1. Financial & Managerial Accounting Information for Decisions
Seventh Edition
Chapter 24
Capital Budgeting and Investment Analysis
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2. Learning Objectives
ANALYTICAL A1 Analyze a capital investment project using break-even time. PROCEDURAL P1 Compute payback period and describe its use. P2 Compute accounting rate of return and explain its use. P3 Compute net present value and describe its use. P4 Compute internal rate of return and explain its use.

3. Capital Budgeting (1 of 2)
Capital budgeting is the process of analyzing alternative long-term investments and deciding which assets to acquire or sell.
Capital Budgeting Process:
Department or plant manager submits proposals
Capital budget committee evaluates proposals
Board of directors approves capital expenditures.
Capital budgeting is the process of analyzing alternative long-term investments and deciding which assets to acquire or sell. Common examples include buying a machine or a building, or acquiring an entire company. An objective for these decisions is to earn a satisfactory return on investment.
Capital budgeting decisions require careful analysis because they are usually the most difficult and risky decisions that managers make.
The process begins with department or plant managers submitting proposals for new investments in property, plant, and equipment. A capital budget committee, usually comprised of members with accounting and finance expertise, evaluates the proposals and forms recommendations for approval or rejection. Finally, the board of directors approves the capital expenditures for the year.

4. Capital Budgeting (2 of 2)
Capital budgeting decisions require careful analysis because they are usually the most difficult and risky decisions that managers make. Specifically, a capital budgeting decision is risky because:
Outcome is uncertain.
Large amounts of money are usually involved.
Investment involves a long-term commitment.
Decision may be difficult or impossible to reverse.
Capital budgeting decisions require careful analysis because they are usually the most difficult and risky decisions that managers make. Specifically, a capital budgeting decision is risky because (1) the outcome is uncertain, (2) large amounts of money are usually involved, (3) the investment involves a long-term commitment, and (4) the decision could be difficult or impossible to reverse, no matter how poor it turns out to be. Risk is especially high for investments in technology due to innovations and uncertainty.

5. Capital Budgeting Cash OutFlows and InFlows
Common Cash Outflows and Inflows over life of typical capital expenditures:
Acquisition – initial cash outflow
Use – generates cash inflows from revenues
Disposal – salvage value can provide cash inflow
Managers use several methods to evaluate capital budgeting decisions. Nearly all of these methods involve predicting future cash inflows and cash outflows of proposed investments, assessing the risk of and returns on those cash flows, and then choosing the investments to make.
The process begins with an initial cash outflow to acquire the depreciable asset. Over that asset’s life, it generates cash inflows from revenues. The machine also creates cash outflows for operating costs, repairs, and maintenance. Finally, the machine is disposed of, and its salvage value can provide another cash inflow.
The time value of money is important when evaluating capital investments, but managers sometimes use methods that ignore it. This section describes four methods for evaluating capital spending proposals.

6. Learning Objective P1: Compute payback period and describe its use.

7. Learning Objective P1: Compute payback period and describe its use..
The payback period of an investment is the amount of time it takes a project to recover its initial investment amount.
All investments, whether they involve the purchase of a machine or another long-term asset, are expected to produce net cash flows. Net cash flow is cash inflows minus cash outflows. Sometimes managers perform simple analyses of the financial feasibility of an investment’s net cash flow without using the time value of money
The payback period is the expected amount of time it takes a project to recover its initial investment amount. If the cash inflows of an investment are equal in each year, we can calculate the payback period by dividing the cost of the investment by the annual net cash inflows. Managers prefer investing in assets with shorter payback periods to reduce the risk of an unprofitable investment over the long run.
Managers prefer investing in projects with shorter payback periods.

8. Payback Period with Even Cash Flows
Learning Objective P1: Compute payback period and describe its use..
FasTrac is considering buying a new machine:
Cost……………………………………………
$16,000
Useful life…………………………………..
8 years
Salvage value……………………………..
$ 0
Expected production………………….
30,000 units
Product selling price per unit……..
$ 30
The management at FasTrac is considering a new machine to use in its manufacturing operations. The new machine has these features:
Cost…………………………………… $16,000
Useful life……………………………… years
Salvage value…………………………. $ 0
Expected production…………………30,000 units
Product selling price per unit…… $ 30
Because the net annual cash inflows are the same each year, we can calculate the payback period easily by dividing the machine’s cost by its annual net cash flows. The payback period is 3.9 years. The new machine will return its original cost in annual net cash flows in 3.9 years, less than half of its expected useful life of 8 years.
The amount of net cash flow from the machinery is computed by subtracting expected cash outflows from expected cash inflows. The Expected Net Cash Flow column of Exhibit 25.4 excludes all noncash revenues and expenses. Since depreciation does not impact cash flows, it is excluded.
Management at FasTrac may have an investment decision rule such as: invest only in projects with a payback period of 5 years or less. If so, the company would invest in the new machine because its payback period is less than 5 years.
Calculate the payback period.

9. Payback Period with Uneven Cash Flows (1 of 4)
Learning Objective P1: Compute payback period and describe its use..
In the previous example, we assumed that the increase in cash flows would be the same each year. Now, let’s look at an example where the cash flows vary each year.
Let’s complicate the payback computation a bit by using unequal annual net cash flows for the same machine.
In this case, the payback period is computed using the cumulative total of net cash flows. The word cumulative refers to the addition of each period’s net cash flows as we progress through time.

10. Payback Period with Uneven Cash Flows (2 of 4)
Learning Objective P1: Compute payback period and describe its use..
FasTrac wants to install a machine that costs $16,000 and has an 8-year useful life with 0 salvage value. Annual net cash flows are: To get the payback period when we have unequal annual net cash flows, we must add the cash flows each year until the total equals the cost of the investment.
Instead of a constant amount of $4,100 per year, annual net cash flows for the new machine now vary from a low of $2,000 to a high of $5,000 per year. We can no longer divide the cost of the new machine by an equal annual net cash inflow to get the payback period.
To get the payback period when we have unequal annual net cash flows, we must add the cash flows each year until the total equals the cost of the investment. Year 0 refers to the date of initial investment at which the $16,000 cash outflow occurs to acquire the machinery. By the end of year 1, the cumulative net cash flow is reduced to $(13,000), computed as the $(16,000) initial cash outflow plus year 1’s $3,000 cash inflow. This process continues throughout the asset’s life.
FasTrac recovers the $16,000 investment cost between 4 and 5 years. So, we can estimate the payback period at about 4.2 years.
Now let’s review what you have learned in the following NEED-TO-KNOW exercise.

11. Payback Period with Uneven Cash Flows (3 of 4)
Learning Objective P1: Compute payback period and describe its use..
Exhibit 24.5
Period*
Expected Net Cash Flows
Cumulative Net Cash Flows
Year 0……………..
$(16,000)
Year 1……………..
3,000
(13,000)
Year 2……………..
4,000
(9,000)
Year 3……………..
(5,000)
Year 4……………..
(1,000)
Year 5……………..
5,000
Year 6……………..
7,000
Year 7……………..
2,000
9,000
Year 8……………..
11,000

12. Payback Period with Uneven Cash Flows (4 of 4)
Learning Objective P1: Compute payback period and describe its use..
Payback occurs between years 4 & 5  1,000 and 4,000
Payback occurs between years 4 and 5  payback period of 4.2 years
Payback period = 4 years + $1,000/$5,000 of year 5 = 4.2 years

13. Evaluating the Payback Period
Learning Objective P1: Compute payback period and describe its use..
Payback period has two strengths:
Uses cash flows, not income
Easy to use
Payback period has three major weaknesses:
1. Does not reflect differences in the timing of net cash flows
2. Ignores all cash flows occurring after the point where an investment’s costs are fully recovered
3. Ignores the time value of money
Companies like short payback periods to increase return and reduce risk. The more quickly a company receives cash, the sooner it is available for other uses and the less time it is at risk of loss. A shorter payback period also improves the company’s ability to respond to unanticipated changes and lowers its risk of having to keep an unprofitable investment.
Payback period has two strengths:
1. It uses cash flows, not income.
It is easy to use.
Payback period has three major weaknesses:
1. It does not reflect differences in the timing of net cash flows within the payback period.
2. It ignores all cash flows occurring after the point where an investment’s costs are fully recovered.
It ignores the time value of money.
To illustrate, if FasTrac had another investment with predicted cash inflows of $9,000, $3,000, $2,000, $1,800, and $1,000 in its first five years, its payback period would also be 4.2 years. However, this alternative is more desirable because it returns cash more quickly. In addition, an investment with a 3-year payback period that stops producing cash after 4 years is likely not as good as an alternative with a 5-year payback period that generates net cash flows for 15 years. Because of these limitations, payback period should never be the only consideration in capital budgeting decisions.

14. Learning Objective P1: Compute payback period and describe its use..
NEED-TO-KNOW 24-1 (1 of 3)
Learning Objective P1: Compute payback period and describe its use..
A company is considering purchasing equipment costing $75,000. Future annual net cash flows from this equipment are $30,000, $25,000, $15,000, $10,000, and $5,000. Cash flows occur uniformly during the year. What is this investment's payback period?
A company is considering purchasing equipment costing $75,000. Future annual net cash flows from this equipment are $30,000, $25,000, $15,000, $10,000, and $5,000. Cash flows occur uniformly during the year. What is this investment's payback period?
The payback period is the point in time where cumulative cash inflows, ignoring the time value of money, are exactly equal to the cost of the investment.
We start out with an immediate cash payment of $75,000 to acquire the equipment.
In the first year, net cash flow is $30,000. $30,000 of the machine’s cost has been “paid back”, with a remaining $45,000 to go.
In year 2, net cash flow is $25,000, bringing the cumulative net cash flow to a negative $20,000.
In year 3, net cash flow is $15,000, $5,000 of the machine’s cost is still unpaid.
In year 4, net cash flow is $10,000, bringing the cumulative net cash flow to a positive $5,000.
Since the investment has gone from a net cash outflow of $5,000 to a net cash inflow of $5,000, the investment is repaid between years 3 and 4. The payback period is greater than 3 years, but less than 4 years.
To calculate the fraction of the year, the numerator is equal to the net cash outflow at the end of year 3, still $5,000 of the investment is unpaid, and the denominator is the amount of the net cash inflow during year 4, $10,000.
The fraction of the year is .5.
The payback period = 3.5 years.

15. Expected Net Cash Flows Cumulative Net Cash Flows
NEED-TO-KNOW 24-1 (2 of 3)
Learning Objective P1: Compute payback period and describe its use..
Period
Expected Net Cash Flows
Cumulative Net Cash Flows
Year 0
($75,000)
Year 1
30,000
(45,000)
Year 2
25,000
(20,000)
Year 3
15,000
(5,000)
Year 4
10,000
5,000
Year 5
Payback between the end of Year 3 and the end of Year 4

16. Learning Objective P1: Compute payback period and describe its use..
NEED-TO-KNOW 24-1 (3 of 3)
Learning Objective P1: Compute payback period and describe its use..
Payback = 3.5 years

17. Learning Objective P2: Compute accounting rate of return and explain its use.

18. Accounting Rate of Return (1 of 3)
Learning Objective P2: Compute accounting rate of return and explain its use.
Two Ways to Calculate Average Annual Investment
The accounting rate of return is the percentage accounting return on annual average investment. It is called an "accounting" return because it is based on net income, rather than on cash flows. It is computed by dividing a project’s after-tax net income by the annual average amount invested in it. The annual average investment in assets is the average book value. If a company uses straight-line depreciation, we can compute the annual average investment as the average of its beginning and ending book values. If a company uses a depreciation method other than straight-line, for example MACRS for tax purposes, the calculation of average book value is more complicated. In this case, the book value of the asset is computed for each year of its life. A general formula for the annual average investment is also shown in this slide.
When accounting rate of return is used to choose among capital investments with similar lives and risk, a company will prefer the investment with the higher accounting rate of return.

19. Accounting Rate of Return (2 of 3)
Learning Objective P2: Compute accounting rate of return and explain its use.
When comparing investments with similar lives and risk, a company will prefer the investment with the higher accounting rate of return.

20. Accounting Rate of Return (3 of 3)
Learning Objective P2: Compute accounting rate of return and explain its use.
Let’s revisit the $16,000 investment being considered by FasTrac. The new machine has an annual after-tax net income of $2,100. Compute the accounting rate of return. Annual Average Investment Calculation:
FasTrac’s new machine costs $16,000 and has an annual after-tax net income of $2,100.
We need to compute the annual average investment, which is calculated as beginning book value plus the ending book value divided by 2. For FasTrac, the beginning book value is $16,000 and, since there is no salvage value, the ending book value is 0. Dividing $16,000 by 2 yields an $8,000 annual average investment. Now, divide the annual after-tax net income of $2,100 by the annual average investment of $8,000 to arrive at the accounting rate of return of 26.25%. FasTrac’s management must decide whether a 26.25% accounting rate of return is satisfactory. To make this decision, we must factor in the investment’s risk. For instance, we cannot say an investment with a 26.25% return is preferred over one with a lower return unless we consider any differences in risk. When comparing investments with similar lives and risk, a company will prefer the investment with the higher accounting rate of return.

21. Evaluating Accounting Rate of Return
Learning Objective P2: Compute accounting rate of return and explain its use.
Accounting Rate of Return has three major weaknesses:
Ignores time value of money
Focuses on income, not cash flows
If income varies each year, project may appear desirable in some years and not in others
The accounting rate of return has three major weaknesses:
1. It ignores the time value of money.
2. It focuses on income, not cash flows.
3. If income (and thus the accounting rate of return) varies from year to year, the project might appear desirable in some years and not in others.
Because of these limitations, the accounting rate of return should never be the only consideration in capital budgeting decisions.
Now let’s review what you have learned in the following NEED-TO-KNOW exercise.

22. NEED-TO-KNOW 24-2 (1 of 2)
Learning Objective P2: Compute accounting rate of return and explain its use.
The following data relate to a company’s decision on whether to purchase a machine:
Cost
$180,000
Salvage value
15,000
Annual after-tax net income
40,000
The following data relate to a company’s decision on whether to purchase a machine:
Assume net cash flows occur uniformly over each year and the company uses straight-line depreciation.
What is the machine's accounting rate of return?
The Accounting Rate of Return (ARR) measures the amount of net income generated from a capital investment.
It's calculated by taking the annual after-tax net income and dividing by the annual average investment.
The annual average investment is calculated by taking cost plus salvage and dividing by two.
$40,000 of annual after-tax net income divided by the asset's cost, $180,000, plus the salvage value, $15,000, $195,000, divided by two.
$40,000 divided by $97,500
is an accounting rate of return of 41%.
Assume net cash flows occur uniformly over each year and the company uses straight-line depreciation. What is the machine's accounting rate of return?

23. NEED-TO-KNOW 24-2 (2 of 2)
Learning Objective P2: Compute accounting rate of return and explain its use.
The Accounting Rate of Return (ARR) measures the amount of net income generated from a capital investment.

24. Learning Objective P3: Compute net present value and describe its use.

25. Learning Objective P3: Compute net present value and describe its use.
Net Present Value (1 of 2)
Learning Objective P3: Compute net present value and describe its use.
Net present value analysis applies the time value of money to future cash inflows and cash outflows so management can evaluate a project’s benefits and costs at one point in time.
We calculate Net Present Value (NPV) by:
Discount the future net cash flows from the investment at the required rate of return.
Subtract the initial amount invested from sum of the discounted cash flows.
Net present value analysis applies the time value of money to future cash inflows and cash outflows so management can evaluate a project’s benefits and costs at one point in time. Specifically, net present value (NPV) is computed by discounting the future net cash flows from the investment at the project’s required rate of return and then subtracting the initial amount invested. A company’s required return, often called its hurdle rate, is typically its cost of capital, which is the rate the company must pay to its long-term creditors and shareholders.

26. Learning Objective P3: Compute net present value and describe its use.
Net Present Value (2 of 2)
Learning Objective P3: Compute net present value and describe its use.
A company’s required return, often called its hurdle rate, is typically its cost of capital, which is the rate the company must pay to its long-term creditors and shareholders.

27. Net Present Value with Equal Cash Flows (1 of 3)
Learning Objective P3: Compute net present value and describe its use.
FasTrac is considering the purchase of a machine costing $16,000, with an 8-year useful life and zero salvage value, that promises annual net cash inflows of $4,100. FasTrac requires a 12 percent annual return on its investments.
FasTrac’s new machine will cost $16,000. It has an eight-year useful life, zero salvage value, and promises annual net cash inflows of $4,100. FasTrac requires a 12 percent annual return on its investments.
To find the present value of a future cash flow, we multiply the annual net cash flow from the first column of the exhibit by the discount factor in the second column (which is the present value of one dollar for 12 percent and the year in which the cash flow occurs). The result, is the present value of the annual cash flow and that is shown in the third column. The present value factors in the exhibit can be found in Table B.1 of Appendix B of your textbook.
To find the net present value, we sum the present values for each year and then subtract the cost of the new machine from the sum. The sum of present values is greater than the cost of the investment, resulting in a net present value of $4,367 dollars. A positive net present value indicates that this project earns more than 12 percent on the investment of $16,000 and FasTrac should invest in the machine. Rule: If NPV > 0, invest.

28. Net Present Value with Equal Cash Flows (2 of 3)
Learning Objective P3: Compute net present value and describe its use.
Exhibit 24.9
Net Cash Flows*
Present Value of 1 at 12%**
Present Value of Net Cash Flows
Year 1…………………………….
$ 4,100
0.8929
$ 3,661
Year 2…………………………….
4,100
0.7972
3,269
Year 3…………………………….
0.7118
2,918
Year 4…………………………….
0.6355
2,606
Year 5…………………………….
0.5674
2,326
Year 6…………………………….
0.5066
2,077
Year 7…………………………….
0.4523
1,854
Year 8…………………………….
0.4039
1,656
Totals……………………………..
$ 32,800
20,367
Initial Investment…….
(16,000)
Net present value……..
$ 4,367
*Cash flows occur at the end of each year

29. Net Present Value with Equal Cash Flows (3 of 3)
Learning Objective P3: Compute net present value and describe its use.
FasTrac should invest in the machine because NPV > 0!

30. Net Present Value Decision Rule
Learning Objective P3: Compute net present value and describe its use.
When an asset's expected future cash flows yield a positive net present value when discounted at the required rate of return, the asset should be acquired.
Present value of net cash flows ($) – Amount Invested ($) = Net present value ($)
Net present value ($)
If NPV > $0, Invest
If NPV < $0, Do not Invest
When comparing several investment opportunities of similar cost and risk, we prefer the one with the highest positive net present value.
The decision rule in applying NPV is as follows: when an asset's expected future cash flows yield a positive net present value when discounted at the required rate of return, the asset should be acquired. This decision rule is reflected in the graphic on this slide. If the net present value is zero or positive, the project is acceptable since the promised return is equal to or greater than the required rate of return. When we have a negative net present value, the project is not acceptable. When comparing several investment opportunities of similar cost and risk, we prefer the one with the highest positive net present value.

31. Net Present Value with Uneven Cash Flows (1 of 2)
Learning Objective P3: Compute net present value and describe its use.
Exhibit 24.10
Net Cash Flows: A
Net Cash Flows: B
Net Cash Flows: C
Present Value of 1 at 10%
Present Value of Net Cash Flows: A
Present Value of Net Cash Flows: B
Year 1…………..
$ 5,000
$ 8,000
$ 1,000
0.9091
$ 4,546
$ 7,273
$ 909
Year 2……………
5,000
0.8264
4,132
Year 3……………
2,000
9,000
0.7513
3,757
1,503
6,762
Totals…………….
$ 15,000
$15,000
12,435
12,908
11,803
Initial Investment…
(12,000)
Net present value….
$ 435
$ 908
$ (197)
Net present value analysis can also be used when net cash flows are uneven (unequal). In this example, we see why investments that have larger returns in the early years are preferable to investments that have larger returns in later years. Each investment returns $15,000 in total cash flows over a three-year period. Each investment costs $12,000, but Project B has a larger cash flow in the first year and therefore has a larger net present value. Project C has a lower cash flow in the first year and therefore has a smaller net present value. The present value of 1 factors assuming 10% required return shown in the chart above, can be found in Table B.1 in Appendix B.
Now let’s review what you have learned in the following NEED-TO-KNOW exercise.

32. Net Present Value with Uneven Cash Flows (2 of 2)
Learning Objective P3: Compute net present value and describe its use.
Although all projects require the same investment and have the same total net cash flows, Project B has a higher net present value because of a larger net cash flow in Year 1.

33. Comparing Positive NPV Projects (1 of 2)
Learning Objective P3: Compute net present value and describe its use.
One way to compare projects when a company cannot fund all positive net present value projects.
When considering several projects of similar investment amounts and risk levels, we can compare the different projects’ NPVs and rank them on the dollar amounts of their NPV’s. However, if the amount invested differs substantially across projects, the NPV is of limited value for comparison purposes. One way to compare projects, especially when a company cannot fund all positive net present value projects, is to use the profitability index, which is computed as the present value of net cash flows for a project divided by its initial investment amount.
On this slide, we see the computation of the profitability index for three potential investments. A profitability index less than 1 indicates an investment with a negative NPV so Investment #3 would be ruled out. Both Investments #1 and #2 have profitability indexes greater than 1, thus they have positive NPVs. If the company was forced to choose, it should select investment #2 as it has the highest profitability index.

34. Comparing Positive NPV Projects (2 of 2)
Learning Objective P3: Compute net present value and describe its use.
Exhibit illustrates the computation of the profitability index for three potential investment. 1 2 3
Present value of net cash flows (a)
$900,000
$375,000
$270,000
Amount invested (b)
750,000
250,000
300,000
Profitability index (a) ÷ (b)
1.2
1.5
0.90
Profitability index, 1.5: Investment #2 has the highest profitability index so it should be chosen. Profitability index, 0.90: A profitability index less than 1 indicates an investment with a negative NPV so Investment #3 would be ruled out.

35. Learning Objective P3: Compute net present value and describe its use.
Capital Rationing
Learning Objective P3: Compute net present value and describe its use.
Capital rationing − constraints that limit firms from accepting all positive NPV projects. Two forms:
Hard rationing − imposed by external forces
Soft rationing − internally imposed by management
Some firms face capital rationing, or financing constraints that limit them from accepting all positive NPV projects. This can be in two forms, hard rationing and soft rationing. Hard rationing is imposed by external forces, such as debt covenants that restrict the firm’s ability to borrow more money. Soft rationing is internally imposed by management and the board of directors. For example, management might place spending limits on certain employees until they show they can make good decisions. Whether due to hard or soft capital rationing, the profitability index can be used to select the best of several competing projects.

36. Learning Objective P3: Compute net present value and describe its use.
NEED-TO-KNOW 24-3 (1 of 4)
Learning Objective P3: Compute net present value and describe its use.
A company can invest in only one of two projects, A or B. Each project requires a $20,000 investment and is expected to generate end-of-period, annual cash flows as follows:
A company can invest in only one of two projects, A or B.
Each project requires a $20,000 investment and is expected to generate end-of-period, annual cash flows as follows:
Assuming a discount rate of 10%, which project has the higher net present value? Net present value is calculated by subtracting the present value of the cash outflows from the present value of the cash inflows. If the investment’s net present value is positive, it's an acceptable investment.
Project A has three annual cash flows of different amounts. To convert these future values to their present value, we multiply by the factor found in the Present Value of 1 chart, Table B.1.
At a required return of 10%, the one payment of $12,000 received one year from now is the equivalent of payments of $12,000 today, $10,909.
One payment of $8,500 received two years from now is the equivalent of payments of $8,500 today, $7,024.
The final payment of $4,000 received three years from now is the equivalent of payments of $4,000 today, $3,005.
The present value of the cash inflows, $20,938, less the present value of the cash outflow, the immediate payment of $20,000 today is a net present value of $938. Since the net present value is positive, the investment return is greater than 10%.
Net Cash Inflows: Year 1
Net Cash Inflows: Year 2
Net Cash Inflows: Year 3
Total
Project A
$12,000
$8,500
$4,000
$24,500
Project B
4,500
8,500
13,000
26,000

37. Learning Objective P3: Compute net present value and describe its use.
NEED-TO-KNOW 24-3 (2 of 4)
Learning Objective P3: Compute net present value and describe its use.
Assuming a discount rate of 10%, which project has the higher net present value?
Project A
Net Cash Inflows
PV of $1 at 10%
PV of Net Cash Inflows
Year 1
$12,000
0.9091
$10,909
Year 2
8,500
0.8264
7,024
Year 3
4,000
0.7513
3,005
$24,500
$20,938

38. Learning Objective P3: Compute net present value and describe its use.
NEED-TO-KNOW 24-3 (3 of 4)
Learning Objective P3: Compute net present value and describe its use.
PV of Net Cash Inflows
$20,938
Amount invested
(20,000)
Net Present Value – Project A
$938
TABLE B.1 Present Value of 1
Periods
10% 1
0.9091 2
0.8264 3
0.7513 4
0.6830 5
0.6209

39. Learning Objective P3: Compute net present value and describe its use.
NEED-TO-KNOW 24-3 (4 of 4)
Learning Objective P3: Compute net present value and describe its use.
Project B
Net Cash Inflows
PV of $1 at 10%
PV of Net Cash Inflows
Year 1
$4,500
0.9091
$4,091
Year 2
8,500
0.8264
7,024
Year 3
13,000
0.7513
9,767
$24,500
$20,882
PV of Net Cash Inflows
$20,882
Amount invested
(20,000)
Net Present Value – Project B
$882
Project A has the higher net present value.

40. Learning Objective P4: Compute internal rate of return and explain its use.

41. Internal Rate of Return (IRR) (1 of 6)
Learning Objective P4: Compute internal rate of return and explain its use.
The interest rate that makes . . .
Present value of cash inflows - Initial investment = $0 cash inflows
The net present value equals zero.
Another means to evaluate capital investments is to use the internal rate of return (IRR), which equals the discount rate that yields an NPV of zero for an investment. Stated another way, this means that if we compute the total present value of a project’s net cash flows using the IRR as the discount rate and then subtract the initial investment from this total present value, we get a zero NPV.

42. Internal Rate of Return (IRR) (2 of 6)
Learning Objective P4: Compute internal rate of return and explain its use.
Projects with even annual cash flows Project life = 3 years Initial cost = $12,000 Annual net cash inflows = $5,000 Determine the IRR for this project.
Consider this example where a project is being considered that costs $12,000, returns annual net cash flows of $5,000, and has a useful life of three years. The two-step process for computing IRR with even cash flows is pictured on this slide. When cash flows are equal, we must first compute the present value factor by dividing the initial investment by its annual net cash flows. In our case, $12,000 divided by $5,000 gives us a present value factor of
Then, in step 2, we use the annuity Table B.3, found in Appendix B, to determine the discount rate equal to this present value factor. Our next slide will show us the line in the table that contains the discount rate.

43. Internal Rate of Return (IRR) (3 of 6)
Learning Objective P4: Compute internal rate of return and explain its use.
Step 1. Compute present value factor for the investment project.
$12,000 ÷ $5,000 per year =
Step 2. Identify the discount rate (IRR) yielding the present value factor.

44. Internal Rate of Return (IRR) (4 of 6)
Learning Objective P4: Compute internal rate of return and explain its use.
Present Value of an Annuity of 1 for Three Periods
Periods
Discount Rate: 1%
Discount Rate: 5%
Discount Rate: 10%
Discount Rate: 12%
Discount Rate: 15%
3………….
2.9410
2.7232
2.4869
2.4018
2.2832
Here’s a portion of Table B.3, the Present Value of an Annuity of 1 for Three Periods, located in Appendix B of our chapter. (You may actually want to turn to Appendix B to work through this exercise. )
First, look across the three-period row of Table B.3 and find the discount rate corresponding to the present value factor of We find the value of , which roughly equals the value for the 12% rate. Therefore, the internal rate of return for this project, is approximately 12 percent.
IRR is approximately 12% =

45. Internal Rate of Return (IRR) (5 of 6)
Learning Objective P4: Compute internal rate of return and explain its use.
Uneven Cash Flows If cash inflows are unequal, it is best to use either a calculator or spreadsheet software to compute the IRR. However, we can also use trial and error to compute the IRR. Use of Internal Rate of Return When we use the IRR to evaluate a project, we compare the internal rate of return on a project to a predetermined hurdle rate (cost of capital). To be acceptable, a project’s rate of return cannot be less than the company’s cost of capital.
Calculating the internal rate of return becomes much more difficult when a project has unequal cash flows. If cash inflows are unequal, it is best to use either a calculator or spreadsheet software to compute the IRR. However, we can also use trial and error to compute the IRR. We do this by selecting any reasonable discount rate and computing the NPV. If the amount is positive (negative), we recomputed the NPV using a higher (lower) discount rate. Hand calculations using interest rate tables involve multiple trial and error solutions. For this reason, electronic spreadsheets such as Excel or advanced hand-held calculators should be used for projects with unequal cash flows.
When we use the IRR to evaluate a project, we compare the internal rate of return on a project to a predetermined hurdle rate (cost of capital) which is a minimum acceptable rate of return. If the IRR is higher than the hurdle rate, the investment is made. Multiple projects are often ranked by the extent to which their IRR exceeds the hurdle rate.
Now let’s review what you have learned in the following NEED-TO-KNOW exercise.

46. Internal Rate of Return (IRR) (6 of 6)
Learning Objective P4: Compute internal rate of return and explain its use.
Internal rate of return (%) – Hurdle rate (%)
If ≥ 0%, Invest
If > 0%, Do not Invest

47. NEED-TO-KNOW 24-4 (1 of 3)
Learning Objective P4: Compute internal rate of return and explain its use.
A machine costing $58,880 is expected to generate net cash flows of $8,000 per year for each of the next 10 years.
Compute the machine’s internal rate of return (IRR).
If a company’s hurdle rate is 6.5%, use IRR to determine whether the company should purchase this machine.
A machine costing $58,880 is expected to generate net cash flows of $8,000 per year for each of the next 10 years.
1. Compute the machine’s internal rate of return (IRR) and 2. If a company’s hurdle rate is 6.5%, use IRR to determine whether the company should purchase this machine.
Internal rate of return (IRR) is the interest rate at which the net present value of the cash flows from a project or investment equals zero.
Net present value equals the present value of the cash inflows minus the amount of the investment.
We know the investment is $58,880, so we need to determine the interest rate where the present value of the net cash inflows is equal to $58,880.
The present value of the net cash inflows is calculated by taking the annual dollar amount and multiplying by the present value of an annuity of one factor.
$58,880 equals $8,000 multiplied by the present value of an annuity factor.
To solve for the factor, we divide $58,880 by $8,000. The present value of an annuity factor is 7.36
Now we go to the present value of an ordinary annuity table, for n equals 10, and we look for the factor of 7.36, and we see the factor of at the intersection of n equals 10 and an interest rate of 6%.
At the intersection of n equals 10 and an interest rate of 6%. The internal rate of return is approximately 6%.
Since this rate is lower than the 6.5% hurdle rate, the machine should not be purchased.

48. NEED-TO-KNOW 24-4 (2 of 3)
Learning Objective P4: Compute internal rate of return and explain its use.
Internal rate of return (IRR) is the interest rate at which the net present value of the cash flows from a project or investment equals zero.
PV of Net Cash Inflows
$58,880
Amount invested
(58,880)
Net Present Value – Project B $0

49. NEED-TO-KNOW 24-4 (3 of 3)
Learning Objective P4: Compute internal rate of return and explain its use.
IRR is approximately 6%. Since this rate is lower than the 6.5% hurdle rate, the machine should not be purchased.
PV of $1
FV of $1
PV Ord Ann
FV Ord Ann

50. TABLE B.1 Present Value of 1 (1 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 1
0.9901
0.9804
0.9709
0.9615
0.9524
0.9434
0.9346
0.9259
0.9174
0.9091
0.8929
0.8696 2
0.9803
0.9612
0.9426
0.9246
0.9070
0.8900
0.8734
0.8573
0.8417
0.8264
0.7972
0.7561 3
0.9706
0.9423
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
0.6575 4
0.9610
0.9238
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
0.5718 5
0.9515
0.9057
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
0.4972 6
0.9420
0.8880
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
0.4323 7
0.9327
0.8706
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
0.3759 8
0.9235
0.8535
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
0.3269 9
0.9143
0.8368
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
0.2843 10
0.9053
0.8203
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
0.2472 11
0.8963
0.8043
0.7224
0.6496
0.5847
0.5268
0.4751
0.4289
0.3875
0.3505
0.2875
0.2149 12
0.8874
0.7885
0.7014
0.6246
0.5568
0.4970
0.4440
0.3971
0.3555
0.3186
0.2567
0.1869

51. TABLE B.1 Present Value of 1 (2 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 13
0.8787
0.7730
0.6810
0.6006
0.5303
0.4688
0.4150
0.3677
0.3262
0.2897
0.2292
0.1625 14
0.8700
0.7579
0.6611
0.5775
0.5051
0.4423
0.3878
0.3405
0.2992
0.2633
0.2046
0.1413 15
0.8613
0.7430
0.6419
0.5553
0.4810
0.4173
0.3624
0.3152
0.2745
0.2394
0.1827
0.1229 16
0.8528
0.7284
0.6232
0.5339
0.4581
0.3936
0.3387
0.2919
0.2519
0.2176
0.1631
0.1069 17
0.8444
0.7142
0.6050
0.5134
0.4363
0.3714
0.3166
0.2703
0.2311
0.1978
0.1456
0.0929 18
0.8360
0.7002
0.5874
0.4936
0.4155
0.3503
0.2959
0.2502
0.2120
0.1799
0.1300
0.0808 19
0.8277
0.6864
0.5703
0.4746
0.3957
0.3305
0.2765
0.2317
0.1945
0.1635
0.1161
0.0703 20
0.8195
0.6730
0.5537
0.4564
0.3769
0.3118
0.2584
0.2145
0.1784
0.1486
0.1037
0.0611 25
0.7798
0.6095
0.4776
0.3751
0.2953
0.2330
0.1842
0.1460
0.1160
0.0923
0.0588
0.0304 30
0.7419
0.5521
0.4120
0.3083
0.2314
0.1741
0.1314
0.0994
0.0754
0.0573
0.0334
0.0151 35
0.7059
0.5000
0.3554
0.2534
0.1813
0.1301
0.0937
0.0676
0.0490
0.0356
0.0189
0.0075 40
0.6717
0.4529
0.3066
0.2083
0.1420
0.0972
0.0668
0.0460
0.0318
0.0221
0.0170
0.0037

52. Table B.2 Future Value 1 (1 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15%
1.0000 1
1.0100
1.0200
1.0300
1.0400
1.0500
1.0600
1.0700
1.0800
1.0900
1.1000
1.1200
1.1500 2
1.0201
1.0404
1.0609
1.0816
1.1025
1.1236
1.1449
1.1664
1.1881
1.2100
1.2544
1.3225 3
1.0303
1.0612
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
1.5209 4
1.0406
1.0824
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
1.7490 5
1.0510
1.1041
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
2.0114 6
1.0615
1.1262
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
2.3131 7
1.0721
1.1487
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
2.6600 8
1.0829
1.1717
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
3.0590 9
1.0937
1.1951
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
3.5179 10
1.1046
1.2190
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
4.0456 11
1.1157
1.2434
1.3842
1.5395
1.7103
1.8983
2.1049
2.3316
2.5804
2.8531
3.4785
4.6524 12
1.1268
1.2682
1.4258
1.6010
1.7959
2.0122
2.2522
2.5182
2.8127
3.1384
3.8960
5.3503

53. Table B.2 Future Value 1 (2 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 13
1.1381
1.2936
1.4685
1.6651
1.8856
2.1329
2.4098
2.7196
3.0658
3.4523
4.3635
6.1528 14
1.1495
1.3195
1.5126
1.7317
1.9799
2.2609
2.5785
2.9372
3.3417
3.7975
4.8871
7.0757 15
1.1610
1.3459
1.5580
1.8009
2.0789
2.3966
2.7590
3.1722
3.6425
4.1772
5.4736
8.1371 16
1.1726
1.3728
1.6047
1.8730
2.1829
2.5404
2.9522
3.4259
3.9703
4.5950
6.1304
9.3576 17
1.1843
1.4002
1.6528
1.9479
2.2920
2.6928
3.1588
3.7000
4.3276
5.0545
6.8660 18
1.1961
1.4282
1.7024
2.0258
2.4066
2.8543
3.3799
3.9960
4.7171
5.5599
7.6900 19
1.2081
1.4568
1.7535
2.1068
2.5270
3.0256
3.6165
4.3157
5.1417
6.1159
8.6128 20
1.2202
1.4859
1.8061
2.1911
2.6533
3.2071
3.8697
4.6610
5.6044
6.7275
9.6463 25
1.2824
1.6406
2.0938
2.6658
3.3864
4.2919
5.4274
6.8485
8.6231 30
1.3478
1.8114
2.4273
3.2434
4.3219
5.7435
7.6123 35
1.4166
1.9999
2.8139
3.9461
5.5160
7.6861 40
1.4889
2.2080
3.2620
4.8010
7.0400

54. TABLE B.3 Present Value of an Annuity 1 (1 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 1
0.9901
0.9804
0.9709
0.9615
0.9524
0.9434
0.9346
0.9259
0.9174
0.9091
0.8929
0.8696 2
1.9704
1.9416
1.9135
1.8861
1.8594
1.8334
1.8080
1.7833
1.7591
1.7355
1.6901
1.6257 3
2.9410
2.8839
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
2.2832 4
3.9020
3.8077
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
2.8550 5
4.8534
4.7135
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
3.3522 6
5.7955
5.6014
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
3.7845 7
6.7282
6.4720
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
4.1604 8
7.6517
7.3255
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
4.4873 9
8.5660
8.1622
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7590
5.3282
4.7716 10
9.4713
8.9826
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
5.0188 11
9.7868
9.2526
8.7605
8.3064
7.8869
7.4987
7.1390
6.8052
6.4951
5.9377
5.2337 12
9.9540
9.3851
8.8633
8.3838
7.9427
7.5361
7.1607
6.8137
6.1944
5.4206

55. TABLE B.3 Present Value of an Annuity 1 (2 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 13
9.9856
9.3936
8.8527
8.3577
7.9038
7.4869
7.1034
6.4235
5.5831 14
9.8986
9.2950
8.7455
8.2442
7.7862
7.3667
6.6282
5.7245 15
9.7122
9.1079
8.5595
8.0607
7.6061
6.8109
5.8474 16
9.4466
8.8514
8.3126
7.8237
6.9740
5.9542 17
9.7632
9.1216
8.5436
8.0216
7.1196
6.0472 18
9.3719
8.7556
8.2014
7.2497
6.1280 19
9.6036
8.9501
8.3649
7.3658
6.1982 20
9.8181
9.1285
8.5136
7.4694
6.2593 25
9.8226
9.0770
7.8431
6.4641 30
9.4269
8.0552
6.5660 35
9.6442
8.1755
6.6166 40
9.7791
8.2438
6.6418

56. TABLE B.4 Future Value of Annuity of 1 (1 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 1
1.0000 2
2.0100
2.0200
2.0300
2.0400
2.0500
2.0600
2.0700
2.0800
2.0900
2.1000
2.1200
2.1500 3
3.0301
3.0604
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
3.4725 4
4.0604
4.1216
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
4.9934 5
5.1010
5.2040
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6.7424 6
6.1520
6.3081
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
8.7537 7
7.2135
7.4343
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872 8
8.2857
8.5830
8.8923
9.2142
9.5491
9.8975 9
9.3685
9.7546 10 11 12

57. TABLE B.4 Future Value of Annuity of 1 (2 of 2)
Periods
Rate: 1%
Rate: 2%
Rate: 3%
Rate: 4%
Rate: 5%
Rate: 6%
Rate: 7%
Rate: 8%
Rate: 9%
Rate: 10%
Rate: 12%
Rate: 15% 13 14 15 16 17 18 19 20 25 30 35 40 1,

58. Exhibit 24.12 Comparison of Capital Budgeting Methods
Learning Objective P4: Compute internal rate of return and explain its use.
Payback Period
Accounting Rate of Return
Net Present Value
Internal Rate of Return
Measurement basis
Cash flows
Accrual income
Measurement unit
Years
Percent
Dollars
Strengths
Easy to understand
Allows comparison of projects
Easy to understand
Allows comparison of projects
Reflects time value of money
Reflects varying risks over project’s life
Allows comparisons of dissimilar projects
Limitations
Ignores time value of money
Ignores cash flows after payback period
Ignores time value of money
Ignores annual rates over life of projects
Difficult to compare dissimilar projects
Ignores varying risks over life of projects
On this screen, we see a summary comparing the strengths and limitations of each of the four capital budgeting methods that we have studied. Recall that the major limitation of the payback method and the accounting rate of return method is that they neglect the time value of money. This limitation is overcome by using either the net present value or internal rate of return methods.

59. Learning Objective A1: Analyze a capital investment project using break-even time.

60. Break-Even Time (1 of 2)
Learning Objective A1: Analyze a capital investment project using break-even time.
Break-even time incorporates time value of money into the payback period method of evaluating capital investments.
The payback example that we saw earlier in the chapter neglected the time value of money. Break-even time is a variation of the payback method that incorporates the time value of money by telling us the number of years an investment requires for its net present value to equal its initial cost.

61. Break-Even Time (2 of 2)
Learning Objective A1: Analyze a capital investment project using break-even time.
Break-even time for this investment is between 5 and 6 years.

62. Learning Objective 24A-Appendix: Using Excel to Compute Net Present Value and Internal Rate of Return.

63. Appendix 24A: Using Excel to Compute NPV and IRR
Computing present values and internal rates of return for projects with uneven cash flows is tedious and error prone. These calculations can be performed simply and accurately by using functions built into Excel.
Appendix 24A: Using Excel to Compute Net Present Value and Internal Rate of Return
Computing present values and internal rates of return for projects with uneven cash flows is tedious and error prone. These calculations can be performed simply and accurately by using functions built into Excel. To illustrate, consider a company that is considering investing in a new machine with the expected cash flows shown on the spreadsheet. Cash outflows are entered as negative numbers, and cash inflows are entered as positive numbers. Assume the company requires a 12% annual return, entered as 0.12 in cell C1.
To compute the net present value of this project, the following is entered into cell C13:
NPV(C1,C4:C11)+C2
To compute the internal rate of return for this project, the following is entered into cell C15:
IRR(C2:C11)

64. End of Presentation