital investment decisions. Capital budgeting is not an exact science. Although the calculations these methods require may appear precise, remember that they are based on estimates—predictions about an uncertain future. These estimates must consider many unknown factors, such as changing consumer preferences, competition, the state of the economy, and government regulations. This makes long-term decisions riskier than short-term decisions. © 2016 Pearson Education, Inc.

Stages of capital budgeting: Screen the potential capital investments using one or both of the methods that do not incorporate the time value of money. Further analyze the potential investments using the net present value and/or internal rate of return methods. The analysis of capital investments sometimes involves a two-stage process. In the first stage, managers screen the potential capital investments using one or both of the methods that do not incorporate the time value of money—payback and accounting rate of return. These simple methods quickly weed out undesirable investments. Potential capital investments that pass Stage 1 go on to a second stage of analysis. In the second stage, managers further analyze the potential investments using the net present value and/or internal rate of return methods. Because these methods consider the time value of money, they provide more accurate information about the potential investment’s profitability. © 2016 Pearson Education, Inc.

Focus on Cash Flows Generally Accepted Accounting Principles (GAAP) are based on accrual accounting. Capital budgeting focuses on cash flows. Exhibit 26-2 summarizes the common cash inflows and outflows from capital investments. Generally Accepted Accounting Principles, or GAAP, are based on accrual accounting, but capital budgeting focuses on cash flows. The desirability of a capital asset depends on its ability to generate net cash inflows—that is, cash inflows in excess of cash outflows—over the asset’s useful life. Recall that operating income based on accrual accounting contains non-cash expenses, such as depreciation expense and bad debts expense. These expenses decrease operating income but do not require a cash outlay. The capital investment’s net cash inflows, therefore, will differ from its operating income. Of the four capital budgeting methods covered in this chapter, only the accounting rate of return method uses accrual-based accounting income. The other three methods use the investment’s projected net cash inflows. © 2016 Pearson Education, Inc.

Focus on Cash Flows Exhibit 26-3 illustrates the life cycle of capital investments, with the time line representing multiple years. Cash inflows include future cash revenue generated from the investment, any future savings in ongoing cash operating costs resulting from the investment, and any future residual value of the asset. Cash inflows are projected by employees from production, marketing, materials management, accounting, and other departments to aid managers in estimating the projected cash flows. Good estimates are a critical part of making the best decisions. To determine an investment’s net cash inflows, the inflows are netted against the investment’s future cash outflows, such as the investment’s ongoing cash operating costs and cash paid for refurbishment, repairs, and maintenance costs. The initial investment itself is also a significant cash outflow. However, in our calculations, we will always consider the amount of the investment separately from all other cash flows related to the investment. The projected net cash inflows are given in our examples and in the assignment material. In reality, much of capital investment analysis revolves around projecting these figures as accurately as possible using input from employees throughout the organization—production, marketing, and so forth—depending on the type of capital investment. © 2016 Pearson Education, Inc.

How Do the Payback and Accounting Rate of Return Methods Work?
Two capital investment analysis methods that companies use to evaluate shorter capital investments are: Payback Accounting rate of return Payback is a capital investment analysis method that measures the length of time it takes to recover, in net cash inflows, the cost of the initial investment. Next, we’ll examine in detail each of the methods used to analyze capital investments, starting with an example of the payback method. Payback is a capital investment analysis method that measures the length of time it takes to recover, in net cash inflows, the cost of the initial investment. The initial investment is also called the capital outlay. All else being equal, the shorter the payback period, the more attractive the asset. Computing the payback depends on whether net cash inflows are equal each year or differ over time. We’ll first look at two examples with equal annual net cash inflows. © 2016 Pearson Education, Inc.

Payback with Equal Annual Net Cash Inflows
Smart Touch Learning is considering investing $240,000 in: Hardware and software to provide a business- to-business (B2B) portal. Smart Touch Learning expects the portal to save $60,000 per year for each of the six years of its useful life. Smart Touch Learning is considering investing $240,000 in hardware and software to provide a business-to-business (B2B) portal. Employees throughout the company will use the B2B portal to access company-approved suppliers. Smart Touch Learning expects the portal to save $60,000 per year for each of the six years of its useful life. The savings will arise from reducing the number of purchasing personnel the company employs and from reduced costs on the goods and services purchased. Net cash inflows arise from an increase in revenues, a decrease in expenses, or both. In Smart Touch Learning’s case, the net cash inflows result from lower expenses. © 2016 Pearson Education, Inc.

Net cash flows arise from an increase in revenues, a decrease in expenses, or both. When net cash inflows are equal each year, managers compute the payback with the following formula: When net cash inflows are equal each year, managers compute the payback with the following formula: Amount invested / Expected annual net cash inflow. © 2016 Pearson Education, Inc.

Smart Touch Learning computes the investment’s payback as: Smart Touch Learning expects to recoup the $240,000 investment in the B2B portal by the end of year 4, when the accumulated net cash inflows total $240,000. © 2016 Pearson Education, Inc.

Assume Smart Touch Learning is considering whether to, instead, invest $240,000 to upgrade its Web site. The company expects the upgraded Web site to generate $80,000 in net cash inflows each year of its three-year life. The payback is: Smart Touch Learning is also considering whether to, instead, invest $240,000 to upgrade its Web site. The company expects the upgraded Web site to generate $80,000 in net cash inflows each year of its three-year life. Smart Touch Learning will recoup the $240,000 investment for the Web site upgrade by the end of year 3, when the accumulated net cash inflows total $240,000. The Web site upgrade project has a shorter payback period than the B2B project—three years compared with four years. Therefore, based on this method of analysis, the Web site upgrade is a more attractive project. © 2016 Pearson Education, Inc.

Payback with Unequal Annual Net Cash Inflows
The payback equation works only when net cash inflows are the same each period. When periodic cash flows are unequal, you must total net cash inflows until the amount invested is recovered. Assume that Smart Touch Learning is considering an alternate investment, the Z80 portal. The Z80 portal differs from the B2B portal and the Web site upgrade in two respects. First, it has unequal net cash inflows during its life; second, it has a $30,000 residual value at the end of its life. The Z80 portal will generate net cash inflows of $100,000 in year 1, $80,000 in year 2, $50,000 each year in years 3 and 4, $40,000 each in years 5 and 6, and $30,000 in residual value when the equipment is sold at the end of the project’s useful life. Exhibit 26-5 shows the payback schedule for these unequal annual net cash inflows. By the end of year 3, the company has recovered $230,000 of the $240,000 initially invested, so it is only $10,000 short of payback. Because the expected net cash inflow in year 4 is $50,000, by the end of year 4, the company will have recovered more than the initial investment. Therefore, the payback is somewhere between three and four years. © 2016 Pearson Education, Inc.

Payback with Unequal Annual Net Cash Inflows
For the payback with unequal cash flows, the payback period is calculated using the following formula: The shortest payback period is for the Web site: Assuming that the cash flow occurs evenly throughout the fourth year, the exact payback is 3 years plus the $10,000 amount needed to complete recovery in year 4 divided by the $50,000 net cash inflow in year 4. Therefore, the exact payback is 3.2 years. Based on the payback method alone, the Web site upgrade provides the shortest payback period of 3 years compared to the Z80 portal payback period of 3.2 years and the B2B portal payback period of 4 years. © 2016 Pearson Education, Inc.

Criticism of Payback Exhibit 26-6 compares the paybacks of the three investments. As the exhibit illustrates, the payback method does not consider the asset’s profitability. The method only tells management how quickly it will recover the cash invested. Therefore, even though the Web site upgrade has the shortest payback, both the B2B portal and the Z80 portal are better investments because they provide profit. The key point is that the investment with the shortest payback is best only if all other factors are the same. Therefore, managers usually use the payback method as a screening device to eliminate investments that will take too long to recoup the initial investment. They rarely use payback as the sole method for deciding whether to invest in an asset. Managers also use accounting rate of return, net present value, and internal rate of return to evaluate capital investments. © 2016 Pearson Education, Inc.

Payback In summary, when using the payback method, managers are guided by the following decision rule: Investments with shorter payback periods are more desirable, all else being equal. © 2016 Pearson Education, Inc.

Accounting Rate of Return (ARR)
The accounting rate of return (ARR) is a capital investment analysis method that measures profitability of an investment. Companies are in business to earn profits. The accounting rate of return (ARR) is a capital investment analysis method that measures the profitability of an investment. ARR = Average annual operating income / Average amount invested Notice that accounting rate of return focuses on the operating income, not the net cash inflow, that an asset generates. ARR measures the average annual rate of return over the asset’s entire life, so it is sometimes called average rate of return or annual rate of return. Also, notice the similarity to ROI (return on investment), used to evaluate investment centers. The primary difference is ARR is used to evaluate the lifetime return of an investment, and ROI is used to evaluate an annual return. © 2016 Pearson Education, Inc.

Before calculating the ARR, first determine the average annual operating income using the following formula: Recall the B2B portal, which costs $240,000 has equal annual net cash inflows of $60,000, a six-year useful life, and no (zero) residual value. Let’s look at the average annual operating income in the numerator first. Its formula is displayed in Exhibit The average annual operating income of an asset is simply the asset’s total operating income over the course of its operating life divided by its life span (number of years). Operating income is based on accrual accounting. Therefore, any non-cash expenses, such as depreciation expense, must be subtracted from the asset’s net cash inflows to arrive at its operating income. © 2016 Pearson Education, Inc.

The B2B portal’s average annual operating income and ARR are as follows: The B2B portal’s average annual operating income is as follows: The total net cash inflow over the life of the asset is $360,000. We then subtract $240,000, which is the total depreciation expense that will be recorded during the life of the asset. This gives us the $120,000 total operating income during the asset’s operating life. Next, we divide by the asset’s operating life of 6 years, for an average operating income of $20,000. The average amount invested in an asset is its book value at the beginning of the asset’s useful life plus the book value at the end of the asset’s useful life divided by 2. In other words, it is the asset’s initial cost plus the asset’s residual value divided by 2. Remember that book value is cost less accumulated depreciation. Because the B2B portal does not have a residual value, the average amount invested is $120,000. © 2016 Pearson Education, Inc.

The Z80 portal’s average annual operating income and ARR are as follows: Now consider the Z80 portal. Recall that the Z80 portal differed from the B2B portal only in that it had unequal net cash inflows during its life and a $30,000 residual value at the end of its life. Its average annual operating income is calculated by determining the total net cash inflow during the operating life of the asset. In this case, that amount is $360,000. Then, subtract the $210,000 total depreciation taken over the operating life of the asset. This results in $150,000 of total operating income during the portal’s operating life. When we divide by the operating life of six years, we arrive at an average operating income of $25,000. Notice that the Z80 portal’s average annual operating income of $25,000 is higher than the B2B portal’s operating income of $20,000. Because the Z80 asset has a residual value at the end of its life, less depreciation is expensed each year, leading to a higher average annual operating income. © 2016 Pearson Education, Inc.

The decision rule for accounting rate of return is that if the expected accounting rate of return meets or exceeds the required rate of return, the company should invest. If the expected accounting rate of return is less than the required rate of return, the company should not invest. © 2016 Pearson Education, Inc.

What Is the Time Value of Money?
A dollar received today is worth more than a dollar to be received in the future. The fact that invested cash earns interest over time is called the time value of money. Two methods of capital investment analysis incorporate the time value of money: Net present value (NPV) Internal rate of return (IRR) A dollar received today is worth more than a dollar to be received in the future because you can invest today’s dollar and earn additional income so you’ll have more cash next year. The fact that invested cash earns income over time is called the time value of money. This concept explains why we would prefer to receive cash sooner rather than later. The time value of money means that the timing of capital investments’ net cash inflows is important. Two methods of capital investment analysis incorporate the time value of money: net present value (NPV) and internal rate of return (IRR). © 2016 Pearson Education, Inc.

Time Value of Money Concepts
The time value of money depends on several key factors: The principal amount (p)—The amount of the investment (Principal is stated as either a single lump sum or an annuity.) The number of periods (n)—The length of time from the beginning of the investment until termination The interest rate (i)—The annual percentage earned on the investment The time value of money depends on several key factors: the principal amount, the number of periods, and the interest rate. The principal (p) refers to the amount of the investment or borrowing. Because this chapter deals with capital investments, we will primarily discuss the principal in terms of investments. However, the same concepts apply to borrowings, such as mortgages payable and bonds payable, which we cover in the financial accounting chapters. We state the principal as either a single lump sum or an annuity. For example, if you win the lottery, you have the choice of receiving all the winnings now (a single lump sum) or receiving a series of equal payments for a period of time in the future (an annuity). An annuity is a stream of equal cash payments made at equal time intervals. For example, $100 cash received per month for 12 months is an annuity. An ordinary annuity is an annuity in which the installments occur at the end of each period. The number of periods (n) is the length of time from the beginning of the investment until termination. All else being equal, the shorter the investment period, the lower the total amount of interest earned. If you withdraw your savings after four years rather than five years, you will earn less interest. In this chapter, the number of periods is stated in years. The interest rate (i) is the annual percentage earned on the investment. Interest can be computed as either simple interest or compound interest. © 2016 Pearson Education, Inc.

Simple Interest Versus Compound Interest
Simple interest means that interest is calculated only on the principal amount. Compound interest means that interest is calculated on the principal and on all previously earned interest. Simple interest is calculated only on the principal amount. Compound interest is calculated on the principal and on all previously earned interest. Compound interest assumes that all interest earned will remain invested and earn additional interest at the same interest rate. © 2016 Pearson Education, Inc.

Simple Interest Versus Compound Interest
Exhibit 26-8 compares simple interest of 6% on a five-year, $10,000 investment with interest compounded yearly (rounded to the nearest dollar). As you can see, the amount of compound interest earned yearly grows as the base on which it is calculated (principal plus cumulative interest to date) grows. Over the life of this investment, the total amount of compound interest is more than the total amount of simple interest. Most investments yield compound interest, so we assume compound interest, rather than simple interest, for the rest of this chapter. Fortunately, time value calculations involving compound interest do not have to be as tedious as those shown in Exhibit Business calculators and spreadsheet software such as Microsoft Excel are programmed with these formulas. In addition, tables with present value factors can be used to simplify the calculations. © 2016 Pearson Education, Inc.

Present Value Factors The future value of the investment in our example is simply its worth at the end of the five-year term. The future value is the principal plus interest earned. The future value or present value of an investment simply refers to the value of an investment at different points in time. We can calculate the future value or the present value of any investment by knowing (or assuming) information about the three factors we listed earlier: (1) principal amount, (2) number of periods, and (3) interest rate. For example, in Exhibit 26-8, we calculated the interest that would be earned on (1) a $10,000 principal, (2) invested for five years, (3) at 6% interest. The future value of the investment is simply its worth at the end of the five-year time frame—the original principal plus the interest earned. In our example, the future value of the investment is the sum of the principal and the interest earned. © 2016 Pearson Education, Inc.

Present Value Factors The future value of a $10,000 principal, for five years, at 6% interest is: Then rearrange the equation: In this case, the future value of a $10,000 investment invested at 6% for five years is $13,383. If we invest $10,000 today, its present value is simply $10,000. So another way of stating the future value is that it is the sum of the present value of the investment and the interest earned. We can rearrange the equation as present value being equal to the future value less interest earned. The only difference between present value and future value is the amount of interest that is earned in the intervening time span. © 2016 Pearson Education, Inc.

Used to calculate the value today of
Present Value Factors Table Used to calculate the value today of Present Value of $1 (Appendix B, Table B-1) One future amount (a lump sum) Present Value of Ordinary Annuity of $1 (Appendix B, Table B-2) A series of equal future amounts (annuities) Calculating each period’s compound interest, as we did in Exhibit 26-8, and then adding it to the present value to determine the future value (or subtracting it from the future value to determine the present value) is tedious. Fortunately, mathematical formulas have been developed that specify future values and present values for unlimited combinations of interest rates and time periods. Separate formulas exist for single lump-sum investments and annuities. These formulas are programmed into most business calculators, so the user only needs to correctly enter the principal amount, interest rate, and number of time periods to find present or future values. These formulas are also programmed into spreadsheet functions in Microsoft Excel. In this section of the chapter, we use present value tables. The Excel formulas are illustrated later in the chapter. Note that because the table values are rounded, the Excel results will differ slightly. The present value tables contain the results of the formulas for various interest rate and time period combinations. The formulas and resulting tables are shown in Appendix B at the end of this book. The present value of $1 is found in Appendix B, Table B-1 and is used to calculate the value today of one future amount (a lump sum). The present value of annuity of $1 is found in Appendix B, Table B-2 and is used to calculate the value today of a series of equal future amounts called annuities. Note that the columns are interest rates, and the rows are periods. © 2016 Pearson Education, Inc.

Present Value of a Lump Sum
How much would you need to invest today (in the present time) to have $13,383 in five years if the interest rate is 6%? Use the PV factor from the table Present Value of $1 (Appendix B, Table B-1). The present value of $1 is found in Appendix B, Table B-1 and is used to calculate the value today of one future amount (a lump sum). The present value of annuity of $1 is found in Appendix B, Table B-2 and is used to calculate the value today of a series of equal future amounts called annuities. Take a moment to look at these tables because we are going to use them throughout the rest of the chapter. Note that the columns are interest rates, and the rows are periods. The data in each table, known as present value factors, are for an investment (or loan) of $1. To find the present value of an amount other than $1, multiply the present value factor by the future amount. We determine the PV factor from the table labeled Present Value $1 (Appendix B, Table B-1). We use this table for lump sum amounts. We look down the 6% column and across the 5 periods row and find the PV factor is If approximately $9,997 is invested today at 6% for five years, at the end of five years, the investment will grow to $13,383. © 2016 Pearson Education, Inc.

Present Value of an Annuity
A series of equal payments over equal intervals (years) is an annuity. Assume instead of receiving a lump sum at the end of five years, you will receive $2,000 at the end of each year. Let’s now assume that instead of receiving a lump sum at the end of the five years, you will receive $2,000 at the end of each year. This is a series of payments ($2,000) over equal intervals (years), so it is an annuity. How much would you have to invest today to receive these payments, assuming an interest rate of 6%? We determine the annuity PV factor from the table labeled Present Value of Ordinary Annuity of $1 (Appendix B, Table B-2). We use this table for annuities. We look down the 6% column and across the 5 periods row and find the annuity PV factor is Let’s verify the calculation. The chart shows that the initial investment of $8,424 is invested for one year, earning $505 in interest. At the end of that period, the first withdrawal of $2,000 takes place, leaving a balance of $6,929, calculated as $8,424 plus $505 less $2,000. At the end of the five years, the ending balance is $0, proving that the present value of the $2,000 annuity is $8,424. © 2016 Pearson Education, Inc.

Summary Assume you have won the lottery after purchasing a $5 lottery ticket. You have the following options: Let’s assume you have just won the lottery after purchasing one $5 lottery ticket. The state offers you three payout options for your after-tax prize money. Option 1 is $1,000,000 now, option 2 is $150,000 at the end of each year for the next 10 years, and option 3 is $2,000,000 at the end of 10 years. Which alternative should you take? You might be tempted to wait 10 years to “double” your winnings. You may be tempted to take the cash now and spend it. However, assume you plan to prudently invest all money received—no matter when you receive it—so that you have financial flexibility in the future. How can you choose among the three payment alternatives when the total amount of each option varies? Comparing these three options is like comparing apples to oranges—we just cannot do it—unless we find some common basis for comparison. Our common basis for comparison will be the prize money’s worth at a certain point in time—namely, today. In other words, if we convert each payment option to its present value, we can compare apples to apples. © 2016 Pearson Education, Inc.

Present Value of an Annuity
Exhibit 26-9 shows that we have converted each payout option to a common basis—its worth today—so we can make a valid comparison among the options. Based on this comparison, you should choose Option #2 because its worth, in today’s dollars, is the highest of the three options. The lottery problem is a good example of how businesses use discounted cash flows to analyze capital investments. Companies make initial investments to purchase the assets. The initial investment is already in present value, similar to lottery Option #1. The purpose of the investments is to increase cash flows in the future, but those future cash flows have to be discounted back to their present value in order to compare them to the initial investment already in present value, similar to lottery Option #2. Some investments also have a residual value, meaning the company can sell the assets at the end of their useful lives and receive a lump sum cash inflow in the future, similar to lottery Option #3. Now that you have reviewed time value of money concepts, in the next section we discuss the two capital investment analysis methods that incorporate the time value of money: net present value (NPV) and internal rate of return (IRR). © 2016 Pearson Education, Inc.

How Do Discounted Cash Flow Methods Work?
Neither payback nor ARR recognizes the time value of money. The methods incorporating compound interest are: Net present value (NPV) Internal rate of return (IRR) Neither payback nor accounting rate of return recognizes the time value of money. That is, these methods fail to consider the timing of the net cash inflows an asset generates. Discounted cash flow methods—the net present value and the internal rate of return (IRR) methods—overcome this weakness. These methods incorporate compound interest by assuming that companies will reinvest future cash flows when they are received. The NPV and IRR methods rely on present value calculations to compare an investment’s initial cost with its expected net cash inflows. Recall that an investment’s net cash inflows includes all future cash flows related to the investment, such as future increased sales or cost savings, netted against the investment’s cash operating costs. Because the cash outflow for the investment occurs now, but the net cash inflows from the investment occur in the future, companies can make valid “apples-to-apples” comparisons only if they convert the cash flows to the same point in time—namely the present value. © 2016 Pearson Education, Inc.

Net Present Value (NPV)
Net present value (NPV) is a capital investment analysis method that measures the net difference between the present value of an investment’s net cash inflows and the investment’s initial cost. The discount rate is management’s minimum desired rate of return on a capital investment. If the present value of an investment’s net cash inflows exceeds the initial cost of the investment, that’s a good investment. In terms of our earlier lottery example, the lottery ticket turned out to be a good investment because the present value of its net cash inflows (the present value of the lottery payout under any of the three payout options) exceeded the cost of the investment (the lottery ticket cost $5 to purchase). Net present value (NPV) is a capital investment analysis method that measures the net difference between the present value of the investment’s net cash inflows and the investment’s cost. The discount rate is management’s minimum desired rate of return on a capital investment. © 2016 Pearson Education, Inc.

Net Present Value (NPV)
Compare two projects: produce laptop computers or produce desktop computers. Smart Touch Learning is considering expanding production to include laptop computers and desktop computers, with each product considered a separate potential capital investment project. The projects each require the purchase of one specialized machine. Each machine costs $1,000,000, has a five-year life, and has zero residual value. The two projects have different patterns of predicted net cash inflows, as shown in Exhibit The laptop project generates more net cash inflows, but the desktop project brings in cash sooner. To decide how attractive each investment is, we find its net present value. © 2016 Pearson Education, Inc.

NPV with Equal Periodic Net Cash Inflows
Smart Touch Learning expects the laptop project to generate $305,450 of net cash inflows each year for five years. The NPV is $48,610 calculated as follows: Smart Touch Learning expects the laptop project to generate $305,450 of net cash inflows each year for five years. Because these cash flows are equal in amount and occur every year, they are an annuity. Therefore, we use the Present Value of Annuity of $1 table (Appendix B, Table B-2) to find the appropriate annuity present value factor for an interest rate of 14% for five years. The present value of the net cash inflows from Smart Touch Learning’s laptop project is $1,048,610, which we find by multiplying the annual cash inflows of $305,450 by the PV factor of Next, we subtract the investment’s initial cost of $1,000,000 from the present value of the net cash inflows of $1,048,610. The difference of $48,610 is the net present value (NPV). A positive NPV means that the project earns more than the required rate of return. A negative NPV means that the project earns less than the required rate of return. © 2016 Pearson Education, Inc.

NPV with Equal Periodic Net Cash Inflows
The decision rule for net present value is that a positive net present value means that the project earns more than the required rate of return, and the company should invest in the project. A negative net present value means that the project earns less than the required rate of return, and the company should not invest in the project. © 2016 Pearson Education, Inc.

NPV with Unequal Periodic Net Cash Inflows
In contrast to the laptop project, for the desktop project the net cash inflows of are unequal—$500,000 in year 1, $350,000 in year 2, and so on—because the company expects to have higher sales volume in the early years of the project than in later years. Because these amounts vary by year, Smart Touch Learning’s managers cannot use the annuity table to compute the present value of the desktop project. They must compute the present value of each individual year’s net cash inflows separately as separate lump sums received in different years using the Present Value of $1 table (Appendix B, Table B-1). The net cash inflow received in year 1 is discounted using a present value factor for 14% for one year, while the $350,000 net cash inflow received in year 2 is discounted using a present value factor for 14% for two years, and so forth. After separately discounting each of the five years’ net cash inflows, we add all the results to find that the total present value of the desktop project’s net cash inflows is $1,078,910. Finally, we subtract the investment’s cost of $1,000,000 (cash outflows) to arrive at the desktop project’s net present value of $78,910. Because the net present value is positive, Smart Touch Learning expects the desktop project to earn more than the 14% required rate of return, making this an attractive investment. © 2016 Pearson Education, Inc.

NPV of a Project with Residual Value
Suppose Smart Touch Learning expects that the laptop project equipment will be worth $100,000 at the end of its five-year life. The revised NPV is as follows: Many assets yield cash inflows at the end of their useful lives because they have residual value. Companies discount an investment’s residual value to its present value when determining the total present value of the project’s net cash inflows. The residual value is discounted as a single lump sum because it will be received only once, when the asset is sold. In short, it is just another type of cash inflow of the project. Suppose Smart Touch Learning expects that the laptop project equipment will be worth $100,000 at the end of its five-year life. To determine the laptop project’s net present value, we discount the residual value of $100,000 using the Present Value of $1 table (Appendix B, Table B-1) for an interest rate of 14% for five years. We then add its present value of $51,900 to the present value of the laptop project’s other net cash inflows we calculated previously as $1,048,610. Because of the expected residual value, the laptop project is now more attractive than the desktop project. If Smart Touch Learning could pursue only the laptop or desktop project because of capital rationing, Smart Touch Learning would now choose the laptop project because its net present value of $100,510 is higher than the desktop project’s net present value of $78,910, and both projects require the same investment of $1,000,000. © 2016 Pearson Education, Inc.

Smart Touch Learning Capital Investment Options
In the previous examples, comparing the net present value of the two projects was valid only because both projects required the same initial cost of $1,000,000. In contrast, Exhibit summarizes three capital investment options faced by Smart Touch Learning. Each capital project requires a different initial investment. All three projects are attractive because each yields a positive net present value. Assuming Smart Touch Learning can invest in only one project at this time, which one should it choose? Project B yields the highest NPV, but it also requires a larger initial investment than the alternatives. © 2016 Pearson Education, Inc.

Profitability Index Choose the project with the highest NPV when comparing projects with similar investments. Use the profitability index when initial investment amounts differ. If Smart Touch Learning had to choose between the laptop and desktop projects, the company would choose the desktop project in the first scenario because it yields a higher NPV ($78,910) and the laptop project in the second scenario because it yields a higher NPV when the residual value is considered ($100,510). However, comparing the NPV of the two projects is valid only because both projects require the same initial cost: $1,000,000. In contrast, Exhibit summarizes three capital investment options faced by Smart Touch Learning. Each capital project requires a different initial investment. All three projects are attractive because each yields a positive net present value. Assuming Smart Touch Learning can invest in only one project at this time, which one should it choose? Project B yields the highest NPV, but it also requires a larger initial investment than the alternatives. © 2016 Pearson Education, Inc.

Profitability Index The profitability index is computed as follows:
To choose among the projects, Smart Touch Learning computes the profitability index (also known as the present value index). The profitability index computes the number of dollars returned for every dollar invested, with all calculations performed in present value dollars. The profitability index is computed as present value of net cash inflows divided by the initial investment. The profitability index allows us to compare alternative investments in present value terms (like the net present value method), but it also considers differences in the investments’ initial cost. © 2016 Pearson Education, Inc.

Profitability Index Let’s compute the profitability index for all three alternatives. The profitability index shows that Project C is the best of the three alternatives because it returns $1.21 (in present value dollars) for every $1.00 invested. Projects A and B return slightly less. © 2016 Pearson Education, Inc.

Profitability Index Comparison of the laptop and desktop projects (without residual value) using the profitability index is as follows: Let’s also compute the profitability index for Smart Touch Learning’s laptop and desktop projects (using the first scenario, without the residual value for the laptop project). The profitability index confirms our prior conclusion that the desktop project is more profitable than the laptop project. The desktop project returns $1.079 (in present value dollars) for every $1.00 invested (beyond the 14% return already used to discount the cash flows). We did not need the profitability index to determine that the desktop project was preferable because both projects required the same investment of $1,000,000. Because Smart Touch Learning chose the desktop project over the laptop project, the laptop project is the opportunity cost. Opportunity cost is the benefit forgone by not choosing an alternative course of action. © 2016 Pearson Education, Inc.

Internal Rate of Return (IRR)
The internal rate of return (IRR) is the rate of return, based on discounted cash flows, of a capital investment. It is the interest rate that makes the NPV of the investment equal to zero. Another discounted cash flow method for capital budgeting is the internal rate of return. The internal rate of return is the rate of return, based on discounted cash flows, of a capital investment. It is the interest rate that makes the NPV of the investment equal to zero. When net present value is calculated, the present value factor is selected using the company’s required rate of return. If the net present value is positive, then you know the actual rate of return is greater than the required rate of return, and it is an acceptable project. However, you do not know the actual rate of return, only that it is greater than the required rate. If the net present value is zero, then you know the actual rate is equal to the required rate. The actual rate of return is called the internal rate of return. In other words, the internal rate of return is the interest rate that makes the initial cost of the investment equal to the present value of the investment’s net cash inflows, which means the net present value is zero. The higher the IRR, the more desirable the project. © 2016 Pearson Education, Inc.

IRR with Equal Periodic Net Cash Inflows
Smart Touch Learning’s laptop project would cost $1,000,000 with five equal yearly cash inflows of $305,450. Use the following formula to find the annuity factor: Then look up the factor to determine the applicable interest rate. Let’s first consider Smart Touch Learning’s laptop project, which would cost $1,000,000 and result in five equal yearly cash inflows of $305,450. We compute the internal rate of return of an investment with equal periodic cash flows (annuity) by taking the following steps: First, the internal rate of return is the interest rate that makes the cost of the investment equal to the present value of the investment’s net cash inflows, so we set up the equation to set the initial investment equal to the present value of net cash inflows. Further expanding the equation, the present value of the net cash inflows can be rewritten as the amount of cash inflow multiplied by the annuity present value factor for an unknown interest rate for the given time period. Finally, we find the interest rate that corresponds to this annuity present value factor. Turn to the Present Value of Annuity of $1 table (Appendix B, Table B-2). Scan the row corresponding to the project’s expected life—five years, in our example. Choose the column or columns with the number closest to the annuity present value factor you calculated. The annuity factor is in the 16% column. Therefore, the internal rate of return of the laptop project is 16%. Smart Touch Learning expects the project to earn an internal rate of return of 16% over its life. © 2016 Pearson Education, Inc.

Internal Rate of Return (IRR)
To decide whether a project is acceptable, compare the internal rate of return with the minimum desired rate of return. The decision rule is that if the internal rate of return meets or exceeds the required rate of return, the company should invest in the project. If the internal rate of return is less than the required rate of return, the company should not invest. Recall that Smart Touch Learning’s required rate of return, or discount rate, is 14%. Because the laptop project’s internal rate of return of 16% is higher than the hurdle rate of 14%, Smart Touch Learning would invest in the project. © 2016 Pearson Education, Inc.

IRR with Unequal Periodic Net Cash Flows
Because the desktop project has unequal cash inflows, Smart Touch Learning cannot use the Present Value of Annuity of $1 table to find the asset’s internal rate of return. Rather, Smart Touch Learning must use a trial-and-error procedure to determine the discount rate making the project’s net present value equal to zero. For example, because the company’s minimum required rate of return is 14%, Smart Touch Learning might start by calculating whether the desktop project earns at least 14%. Recall from the net present value calculation that the desktop’s net present value using a 14% discount rate is $78,910. Because the net present value is positive, the internal rate of return must be higher than 14%. Smart Touch Learning continues the trial-and-error process, using higher discount rates until the company finds the rate that brings the net present value of the desktop project to zero. This table shows the net present value calculations using discount rates of 16% and 18%. At 18%, the net present value is $3,980, which is very close to zero. Thus, the IRR must be slightly higher than 18%. If we use a business calculator or Excel, rather than the trial-and-error procedure, we find the internal rate of return is 18.23%. The desktop project’s internal rate of return is higher than Smart Touch Learning’s 14% required rate of return, so the desktop project is acceptable. © 2016 Pearson Education, Inc.

Comparing Capital Investment Analysis Methods
We have discussed four capital budgeting methods commonly used by companies to make capital investment decisions. Two of these methods do not incorporate the time value of money: payback and accounting rate of return. The discounted cash flow methods are superior because they consider both the time value of money and profitability. These methods compare an investment’s initial cost (cash outflow) with its future net cash inflows—all converted to the same point in time—the present value. Profitability is built into the discounted cash flow methods because they consider all cash inflows and outflows over the project’s life. Exhibit compares the four methods of capital investment analysis. Managers often use more than one method to gain different perspectives on risks and returns. For example, Smart Touch Learning could decide to pursue capital projects with positive net present values, provided that those projects have a payback of less than or equal to four years. © 2016 Pearson Education, Inc.

Sensitivity Analysis Microsoft Excel can be used to perform “what if” analysis. The examples of capital investment analysis methods illustrated in the chapter used the present value tables located in Appendix B. These calculations can also be completed using a business calculator with net present value and internal rate of return functions. Using computer spreadsheet software, such as Microsoft Excel, can be more beneficial, however, because it allows for easy manipulation of the figures to perform sensitivity analysis. Remember that sensitivity analysis is a “what if ” technique that shows how results differ when underlying assumptions change. Capital budgeting decisions affect cash flows far into the future. Smart Touch Learning managers might want to know whether their decision would be affected by any of their major assumptions. Examples include changing the discount rate from 14% to 12% or 16% or increasing or decreasing the net cash inflows by 10%. After reviewing the basic information for net present value analysis, managers perform sensitivity analyses to recalculate and review the results. Let’s use Excel to calculate the net present value and the internal rate of return for the two projects Smart Touch Learning is considering: laptop computers and desktop computers. Recall that both projects require an initial investment of $1,000,000 and have no residual value. Their annual net cash inflows are shown here. © 2016 Pearson Education, Inc.

Sensitivity Analysis One method of setting up Excel spreadsheets is to have areas of the spreadsheet designated for inputs and outputs. Cells for entering the inputs are at the top of the spreadsheet. Cells with formulas to calculate the outputs are in a section below the inputs. All outputs are calculated by Excel based on the formulas entered, which reference the cells with the inputs. This method of setup allows the user to make changes to any input cell and have Excel automatically recalculate the outputs. Exhibit shows an Excel spreadsheet set up in this manner with Smart Touch Learning’s capital investment analysis for the two projects. Notice that the initial investment is entered as a negative amount because it is a cash outflow, and the cash inflows are entered as positive amounts. In the output section, Excel calculated the net present value of the laptop project as $48,635, which is $25 more than the $48,610 amount previously calculated using the present value tables. The difference is because the present value factors in the tables are rounded to three decimal places. The difference for the desktop project is $286 higher than the $78,910 calculated with the present value tables. However, for a project with an investment of $1,000,000, this difference is less than 0.03% (calculated as $286 / $1,000,000) and should not be considered significant. © 2016 Pearson Education, Inc.

Sensitivity Analysis Exhibit shows the formulas used to calculate the net present value and internal rate of return of the two projects. The formula to calculate net present value is =NPV(rate,value1,value2, ). For the laptop project, the discount rate is entered in cell B8, and the cash inflows are in cells B12 through B16. Notice that the initial investment amount in cell B10 is added. Excel calculated the present value of the cash inflows and then added the negative amount of the cash outflow to determine the net present value. So, the formula is =NPV(B8,B12:B16)+B10. The internal rate of return formula includes the range of all the cash flows, including the initial investment. Keep in mind that it is imperative to list the cash flows in the proper order! The time value of money considers the timing of the cash flows, and Excel is calculating the net present value and internal rate of return based on the order of the entries. Now that the spreadsheet is set up, Smart Touch Learning can easily change any amounts in the input section to complete a sensitivity analysis. Also, the spreadsheet can be used to analyze any other projects by simply changing the inputs. If other projects have longer lives, then rows can be inserted to accommodate the additional cash inflows and then the formulas adjusted to include those rows. © 2016 Pearson Education, Inc.

Capital Rationing We have mentioned capital rationing several times, but it is worthwhile to revisit the topic. Most companies have limited resources and have to make hard decisions about which projects to pursue and which ones to delay or reject. These decisions are not just based on the quantitative factors of payback, accounting rate of return, net present value, and internal rate of return. Qualitative factors must also be considered. For example, a company may choose manufacturing equipment with a lower net present value because it is more environmentally friendly or accept a project that is not profitable but adds value to the community. Companies should also consider the opportunity costs of rejecting certain projects and the possibility of lost business if there is negative public perception of the company’s choices. Exhibit shows a decision tree for capital rationing. © 2016 Pearson Education, Inc.

Chapter 26 Capital Investment Decisions

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