1. Capital Investment Decisions and the Time Value of Money
Chapter 20
Chapter 20 explains capital investment decisions and the time value of money.

2. Learning Objective 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.

3. Capital Budgeting Making capital investment decisions
Examples include:
Purchasing new equipment
Building new facilities
Automating production
Developing Web sites
Affects operations for many years
Requires large sums of money
The process of making capital investment decisions is often referred to as capital budgeting.
Companies make capital investments when they acquire capital assets—assets used for a long period of time.
Examples of 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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4. Methods of Capital Budgeting
Payback period
Accounting rate of return
Net present value
Internal rate of return
Quick and easy; work well for investments with a shorter life span
Use the time value of money; work well for investments with a longer life span
There are four popular methods of analyzing potential capital investments:
1. Payback period
2. Accounting rate of return (ARR)
3. Net present value (NPV)
4. Internal rate of return (IRR)
The first two methods, payback period and accounting rate of return, are fairly quick and easy and work well for capital investments that have a relatively short life span, such as computer equipment and software. Payback period and accounting rate of return are also used to screen potential investments from those that are less desirable. The payback period 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. Why? 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 predictions about an uncertain future--estimates. These estimates must consider many unknown factors, such as changing consumer preferences, competition, the state of the economy, and government regulations. The further into the future the decision extends, the more likely the actual results will differ from predictions. Long-term decisions are riskier than short-term decisions.
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5. Focus on Cash Flows Operating income differs from cash flows
Cash flows do not include noncash expenses
Cash inflows
Future cash revenue generated
Future savings in ongoing cash operating costs
Future residual value
Cash outflows
Initial investment
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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6. Capital Budgeting Process
Identify potential investments
Project net cash inflows
Analyze using one or more of the methods
Capital rationing
Post-audits
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 investments’ 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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7. Learning Objective 2
Use the payback and accounting rate of return methods to make capital investment decisions
The second learning objective is to use the payback and accounting rate of return methods to make capital investment decisions.

8. Payback Period
Length of time it takes to recover the cost of the capital outlay
Measures how quickly the amount invested will be recovered
The shorter the payback period, the more attractive the asset
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.
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9. Calculating Payback Period
Equal annual net cash inflows
Amount invested
Payback period
Expected annual net cash inflow
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.
Unequal annual net cash inflows
Total net cash inflows until amount equals investment
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10. Criticisms of the Payback Period Method
Focuses only on time, not profitability
Ignores cash flows after the payback period
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.
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11. Payback Period
Payback Period
DECISION RULE:
Investments with shorter payback periods are more desirable, all else being equal.
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.

12. Expected annual net cash inflow
Exercise 20-15
Amount invested
Payback period
Expected annual net cash inflow
$1,300,000
4.1 years
Exercise provides practice calculating the payback period. Stenback Co. is considering acquiring a manufacturing plant. The purchase price is $1,300,000. The owners believe the plant will generate net cash inflows of $314,000 annually. It will have to be replaced in seven years. To compute the payback period, the purchase price is divided by the net annual cash inflows of $314,000. The payback period is slightly over four years.
$314,000
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13. Accounting Rate of Return
Average annual operating income from asset
Average amount invested in asset
Companies are in business to earn profits.
One measure of profitability is the accounting rate of return (ARR) on an asset.
The ARR focuses on the operating income that an asset generates, not the net cash inflow.
The ARR measures the average rate of return over the asset’s entire life.
The formula to compute accounting rate of return is the average annual operating income from the asset divided by the average amount invested in the asset.
To determine the average investment, the original cost of the investment plus any residual value is divided by two.
Original investment + Residual value 2
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14. Accounting Rate of Return
DECISION RULE: Invest in capital assets?
If expected accounting rate of return exceeds the required rate of return?
Invest
If expected accounting rate of return is less than required rate of return?
Do not invest
Companies that use the ARR model set a minimum required accounting rate of return.
When choosing among several acceptable projects,
the higher the rate of return for a given risk, the more attractive the investment.
The decision rule for the accounting rate of return states that
a company should invest in a capital asset if its expected rate is greater than the required rate.

15. ?Review?
Questions?
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16. 1. Which of the following decisions would NOT fall under capital budgeting? A. Purchasing new equipment B. Building a new facility C. Buying a short-term investment D. Automating production
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17. 1. Which of the following decisions would NOT fall under capital budgeting? A. Purchasing new equipment B. Building a new facility C. Buying a short-term investment D. Automating production
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18. 2. When estimating future cash inflows from a capital investment, which of the following are included? A. Future cash revenue generated B. Future savings in operating costs C. Future residual value D. All of the above
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19. 2. When estimating future cash inflows from a capital investment, which of the following are included? A. Future cash revenue generated B. Future savings in operating costs C. Future residual value D. All of the above
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20. 3. The decision rule regarding the payback period states that the: A
3. The decision rule regarding the payback period states that the: A. shorter the payback period, the more attractive the investment. B. longer the payback period, the more attractive the investment. C. payback period should exceed the asset’s life. D. payback period should be compared to the internal rate of return.
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21. 3. The decision rule regarding the payback period states that this: A
3. The decision rule regarding the payback period states that this: A. shorter the payback period, the more attractive the investment. B. longer the payback period, the more attractive the investment. C. payback period should exceed the asset’s life. D. payback period should be compared to the internal rate of return.
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22. 4. A criticism of the payback period is that it: A
4. A criticism of the payback period is that it: A. uses operating income instead of cash flows. B. focuses only on the time value of money. C. de-emphasizes risk of assets with longer lives. D. ignores cash flows after the payback period.
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23. 4. A criticism of the payback period is that it: A
4. A criticism of the payback period is that it: A. uses operating income instead of cash flows. B. focuses only on the time value of money. C. de-emphasizes risk of assets with longer lives. D. ignores cash flows after the payback period.
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24. 5. The unique element of the accounting rate of return method is: A
5. The unique element of the accounting rate of return method is: A. its focus on operating income instead of cash flows. B. its use of time value of money. C. that it ignores cash flows later in the asset’s life. D. that it generates a unique rate of return.
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25. 5. The unique element of the accounting rate of return method is: A
5. The unique element of the accounting rate of return method is: A. its focus of operating income instead of cash flows. B. its use of time value of money. C. that it ignores cash flows later in the asset’s life. D. that it generates a unique rate of return.
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26. Objective 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.

27. Time Value of Money Invested money earns income over time
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. 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.
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28. Factors That Affect Time Value of Money
Principal (p) – amount of the investment
Lump sum
Annuity
Stream of equal installments at regular time periods
Number of periods (n)
From the beginning of the investment until termination
Interest rate (i) – annual percentage
Simple interest
Calculated only on principal
Compound interest
Interest earned is added to principal
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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29. Present and Future Value Along a Time Continuum
Present value
Future value
Future value
Consider the time line 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.
Present value
Interest earned
Present value
Future value
Interest earned
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30. Factors for Present Value and Future Value
Mathematical formulas developed to compute present and future values
These factors are programmed into business calculators and spreadsheet programs
See Appendix B for present and future factor tables:
Present Value of $1 & Future Value of $1 – for lump sum amounts (one-time investments)
Present Value of Annuity & Future Value of Annuity – for a series of equal installments
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 book.
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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31. Using PV and FV factors Lump sum Annuity
Multiply amount by factor found in table
Table based on interest rate and number of periods
Annuity
Multiply one period’s installment by the factor found in the table
To find the future value of an amount, you multiply the FV factor by the Present amount.
To find the present value of an amount other than $1, you multiply the PV factor by the future amount.
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.
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32. Use discounted cash flow models to make capital investment decisions
Objective 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.

33. Discounted Cash Flows Models
Recognize time value of money
Two methods:
Net present value (NPV)
Internal rate of return (IRR)
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 comparison
Neither the payback period nor the ARR 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 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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34. Net Present Value (NPV)
Present value of net cash inflows
Less: Investment cost
Equals: Net present value
Interest rate used is desired rate of return
The higher the risk, the higher the rate
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.
Also called “discount rate”
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35. DECISION RULE: Invest in capital assets?
Net Present Value
DECISION RULE: Invest in capital assets?
If NPV is positive
Invest
If NPV is negative
Do not invest
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. This leads to the decision rule shown here.

36. 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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37. Exercise 20-23 Project A Present value of net cash inflows $ 264,423
57,000 x (PVA 14%, 8 periods)
Investment cost
(290,000)
Net present value
($25,557)
Exercise provides practice using the NPV method. Use the NPV method to determine whether Stenback Products should invest in the following projects:
Project A: Costs $290,000 and offers eight annual net cash inflows of $57,000. Stenback Products requires an annual return of 14% on projects like A.
Computations show that Project A has a negative present value. The present value of the cash flows are less than the cost. Stenback should not accept this project. The most it should invest in Project A is $264,423.
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38. Exercise 20-23 (continued)
Project B
Present value of net cash inflows
$410,256
77,000 x (PVA 12%, 9 periods)
Investment cost
(380,000)
Net present value
$30,256
Project B: Costs $380,000 and offers nine annual net cash inflows of $77,000. Stenback Products demands an annual return of 12% on investments of this nature.
Project B has a positive net present value. Stenback should accept this project and could pay up to $410,256.
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39. Present value of net cash inflows
Profitability Index
Number of dollars returned for every dollar invested
Present value of net cash inflows
To choose among the projects, companies compute the profitability index (also known as the present value index). The profitability index is computed as the present value of net cash inflows divided by the 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 also considers differences in the investments’ initial cost.
Investment
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40. Internal Rate of Return (IRR)
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
Investment’s cost
Present value of net cash flows
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 the project.
It is the interest rate that makes the NPV of the investment equal to zero.
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41. Computing IRR: Equal Cash Flows
Investment’s cost
PVA Factor
Annual net cash inflow
Locate PVA factor in table using the project’s life as the number of periods
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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42. Internal Rate of Return
DECISION RULE: Invest in capital assets?
If the IRR exceeds the required rate of return?
Invest
If the IRR is less than required rate of return?
Do not invest
To decide whether the project is acceptable, compare the IRR with the minimum desired rate of return.
The decision rule is shown here.

43. Comparing Capital Budgeting Methods
Methods that Ignore the Time Value of Money
Payback Period
Accounting rate of return
Simple to compute
Uses accrual accounting
Focuses on time it takes to recover cost of asset
Shows how investment will impact operating income, which is important to investors
Ignores cash flows after the payback period
Highlights risks of assets with longer cash recovery periods
Measures the profitability over the asset’s life
Ignores time value of money
This table compares the two methods that do not use the time value of money –
the payback period and the accounting rate of return.
The main benefit of the payback period is that it is simple and highlights the risks of assets with longer recovery periods.
The accounting rate of return is the only method that uses accrual accounting,
and thus estimates operating income, which is important to investors.

44. Comparing Capital Budgeting Methods
Methods that Incorporate the Time Value of Money
Net present value
Internal rate of return
Uses time value of money and asset’s cash flows over its entire life
Indicates whether the asset will earn the minimum required rate of return
Computes the project’s unique rate of return
Shows excess or deficiency of asset’s present value of net cash flows over its initial cost
Profitability index should be computed when assets have differing investment amounts
No additional steps needed for capital rationing decisions
The two methods that use the time value of money are the net present value method and the internal rate of return. The net present value method results in a dollar amount that  indicates if the initial cost is greater or less than the present value of the investment’s cash flows.
The profitability index should be used to compare investments with differing initial costs. The internal rate of return computes the project’s unique rate of return. It is not necessary to use a profitability index with IRR.

45. ?Review ?
Question?
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46. 6. You want to invest in an account today that earns 10% interest, so that you can have a $10,000 down payment on a home in five years. The formula used to compute the amount to invest is: A. PV factor (i = 10%, n = 5) x $10,000. B. Annuity PV factor (i = 10%, n = 5) x $10,000. C. FV factor (i = 10%, n = 5) x $10,000. D. Annuity FV factor (i = 10%, n = 5) x $10,000.
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47. 6. You want to invest in an account today that earns 10% interest, so that you can have a $10,000 down payment on a home in five years. The formula used to compute the amount to invest is: A. PV factor (i = 10%, n = 5) x $10,000. B. Annuity PV factor (i = 10%, n = 5) x $10,000. C. FV factor (i = 10%, n = 5) x $10,000. D. Annuity FV factor (i = 10%, n = 5) x $10,000.
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48. 7. What factor affects the time value of money. A
7. What factor affects the time value of money? A. Principal – the amount of the invested B. Interest rate C. Time amount is invested D. All of the above
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49. 7. What factor affects the time value of money. A
7. What factor affects the time value of money? A. Principal – the amount of the invested B. Interest rate C. Time amount is invested D. All of the above
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50. 8. Which of the following capital budgeting methods uses the time value of money? A. Payback period B. Accounting rate of return C. Internal rate of return D. All of the above
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51. 8. Which of the following capital budgeting methods uses the time value of money? A. Payback period B. Accounting rate of return C. Internal rate of return D. All of the above
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52. 9. The profitability index would most likely be used with which of the following capital budgeting methods? A. Payback period B. Accounting rate of return C. Internal rate of return D. Net present value method
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53. 9. The profitability index would most likely be used with which of the following capital budgeting methods? A. Payback period B. Accounting rate of return C. Internal rate of return D. Net present value method
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54. 10. Which of the following capital budgeting methods sets the cost of the investment to equal the present value of its expected cash inflows? A. Payback period B. Accounting rate of return C. Internal rate of return D. Net present value
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55. 10. Which of the following capital budgeting methods sets the cost of the investment to equal the present value of its expected cash inflows? A. Payback period B. Accounting rate of return C. Internal rate of return D. Net present value
Copyright (c) 2009 Prentice Hall. All rights reserved.

56. End of Chapter 20
This concludes Chapter 20.