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**Capital Investment Decisions and the Time Value of Money**

Chapter 21 Chapter 21 explains capital investment decisions and the time value of money.

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Learning Objectives Describe the importance of capital investments and the capital budgeting process Use the payback period and rate of return methods to make capital investment decisions Use the time value of money to compute the present and future values of single lump sums and annuities Use discounted cash flow models to make capital investment decisions Learning objectives for this chapter include to: Describe the importance of capital investments and the capital budgeting process. Use the payback period and rate of return methods to make capital investment decisions. Use the time value of money to compute the present and future values of single lump sums and annuities. Use discounted cash flow models to make capital investment decisions.

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1 Describe the importance of capital investments and the capital budgeting process The first learning objective is to describe the importance of capital investments and the capital budgeting process.

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Short term vs. Long term Last chapter looked at recurring parallel options Took place in the same time sequence Revenues and expenses primarily This chapter we remove that timing restriction Any time you want Revenues, expenses, and investments How do we compare return and investment if they come in different amounts at different times?

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**You are the Decider: Should we make the capital investment?**

Should we start this new business? Should we open another store or open an online store? Should we install solar panels? Should we buy new, or rebuild? The process of making capital investment decisions is often referred to as capital budgeting. Capital budgeting is planning to invest in long-term assets in a way that returns the most profitability to the company. Companies make capital investments when they acquire capital assets—assets used for a long period of time. Capital investments include buying new equipment, building new plants, automating production, and developing major commercial Web sites. In addition to affecting operations for many years, capital investments usually require large sums of money.

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**Capital Budgeting Process**

Identify potential investments Estimate net cash inflows/outflows Analyze investment using method(s) Choose option(s) Post-audit to measure outcomes The first step in the capital budgeting process is to identify potential investments—for example, new technology and equipment that may make the company more efficient, competitive, and/or profitable. Employees, consultants, and outside sales vendors often offer capital investment proposals to management. After identifying potential capital investments, managers project the investment’s net cash inflows and then analyze the investments using one or more of the four capital budgeting methods described. Sometimes the analysis involves a two-stage process. In the first stage, managers screen the investments using one or both of the methods that do not incorporate the time value of money—payback period or accounting rate of return. These simple methods quickly weed out undesirable investments. Potential investments that “pass stage one” 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, other companies must engage in capital rationing, and choose among alternative capital investments. Based on the availability of funds, managers determine if and when to make specific capital investments. For example, management may decide to wait three years to buy a certain piece of equipment because they consider other investments more important. In the intervening three years, the company will reassess whether it should still invest in the equipment. Perhaps technology has changed, and even better equipment is available. Perhaps consumer tastes have changed so the company no longer needs the equipment. Because of changing factors, long-term capital budgets are rarely set in stone. Most companies perform post-audits of their capital investments. After investing in the assets, they compare the actual net cash inflows generated from the investment to the projected net cash inflows. Post-audits help companies determine whether the investments are going as planned and deserve continued support, or whether they should abandon the project and sell the assets. Managers also use feedback from post-audits to better estimate net cash flow projections for future projects. If managers expect routine post-audits, they will more likely submit realistic net cash flow estimates with their capital investment proposals.

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What We’ll look at Simple techniques The payback method (Simple) rate of return (ROR) Techniques using time value of money Present & future value of a single amount (lump sum) Present & future value of a payment stream (annuity) Net present value (NPV) Profitability index Internal rate of return (IRR) What we won’t look at today Sensitivity analysis Monte Carlo analysis Other advanced computer models Our simple and TVM techniques cover virtually all of the analysis needs most of us are likely to ever need.

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**Capital Budgeting Focuses On Cash Flows**

Operating income based on accrual accounting Contains noncash expenses Capital investment’s net cash inflows will differ from its operating income Cash inflows: Future cash revenue generated Future savings in ongoing cash operating costs Future residual value Cash outflows: Initial investment Ongoing operating costs, maintenance, repairs Generally accepted accounting principles (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, inflows in excess of outflows—over the asset’s useful life. Recall that operating income based on accrual accounting contains noncash expenses, such as depreciation expense and bad-debt expense. 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. What do the projected net cash inflows include? 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. To determine the 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 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).

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2 Use the payback and rate of return methods to make capital investment decisions The second learning objective is to use the payback and rate of return methods to make capital investment decisions.

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Payback Period Measures how quickly managers expect to recover their investment dollars The shorter the payback period, the more attractive the investment Used to screen capital investment choices May be the only tool in simple situations Payback is the length of time it takes to recover, in net cash inflows, the cost of the capital outlay. The payback model measures how quickly managers expect to recover their investment dollars. All else being equal, the shorter the payback period, the more attractive the asset. Computing the payback period depends on whether net cash inflows are equal each year, or whether they differ over time. We consider each in turn.

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**Calculating Payback Period**

If the project provides equal annual returns, then use this formula: To compute the payback period when the investment has equal cash inflows, divide the amount invested by the expected annual net cash inflow. The result will be the number of years the investment takes to pay for itself. If the investment has unequal cash flows, the payback period occurs when the cumulative total of the cash inflows equal the cost of the investment.

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**Calculating Payback Period**

Unequal annual net cash inflows Total net cash inflows until the amount invested is recovered The payback equation only works 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. The Z80 portal differs from the B2B portal and the Web site in two respects: (1) It has unequal net cash inflows during its life and (2) 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 it is sold at the end of its life. Exhibit 21-3 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 period is somewhere between three and four years.

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Caffeinated practice Consider the following two investment options for the My Coffee: Sell Caffe Rent Caffe Machines Machines Initial investment $100,000 $100,000 Year 1 net cash inflows $50,000 $30,000 Year 2 net cash inflows $50,000 $30,000 Year 3 net cash inflows $50,000 $30,000 Year 4 net cash inflows $50, $30,000 Years 5-10 net cash inflows $ $30,000 Based on the payback period. Which project would you prefer and why?

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**E21-15: Preston Co. Capital Budgeting**

Preston, Co. is considering buying a manufacturing plant for $1,100,000. They expect the plan to generate average annual cash inflows of $297,000. What is the payback period of this project? They impose a 6 year hurdle: should they buy?

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**Af/Neg of the Payback Period Method**

So much better than nothing Emphasis on payback, not additional profits Easy story telling, good for sales Ignores cash flows after the payback period An experienced user can do well with it Requires human thought “seat of the pants” additional analysis A major criticism of the payback method is that it focuses only on time, not on profitability. The payback period considers only those cash flows that occur during the payback period. This method ignores any cash flows that occur after the payback period. The key point is that the investment with the shortest payback period is best only if all other factors are the same. Therefore, managers usually use the payback method as a screening device to “weed out” investments that will take too long to recoup. They rarely use payback period as the sole method for deciding whether to invest in the asset. When using the payback period method, managers are guided by the decision rule shown here.

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Rate of Return (ROR) ROR measures the average accounting rate of return over the asset’s entire life Focuses on the operating income, from the financials Maximize reported profitability, not necessarily cash flows Formula Average annual operating income The asset’s total operating income over the course of its operating life divided by its lifespan Average amount invested Net book value at the beginning of the asset’s useful life plus the net book value at the end of the asset’s useful life divided by 2 Companies are in business to earn profits. One measure of profitability is the rate of return (ROR) on an asset. The ROR focuses on the operating income, not the net cash inflow, an asset generates. The ROR measures the average accounting rate of return over the asset’s entire life. Let’s look at the average annual operating income in the numerator first. 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 lifespan (number of years). Operating income is based on accrual accounting. Therefore, any noncash expenses, such as depreciation expense, must be subtracted from the asset’s net cash inflows to arrive at its operating income. Now let’s look at the denominator of the ROR equation. The average amount invested in an asset is its net book value at the beginning of the asset’s useful life plus the net book value at the end of the asset’s useful life divided by 2. Another way to say that is the asset’s cost plus the asset’s residual value divided by 2. The net book value of the asset decreases each year because of the annual depreciation.

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**E21-15 bonus: Preston Co. Capital Budgeting**

Preston, Co. is considering buying a manufacturing plant for $1,100,000. They expect the plan to generate average annual cash inflows of $297,000 for 6 years. They expect to salvage the obsolete factory for $550,000 after 6 years. What is the rate of return of this project?

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**Rate of Return Decision Rule**

Accounting Rate of Return Decision Rule: Invest in capital assets? If the expected rate of return exceeds the required rate of return, invest. If the expected rate of return is less than the required rate of return, do not invest.

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**Rate of Return Calculating average annual operating income from asset**

Calculating average annual operating income from an asset involves: Total net cash inflows during operating life of the asset ($60,000 × 6 years) Less: Total depreciation during operating life of asset (cost – any salvage value) Total operating income during operating life of asset Divide by: Asset’s operating life (in years) Equals average annual operating income from asset

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**Accounting Rate of Return**

Calculating rate of return If the company required a ROR of at least 20%, this project would be rejected In this case, calculate the rate of return as $20,000 divided by $240,000 plus zero, then divide by two equaling $20,000 divided by $120,000 equals or 16.7 percent. Companies that use the ROR model set a minimum required rate of return. If Smart Touch requires a ROR of at least 20%, then its managers would not approve an investment in the B2B portal.

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**S21-2: Using the payback period and rate of return methods to make capital investment decisions**

Consider how Smith Valley Snow Park Lodge could use capital budgeting to decide whether the $13,500,000 Snow Park Lodge expansion would be a good investment. Assume Smith Valley’s managers developed the following estimates concerning the expansion: Assume that Smith Valley uses the straight-line depreciation method and expects the lodge expansion to have a residual value of $1,000,000 at the end of its 10-year life. Short exercise 21-2 focuses on the payback period and rate of return methods to make capital investment decisions.

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**Average cash received from each skier per day $ 236 **

S21-2: Using the payback period and rate of return methods to make capital investment decisions 1. Compute the average annual net cash inflow from the expansion. Average cash received from each skier per day $ Average variable cost of serving each skier per day (76) Average net cash inflow per skier per day $ Number of additional skiers per day × 117 Average net cash inflow per day $ 18,720 Number of ski days per year × Average annual net cash inflow per year $2,658,240 2. Compute the average annual operating income from the expansion. = Average annual net cash inflow − depreciation = $2,658,240 − $1,250,000 = $1,408,240 The exercise continues on this slide.

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**S21-3: Using the payback method to make capital investment decisions**

Refer to the Smith Valley Snow Park Lodge expansion project in S21-2 Compute the payback period for the expansion project. Payback period = Amount invested / Expected annual net cash inflow = $13,500,000 / $ 2,658,240 = 5.1 years (Rounded to one decimal place) Short exercise 21-3 addresses using the payback method to make capital investment decisions.

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**Refer to the Smith Valley Snow Park Lodge expansion project in S21-2. **

S21-4: Using the rate of return method to make capital investment decisions Refer to the Smith Valley Snow Park Lodge expansion project in S21-2. 1. Calculate the ROR. Accounting rate of return = Average annual operating income from investment Average amount invested = $2,658,240 − $1,250,000 [$13,500,000 + $1,000,000] / 2 1,408,240 $ 7,250,000 19.42% (Round to nearest hundredths) Short exercise 21-4 reviews using the rate of return to make capital investment decisions.

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3 Use the time value of money to compute the present and future values of single lump sums and annuities The third learning objective is to use the time value of money to compute the present and future values of single lump sums and annuities.

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**Time Value of Money (TVM)**

Invested money earns income over time Timing of capital investments’ net cash inflows is important Two methods of capital investment using TVM The 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. Why? Because you can invest today’s dollar and earn extra income so you’ll have more money next year. The fact that invested money earns income over time is called the time value of money, and this 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—the net present value (NPV) and internal rate of return (IRR). This section reviews time value of money to make sure you have a firm foundation for discussing these two methods.

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**Factors That Affect Time Value of Money**

Principal (p)–amount of the investment Lump sum Single quantity of money Annuity Stream of equal installments at equal time intervals Number of periods (n) From the beginning of the investment until termination Interest rate (i)–annual percentage Simple interest Compound interest The time value of money depends on several key factors: 1. the principal amount (p) 2. the number of periods (n) 3. the interest rate (i) The principal (p) refers to the amount of the investment or borrowing. 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 installments made at equal time intervals under the same interest rate. 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. The number of periods is often stated in years. The interest rate (i) is the annual percentage earned on the investment. 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 interest earned to date. Compound interest assumes that all interest earned will remain invested and earn additional interest at the same interest rate. Most investments yield compound interest.

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**Interest and the Time Value of Money**

Let’s take a look at what those fancy tables do on the board! Watch closely as I turn $1 into $2! i=15%, N=5

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**Interest Simple interest Compound interest**

Interest calculated only on the principal amount Compound interest Interest is calculated on the principal and on all previously earned interest Assumes that all interest earned will remain invested and earn additional interest at the same interest rate Capital investments yield compound interest Assume compounding interest for rest of this chapter The interest rate (i) is the annual percentage earned on the investment. 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. Compound interest assumes that all interest earned will remain invested and earn additional interest at the same interest rate. 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.

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**Present and Future Value Along a Time Continuum**

The value of an investment at different points in time Consider the timeline shown here. 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) the principal amount, (2) the period of time, and (3) the interest rate. 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. So, another way of stating the future value is—present value plus interest earned. The only difference between present value and future value is the amount of interest that is earned in the intervening time span. So, present value is future value minus any interest earned.

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**Appendix B: Factors for Present Value and Future Value**

Simplify present and future value math Programmed into business calculators and spreadsheet programs See Appendix B for present and future factor tables: Let’s play with the future value table first. Calculating each period’s compound interest, then adding it to the present value to figure the future value (or subtracting it from the future value to figure the present value) is tedious. Fortunately, mathematical formulas have been developed that specify future values and present values for unlimited combinations of interest rates (i) and time periods (n). Separate formulas exist for single lump-sum investments and annuities. These formulas are programmed into most business calculators so that 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 spreadsheets functions in Microsoft Excel. Because the specific steps to operate business calculators differ between brands, we will use tables instead. These 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 your textbook. The data in each table, known as future value factors (FV factors) and present value factors (PV factors), are for an investment (or loan) of $1. The annuity tables are derived from the lump-sum tables. For example, the Annuity PV factors (in the Present Value of Annuity of $1 table) are the sums of the PV factors found in the Present Value of $1 tables for a given number of time periods.

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**Using Future Value Factors**

Lump sum Multiply amount by the factor number found in table Table based on interest rate and number of periods $10,000 invested for 5 periods at 6% Let’s go back to our $10,000 lump-sum investment. If we want to know the future value of the investment five years from now at an interest rate of 6%, we determine the FV factor from the table labeled Future Value of $1 (Appendix B, Table B-3). We use this table for lump-sum amounts. We look down the 6% column, and across the 5 periods row, and find the future value factor is Tables ranges from 3 decimal places up to 5 or 6. The more decimal places, the more accurate to final answer. The data in each table, known as future value factors (FV factors) and present value factors (PV factors), are for an investment (or loan) of $1. To find the future value of an amount other than $1, you simply multiply the FV factor by the present amount. This figure materially agrees with our earlier calculation of the investment’s future value of $13,383 in Exhibit (The difference of $3 is due to two facts: (1) The tables round the FV and PV factors to three decimal places and (2) we rounded our earlier yearly interest calculations in Exhibit 21-7 to the nearest dollar.) $10,000 X = $13,382 Differences due to table decimal places

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Your turn: If you invested $1,000 today into a 6% fixed rate security, how much would it be worth in 50 years? Draw a time line indicating knowns and unknowns Identify table needed and go to it Look up the factor for the rate and time indicated Set up the formula and calculate Ask yourself if your answer makes sense $18,420

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**Using Present Value Factors**

Lump sum Multiply amount by the factor found in table Table based on interest rate and number of periods $13,383 to be received in 5 periods at 6% The process for calculating present values—often called discounting cash flows—is similar to the process for calculating future values. The difference is the point in time at which you are assessing the investment’s worth. Rather than determining its value at a future date, you are determining its value at an earlier point in time (today). To find the present value of an amount other than $1, you multiply the PV factor by the future amount. $13,382 X = $10,000 Differences due to table decimal places

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Your turn again: How much would you have to invest today so that you could buy a $10,000 car for cash 5 years from today? We earn 3% on our money. Draw a time line indicating knowns and unknowns Identify table needed and go to it Look up the factor for the rate and time indicated Set up the formula and calculate Ask yourself if your answer makes sense $18,420

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**Annuities: Future and Present value**

Annuity: A cash flow that occurs in identical amounts at repeating intervals. You could take each and every year and calculate present/future values for each year….. OR, you could recognize the annuity and take just one calculation using the annuity table. Future Value ? Present Value ? 1 2 3 4 5 6 $100

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**Using Future Value Factors for Annuities**

If we Invest $2,000 at 6%, at the end of each year for 5 years, how much do we have at the end? The annuity tables are derived from the lump-sum tables. For example, the Annuity PV factors (in the Present Value of Annuity of $1 table) are the sums of the PV factors found in the Present Value of $1 tables for a given number of time periods. The annuity tables allow us to perform “one-step” calculations rather than separately computing the present value of each annual cash installment and then summing the individual present values. Let’s also consider our alternative investment strategy, investing $2,000 at the end of each year for five years. The procedure for calculating the future value of an annuity is quite similar to calculating the future value of a lump-sum amount. This time, we use the Future Value of Annuity of $1 table (Appendix B, Table B-4). Assuming 6% interest, we once again look down the 6% column. Because we will be making five annual installments, we look across the row marked 5 periods. The Annuity FV factor is $2,000 X 11,274.20

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**Using Present Value Factors for Annuities**

How much do we need to squirrel away today , so we can pull $2,000 out to spend at the end of every year for 5 years? Assume 6% interest. $8,424 The annuity tables are derived from the lump-sum tables. For example, the Annuity PV factors (in the Present Value of Annuity of $1 table) are the sums of the PV factors found in the Present Value of $1 tables for a given number of time periods. The annuity tables allow us to perform “one-step” calculations rather than separately computing the present value of each annual cash installment and then summing the individual present values. Let’s also consider our alternative investment strategy, investing $2,000 at the end of each year for five years. The procedure for calculating the future value of an annuity is quite similar to calculating the future value of a lump-sum amount. This time, we use the Future Value of Annuity of $1 table (Appendix B, Table B-4). Assuming 6% interest, we once again look down the 6% column. Because we will be making five annual installments, we look across the row marked 5 periods. The Annuity FV factor is Draw a time line indicating knowns and unknowns Identify table needed and go to it Look up the factor for the rate and time indicated Set up the formula and calculate Ask yourself if your answer makes sense $2,000 X $8.424

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**Retirement Planning How much do you need?**

Annual expenditure expectations Solve for balance at the beginning of retirement How are you going to get it there? Lump sum deposit now Annual retirement contributions

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**Use discounted cash flow models to make capital investment decisions**

4 Use discounted cash flow models to make capital investment decisions The fourth learning objective is to use discounted cash flow models to make capital investment decisions.

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**Discounted Cash Flows Models**

Payback and ROR do not recognize time value of money Net present value (NPV) and internal rate of return (IRR) do recognize time value of money Both compare amount of investment with its expected net cash inflows Cash outflow for investment usually occurs now Cash inflows usually occur in the future Companies use present value to make the investment comparison, not future value Neither the payback period nor the ROR recognizes the time value of money. That is, these models fail to consider the timing of the net cash inflows an asset generates. Discounted cash flow models—the NPV and the IRR—overcome this weakness. These models incorporate compound interest by assuming that companies will reinvest future cash flows when they are received. Over 85% of large industrial firms in the United States use discounted cash-flow methods to make capital investment decisions. Companies that provide services also use these models. The NPV and IRR methods rely on present value calculations to compare the amount of the investment (the 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 only make valid “apple-to-apple” comparisons if they convert the cash flows to the same point in time—namely the present value. Companies use the present value to make the comparison (rather than the future value) because the investment’s initial cost is already stated at its present value.

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**Net Present Value (NPV)**

NPV—the net difference between the present value of the investment’s net cash inflows and the investment’s cost (cash outflows) Discount rate—the interest rate that discounts or reduces future amounts to their lesser value in the present (today). Discount rate uses the firms desired rate of return Based on cost of capital If present value of the investment’s net cash inflows exceeds the initial cost of the investment, then it is a good investment To decide how attractive each investment is, we find its net present value (NPV). The NPV is the net difference between the present value of the investment’s net cash inflows and the investment’s cost (cash outflows). We discount the net cash inflows using management’s minimum desired rate of return. This rate is called the discount rate because it is the interest rate used for the present value calculations. It is also called the required rate of return because the investment must meet or exceed this rate to be acceptable. The discount rate depends on the riskiness of investments. The higher the risk, the higher the discount (interest) rate. We then compare the present value of the net cash inflows to the investment’s initial cost to decide which projects meet or exceed management’s minimum desired rate of return.

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**Using the annuity table: Buy or Rent Decision**

Buy a new welder for cash. Cost $10,000 Lease the welder for $1,500/year for 10 years Assume: Discount rate 10% Zero salvage Average welder life in our hands is 10 years.

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**Will this new pizza store be worthwhile?**

Investment required: $250,000 Annual earnings of $50,000 You will own it for 20 years. You will then sell it for $1,000,000. Your cost of capital is 10% What is the NET present value of this project?

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**Annual costs $500 more than Kawasaki. Kawasaki Purchase cost $12,000 **

Which is the cheaper Police bike? Use a discount rate of 6% & useful life of 5 years Harley Davidson Purchase cost $25,000 Salvage value $17,000 Annual costs $500 more than Kawasaki. Kawasaki Purchase cost $12,000 Salvage value $1,000

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**Using Present Value Factors for Annuities**

Assume you win the lottery Option #1: $1,000,000 now Option #2: $150,000 the end of each year for next ten years Option #3: $2,000,000 ten years from now Which option is the best? Use PV factors for single sum and annuities to find out Option #1 is $1,000,000 in your hand today Option #2 is an annuity, 10 payments Using PV annuity tables, assuming 8% The annuity tables are derived from the lump-sum tables. For example, the Annuity PV factors (in the Present Value of Annuity of $1 table) are the sums of the PV factors found in the Present Value of $1 tables for a given number of time periods. The annuity tables allow us to perform “one-step” calculations, rather than separately computing the present value of each annual cash installment and then summing the individual present values. How can you choose among the three payment alternatives, when the total amount of each option varies ($1,000,000 versus $1,500,000 versus $2,000,000) and the timing of the cash flows varies (now versus some each year versus later)? 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. $150,000 x = $1,006,515 10 payments yield a present value of $1,006,515 and more than $1,000,000

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**Using Present Value Factors for Annuities**

Assume you win the lottery Option #1: $1,000,000 now Option #2: $150,000 the end of each year for next ten years Option #3: $2,000,000 ten years from now Use PV factors for single sum to find out what option #3 is worth today Option #3 $2,000,000 x = $ 926,400 Option #1 = $1,000,000 Option #2 = $1,006,515 Option #3 = $ 926,400 Option #2 is the highest of the three 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, we should choose Option #2 because its worth, in today’s dollars, is the highest of the three options. Now that you have reviewed time value of money concepts, we will discuss the two capital budgeting methods that incorporate the time value of money—net present value (NPV) and internal rate of return (IRR).

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S21-7: Using the time value of money to compute the present and future values of single lump sums and annuities Your grandfather would like to share some of his fortune with you. He offers to give you money under one of the following scenarios (you get to choose): $8,750 a year at the end of each of the next seven years. $50,050 (lump sum) now. $100,250 (lump sum) seven years from now. Calculate the present value of each scenario using a 6% discount rate. Which scenario yields the highest present value? Would your preference change if you used a 12% discount rate? Short exercise 21-7 focuses on using the time value of money to compute the present and future values of single lump sums and annuities.

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S21-7: Using the time value of money to compute the present and future values of single lump sums and annuities Calculate the present value of each scenario using a 6% discount rate. Which scenario yields the highest present value? Would your preference change if you used a 12% discount rate? Scenario #1 Present value = $ 8,750 × (Annuity PV factor, i = 6%, n = 7) $ 8,750 × 5.582 $ 48,843 Scenario #2 $50,050 (since it would be received now) Scenario #3 $100,250 × (PV factor, i = 6%, n = 7) $100,250 × .665 $ 66,666 The exercise continues on this slide. Scenario #3 appears to be the best option. Based on a 6% interest rate, its present value is the highest.

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**Would your preference change if you used a 12% discount rate?**

S21-7: Using the time value of money to compute the present and future values of single lump sums and annuities Would your preference change if you used a 12% discount rate? Scenario #1 Present value = $ 8,750 × (Annuity PV factor, i = 12%, n = 7) $ 8,750 × 4.564 $ 39,935 Scenario #2 $50,050 (since it would be received now) Scenario #3 $100,250 × (PV factor, i = 12%, n = 7) $100,250 × . 452 $ 45,313 The exercise concludes on this slide. Scenario #2 appears to be the best option. Based on a 12% interest rate, its present value is the highest.

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**Net Present Value (NPV)**

Choose between two alternatives by comparing NPVs Consider these two projects: CD players generates higher total cash inflows DVRs generate cash flows sooner Greg’s Tunes is considering producing CD players and digital video recorders (DVRs). The products require different specialized machines that each cost $1,000,000. Each machine has a five-year life and zero residual value. The two products have different patterns of predicted net cash inflows. The CD-player project generates more net cash inflows, but the DVR project brings in cash sooner. To decide how attractive each investment is, we find its net present value (NPV). The NPV is the net difference between the present value of the investment’s net cash inflows and the investment’s cost (cash outflows).

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**NPV with Equal Periodic Net Cash Inflows (Annuity)**

CD players project generates equal cash flows Using Present Value of Annuity of $1, the NPV is: Greg’s expects the CD-player 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 PV factor for i = 14%, n = 5. Next, we simply subtract the investment’s initial cost of $1,000,000 (cash outflows) 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. In Greg’s Tunes’ case, the CD-player project is an attractive investment. The $48,610 positive NPV means that the CD-player project earns more than Greg’s Tunes’ 14% target rate of return.

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**NPV with Unequal Periodic Net Cash Inflows**

DVR project has unequal net cash flows PV each inflow to find Net Present Value DVR project will generate net present value of $78,910 In contrast to the CD-player project, the net cash inflows of the DVR project are unequal—$500,000 in year 1, $350,000 in year 2, and so on. Because these amounts vary by year, Greg’s Tunes’ managers cannot use the annuity table to compute the present value of the DVR 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). Exhibit shows that the $500,000 net cash inflow received in year 1 is discounted using a PV factor of i = 14%, n = 1, while the $350,000 net cash inflow received in year 2 is discounted using a PV factor of i = 14%, n = 2, and so forth. After separately discounting each of the five year’s net cash inflows, we add each result to find that the total present value of the DVR 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 DVR project’s NPV—$78,910.

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**Net Present Value Decision Rule**

Both projects, CD player and DVRs, had a positive NPV Both require the same investment amount Resources are limited, which project will be selected? To choose among the projects, compute the profitability index (present value index) Exhibits and show that both the CD player and DVR projects have positive NPVs. Therefore, both are attractive investments. Because resources are limited, companies are not always able to invest in all capital assets that meet their investment criteria. As mentioned earlier, this is called capital rationing. Greg’s may not have the funds to invest in both the DVR and CD-player projects at this time. In this case, Greg’s should choose the DVR project because it yields a higher NPV. The DVR project should earn an additional $78,910 beyond the 14% required rate of return, while the CD-player project returns an additional $48,610. This example illustrates an important point. The CD-player project promises more total net cash inflows. But the timing of the DVR cash flows—loaded near the beginning of the project—gives the DVR investment a higher NPV. The DVR project is more attractive because of the time value of money. Its dollars, which are received sooner, are worth more now than the more-distant dollars of the CD-player project. If Greg’s had to choose between the CD and DVR project, the company would choose the DVR project because it yields a higher NPV ($78,910). However, comparing the NPV of the two projects is only valid because both projects require the same initial cost—$1,000,000. When projects have different investments amounts, compute the profitability index, also called present value index.

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Profitability Index Computes the number of dollars returned for every dollar invested Present value of net cash inflows Investment Profitability index = The profitability index is computed as follows: Profitability index = Present value of net cash inflows divided by Investment The profitability index computes the number of dollars returned for every dollar invested, with all calculations performed in present value dollars. It allows us to compare alternative investments in present value terms (like the NPV method), but it also considers differences in the investments’ initial cost. 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.

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**Equal and Unequal Cash Flows**

If investment is expected to bring in even cash flows, use Present Value of Annuity (PVA) table If amounts are unequal: Present value of each individual cash flow is computed Use Present Value of $1 (PV) table When cash flows are equal in amount, and occur every year, they are an annuity. Therefore, we use the Present Value of Annuity table. If amounts vary by year, managers cannot use the annuity table to compute the present value of a 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.

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**NPV of a Project with Residual Value**

Residual Values Cash inflows at the end of their useful lives Its present value is added to determine the total present value of the project(s) Discounted as a single lump sum 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—not an annuity—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.

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**Internal Rate of Return (IRR)**

Another discounted cash flow model for capital budgeting Rate of return a company can expect to earn by investing in the project The interest rate that will cause the present value to equal zero Present value of the investment’s net cash inflows – Investment’s cost (Present value of cash outflows) $ 0 Another discounted cash flow model for capital budgeting is the internal rate of return. The internal rate of return (IRR) is the rate of return (based on discounted cash flows) a company can expect to earn by investing in a capital asset. It is the interest rate that makes the NPV of the investment equal to zero. IRR = Present value of the investment’s net cash inflows – Investment’s cost (Present value of cash outflows) = 0 In other words, the IRR is the interest rate that makes the cost of the investment equal to the present value of the investment’s net cash inflows. The higher the IRR, the more desirable the project.

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IRR Decision Rule The internal rate of return measures the real rate of return provided by the project. Higher return better Lower return worse To decide whether the project is acceptable, compare the IRR with the minimum desired rate of return. If the IRR exceeds the required rate of return, invest. If the IRR is less than the required rate of return, do not invest. Many times, the exact factor will not appear in the table. If this happens, say a 4.00 factor find the closest two factors is found between (at 14%) and (at 12%). Thus, the IRR must be somewhere between 12% and 14%.

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Demo: IRR

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**Net Present Value vs. Internal Rate of Return**

NPV is easier to use. NPV Provides $$ results to compare: $$ pay the bills! IRR provides a comparable % return vs. strict dollar value. This can facilitate better evaluation of different scale/size/cost projects. Too much voodoo math?

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**Ranking Investment Projects using the Profitability Index**

The Profitability Index factors in the investment size. This allows easier comparison amongst different size projects. The higher the profitability index, the more desirable the project. This provides the easily comparable result of IRR with most of the simplicity of NPV. Profitability Present value of the project index Investment required =

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**Ranking Investment Projects using the Profitability Index**

Profitability Net Present Value index Investment required = The higher the profitability index, the more desirable the project.

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**Computing IRR: Equal Cash Flows**

Steps for computing the IRR of an investment with equal periodic cash flows: IRR is the interest rate that makes the cost of the investment equal to the present value of the investment’s net cash inflows Plug into the equation any information we do know Rearrange the equation and solve for the Annuity PV factor (i = ?, n = 5) Find the interest rate that corresponds to this Annuity PV factor If an investment will result in equal annual cash flows, the computation of the internal rate of return is as follows: Divide the cost of the investment by the annual net cash flow. The results is the present value of annuity factor. Using the PVA table, locate the row where the number of periods equals the life of the asset. Go across the row, until you find the factor that is closest to the amount in step one. Look at the column heading to determine the interest rate.

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**Computing IRR: Equal Cash Flows**

Consider Greg’s CD-player project, which would cost $1,000,000 and result in five equal yearly cash inflows of $305,450 Investment’s cost = Amount of each equal net cash inflow X Annuity PV factor $1,000,000 = $305,450 X Annuity PV factor (i = ?, n = 5) $1,000,000 ÷ $305,450 = Annuity PV factor (i = ?, n = 5) $1,000,000 ÷ $305,450 = rounded to 3.274 = Annuity PV factor (i = ?, n = 5) Let’s first consider Greg’s CD-player project, which would cost $1,000,000 and result in five equal yearly cash inflows of $305,450. We compute the IRR of an investment with equal periodic cash flows (annuity) by taking the following steps: The IRR 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 following equation: Investment’s cost equals Present value of investment’s net cash inflows Investment’s cost equals Amount of each equal net cash inflow times Annuity PV factor (i = ?, n = given) 2. Next, we plug in the information we do know—the investment cost, $1,000,000, the equal annual net cash inflows, $305,450, but assume there is no residual value, and the number of periods (five years): $1,000,000 = $305,450 times Annuity PV factor (i = ?, n = 5) 3. We then rearrange the equation and solve for the Annuity PV factor (i = ?, n = 5): $1,000,000 ÷ $305,450 = Annuity PV factor (i = ?, n = 5) 3.274 = Annuity PV factor (i = ?, n = 5) 4. Finally, we find the interest rate that corresponds to this Annuity PV 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(s) with the number closest to the Annuity PV factor you calculated in step 3. The annuity factor is in the 16% column. Therefore, the IRR of the CD-player project is 16%. Greg’s expects the project to earn an internal rate of return of 16% over its life. Exhibit confirms this result. Using a 16% discount rate, the project’s NPV is zero. In other words, 16% is the discount rate that makes the investment cost equal to the present value of the investment’s net cash inflows. To decide whether the project is acceptable, compare the IRR with the minimum desired rate of return.

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**Comparing Capital Budgeting Methods**

Methods that Ignore the Time Value of Money When comparing capital budgeting methods, the payback period and the rate of return ignore the time value of money.

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**Comparing Capital Budgeting Methods**

Methods that Incorporate the Time Value of Money 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. Methods that incorporate the time value of money include net present value and internal rate of return.

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**S21-2 Information For The Next Problems**

Consider how Smith Valley Snow Park Lodge could use capital budgeting to decide whether the $13,500,000 Snow Park Lodge expansion would be a good investment. Assume Smith Valley’s managers developed the following estimates concerning the expansion: Assume that Smith Valley uses the straight-line depreciation method and expects the lodge expansion to have a residual value of $1,000,000 at the end of its 10-year life. Short exercise 21-2 provides information for use in the next problems.

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**Refer to the Smith Valley Snow Park Lodge expansion project in S21-2. **

S21-11: Using discounted cash flow models to make capital investment decisions Refer to the Smith Valley Snow Park Lodge expansion project in S21-2. 1. What is the project’s NPV? Is the investment attractive? Why? PV factor at 10% Net Cash Inflow Total Present Value Present value of annuity of equal annual net cash inflows for 10 years at 10% × $2,658,240 $16,334,885 Present value of residual value .386 × $1,000,000 386,000 Total present value $16,720,885 Investment (13,500,000) Net present value of expansion $ 3,220,885 Short exercise reviews using discounted cash flow models to make capital investment decisions. The expansion is attractive project because its NPV is positive.

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**Annuity PV factor at i=12%, n= 12**

S21-12: Using discounted cash flow models to make capital investment decisions Refer to S21-2. Assume the expansion has no residual value. 1. What is the project’s NPV? Is the investment attractive? Why? Annuity PV factor at i=12%, n= 12 Net Cash Inflow Total Present Value Present value of annuity of equal annual net cash inflows for 12 years at 12% × $2,658,240 $16,334,885 Investment (13,500,000) Net present value of expansion $ 2,834,885 Short exercise also focuses on using discounted cash flow models to make capital investment decisions. Without a residual value, the expansion is still attractive project because it’s NPV is positive

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**1. What is the project’s IRR? Is the investment attractive? Why?**

S21-13: Using discounted cash flow models to make capital investment decisions Refer to S Continue to assume that the expansion has no residual value. 1. What is the project’s IRR? Is the investment attractive? Why? Investment cost = Expected annual net cash inflows × Annuity PV factor (n=10, i = ?) $13,500,000 $2,658,240 Annuity PV factor (n = 10, i = ?) Annuity PV factor (n = 10, i = ?) 5.079 Short exercise also reviews using discounted cash flow models to make capital investment decisions. The IRR is somewhere between %. The project attractive since it will earn a higher return than the company’s 10% hurdle rate.

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Chapter 21Summary Capital budgeting is planning to invest in long-term assets in a way that returns the greatest profitability to the company. Capital rationing occurs when the company has limited assets available to invest in long-term assets. The four most popular capital budgeting techniques used are payback period, rate of return (ROR), net present value (NPV), and internal rate of return (IRR). Capital budgeting is planning to invest in long-term assets in a way that returns the greatest profitability to the company. Capital rationing occurs when the company has limited assets available to invest in long-term assets. The four most popular capital budgeting techniques used are payback period, rate of return (ROR), net present value (NPV), and internal rate of return (IRR).

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Chapter 21Summary The payback period focuses on the time it takes for the company to recoup its cash investment, but ignores all cash flows occurring after the payback period. Because it ignores any additional cash flows (including any residual value), the method does not consider the profitability of the project. The ROR, however, measures the profitability of the asset over its entire life using accrual accounting figures. It is the only method that uses accrual accounting rather than net cash inflows in its computations. The payback period and ROR methods are simple and quick to compute, so managers often use them to screen out undesirable investments. However, both methods ignore the time value of money. The payback period focuses on the time it takes for the company to recoup its cash investment, but ignores all cash flows occurring after the payback period. Because it ignores any additional cash flows (including any residual value), the method does not consider the profitability of the project. The ROR, however, measures the profitability of the asset over its entire life using accrual accounting figures. It is the only method that uses accrual accounting rather than net cash inflows in its computations. The payback period and ROR methods are simple and quick to compute, so managers often use them to screen out undesirable investments. However, both methods ignore the time value of money.

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Chapter 21 Summary Invested money earns income over time. This is called the time value of money, and it 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. The cash inflows and outflows are either single amounts or annuities. An annuity is equal cash flows over equal time periods at the same interest rate. Time value of money tables in Appendix B help us to adjust the cash flows to the same time period (i.e., today or the present value, or a future date or the future value). Invested money earns income over time. This is called the time value of money, and it 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. The cash inflows and outflows are either single amounts or annuities. An annuity is equal cash flows over equal time periods at the same interest rate. Time value of money tables in Appendix B help us to adjust the cash flows to the same time period (i.e., today or the present value, or a future date or the future value).

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Chapter 21 Summary The NPV is the net difference between the present value of the investment’s net cash inflows and the investment’s cost (cash outflows), discounted at the company’s required rate of return (hurdle) rate. The investment must meet or exceed the hurdle rate to be acceptable. The IRR is the interest rate that makes the cost of the investment equal to the present value of the investment’s net cash inflows. Capital investment (budgeting) methods that consider the time value of money (like NPV and IRR) are best for decision making. The NPV is the net difference between the present value of the investment’s net cash inflows and the investment’s cost (cash outflows), discounted at the company’s required rate of return (hurdle) rate. The investment must meet or exceed the hurdle rate to be acceptable. The IRR is the interest rate that makes the cost of the investment equal to the present value of the investment’s net cash inflows. Capital investment (budgeting) methods that consider the time value of money (like NPV and IRR) are best for decision making.

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**Are there any questions?**

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Copyright © 2013 Pearson Education, Inc. All rights reserved Chapter 11 Simple Linear Regression.

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