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ACCG404 Lecture 12: Capital Budgeting Lecture Objective At the conclusion of this lecture, students should be able to understand the concepts and techniques used to evaluate capital projects, referred to as long term projects, in that they have a useful life extending over 2 or more years. Lecture Outline 1. 2. 3. 4. 5. 6. 7. Introductory Concepts. Cash Flows Capital Investment Evaluation Methods. Payback Period - Computations and Evaluation Accounting Rate of Return (ARR) - Computations and Evaluation Net Present Value (NPV) Internal Rate of Return (IRR) - Independent Projects. Appendix to Lecture 8 Capital Budgeting using Microsoft Excel ACCG404 – Lecture 12 Capital Budgeting -2- 1. Introductory Concepts The decision making process generally referred to as CAPITAL BUDGETING is often used as a guide to non-recurring decisions which have a long range impact on the organisation. Essentially, the process is one where a firm must decide whether or not an investment is worthwhile undertaking. Capital budgeting is the making of long term planning decisions for investment and their financing. Most expenditure in these investment areas are large, permanent commitments which will effect future flexibility and earning power. Investment decisions require a comparison of the COSTS expected to be incurred by the investment with the BENEFITS expected to be gained from the investment. If the benefits exceed the costs, then the firm will be in a stronger economic position. 2 Cash Flows Capital budgeting operations require the evaluation of CASH FLOWS. All investments must yield a positive cash flow over time, taking into account the time value of money. The determination of cash flows requires Depreciation to be added back to net profit after tax to determine the AFTER TAX CASH FLOW. To demonstrate the determination of net cash flows after tax, consider the following data: Illustrative Example 1: Cash Flow Determination A company is considering a proposal to invest in new equipment that will be used to produce a new product line. The outlay required is $500,000. The equipment is expected to have a life of 5 years and have no salvage value at that time. Straight line depreciation over 5 years is acceptable for tax purposes and the tax rate is 40%. For each year of the 5 year period cash revenues of $750,000 and cash expenses of $500,000 are expected. Annual depreciation: • straight line over 5 years = $100,000 p.a. ACCG404 – Lecture 12 Capital Budgeting -3- Solution to Illustrative Example 1: Annual Net Cash Inflows: Revenue Less Expenses: Cash Expenses Depreciation Total Expenses NET PROFIT BEFORE TAX Less Taxation (40%) NET PROFIT AFTER TAX Add Back Depreciation NET AFTYER TAX CASH FLOW In the above example depreciation is included to determine the amount of tax that has to be paid. However, depreciation is not a cash flow and is then added back to the profit after tax to determine the net cash flows. 3. Capital Investment Evaluation Methods There are a number of capital investment evaluation methods available to evaluate investment decisions. The main methods used are as follows: • the payback period, • the accounting rate of return, • net present value methods, • the internal rate of return. ACCG404 – Lecture 12 Capital Budgeting -4- 4. The Payback Method The payback period is the time taken for a project to recover its original outlay cost. It is the time taken for the cash inflows from a capital investment to equal the cash outlay cost. Assume a project has an original outlay cost of $10,000 to be followed by annual net cash inflows of $2,000. In this example the payback period will be 5 years. In that time the net cash inflows will accumulate to an amount equal to the outlay cost of $10,000. Calculation of the payback Period: Equal Annual Cash Flows: Illustrative Example 2: If the original investment is $150,000 and the firm expects to generate equal annual net cash flows of $40,000, then the payback period is 3.75 years. We assume that cash flows are evenly spread throughout a year. Solution to Illustrative Example 2: Payback Period = Original Investment Annual Net Cash Flows = = Unequal Annual Cash Flows: If the annual cash flows are unequal or uneven, the payback period is calculated by cumulating or adding the annual cash flows until the original cash flows are recovered. Illustrative Example 3: Assume the original investment was $100,000 and the annual net cash flows over the next 5 years were $15,000, $30,000, $30,000, $40,000 and $25,000 respectively. Year 1 2 3 4 5 Cash Flow $ 15,000 30,000 30,000 40,000 25,000 ACCG404 – Lecture 12 Capital Budgeting -5- Solution to Illustrative Example 3: Cumulative Cash Flow Years Required Year 1 2 3 4 5 Cash Flow $15,000 30,000 30,000 40,000 25,000 Check Answer Payback Period = = 3 + (25000 / 40,000) = 3.625 Years 5. Accounting Rate of Return (ARR) The accounting rate of return is a measure of a projects accounting profit as a percentage of its investment outlay. Because projects returns or profits will vary over the life of a project it is necessary to average the annual profit over the projects life. Average Accounting Profit 100 = ---------------------------------- * ----Average Investment 1 ARR (%) The AVERAGE ACCOUNTING PROFIT can be found by adding together the net income (after tax) for each year and dividing by the number of years. A similar evaluation could be made using net income before tax. The Investment is best represented by the AVERAGE INVESTMENT which is calculated using the following formula: 2 (Cost of Investment + Residual Value) 2 ACCG404 – Lecture 12 Capital Budgeting -6- Illustrative Example 3 Assume a company is considering an investment project which will cost $6,000 and return after-tax accounting profit as shown below over a 5 year period. year 1 $2,100 year 2 $2,000 year 3 $1,800 year 4 $1,600 year 5 $1,500 A salvage value of $500 is expected at the end of the life of the asset. Solution to Illustrative Example 3 Average Accounting Net Profit = Average Investment = 6. Net Present Value (NPV) The Net Present Value (NPV) method uses discounted cash flow (DCF) methods as the basis of its evaluation process. The term "Net", is simply the difference between the present value of cash inflows and the present value of cash outflows. NPV = PV (inflows) - PV (outflows) The interest rate used to discount project cash flows is the firm's weighted average cost of capital (WACC). A project with a positive net present value represents an investment which has net returns in excess of the firm's cost of capital invested in the project. This means that the project net returns are more than sufficient to pay for the funds necessary to finance the project. The bigger the excess return the more attractive will the project be to the firm. Economic profit is implied in the concept of a positive net present value. ACCG404 – Lecture 12 Capital Budgeting -7- Illustrative Example 4 Single Investment Decisions. - Even Cash Flows Assume a project has an initial investment of $15,000 followed by equal annual cash inflows of $5,000 for the next 4 years. We will also assume a 7% cost of capital as the appropriate discount rate. Dropping dollar signs ($) our cash flows are as follows: T0 T1 T2 T3 T4 (15000) 5000 5000 5000 5000. Solution to Illustrative Example 4 Discount factor Present Value Years 0 1-4 Cash Flow -15,000 5,000 NPV = ** Note: the discount factor is obtained from the Present Value tables, ie., PVIFA(4,7%) = 3.3872. Decision: As the NPV is positive the project is profitable in economic terms and is therefore acceptable. Illustrative Example 5 Single Investment Decisions - Uneven Cash Flows Assume a project has an initial investment of $10,000 followed by annual after tax cash inflows of $4,000 in years 1 and 2, $3,000 in year 3, $2,000 in year 4 and $4,000 in year 5. In addition the investment is expected to have a Disposal cost of $1,000 at the end of year 6. We will also assume a 10% cost of capital as the appropriate discount rate. Dropping dollar signs ($) the cash flows are as follows: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 ($10,000) $4,000 $4,000 $3,000 $2,000 $4,000 -$1,000 ACCG404 – Lecture 12 Capital Budgeting -8- Solution to Illustrative Example 5 Years 0 1 2 3 4 5 6 Cash Flow -10,000 4,000 4,000 3,000 2,000 4,000 - 1,000 NPV = Discount factor Present Value ** Note: the discount factor is obtained from PVIF tables. Decision: As the NPV is positive the project is profitable in economic terms and is therefore acceptable. Illustrative Example 6 - Taxation. The Zenith Company is considering the introduction of a new product to add to its existing product line. The company expects a reasonable level of sales for the next 5 years after this period the product sales are expected to be zero. Specialised equipment will need to be purchased to produce the new product at a cost of $25,000. Additional working capital will need to be introduced over the life of the product. All of this capital will be recovered at the end of the product's life. Year 0 Before Tax Net Cash Flows ($25,000) Year 1 $10,000 Year 2 $20,000 Year 3 $30,000 Year 4 $30,000 Year 5 $20,000 Additional information : • Depreciation is 20% prime cost (to be written off over 5 years) • The tax rate is 40%. • There is zero salvage value at the end of the project. • The company uses at after-tax cost of capital of 10%. Required: Should the company accept this project? ACCG404 – Lecture 12 Capital Budgeting -9- Solution to Illustrative Example 6 Year 0 1 2 3 4 5 Cash flows before tax Less Depreciation Operating profit before tax Less Taxation @ 40% After Tax Operating Cash flows Add Back Depreciation After Tax CASH FLOWS Initial Investment Total After Tax Cash Flows 10% Discount Factor Present Value 7. Internal Rate of Return (IRR) The Internal Rate of Return (IRR) is a discounted cash flow method which takes into account the time value of money. It is that discount rate that equates the present value of expected cash inflows with the present value of expected cash outflows. It is therefore that interest rate that produces a zero net present value for a project. The IRR is also known as the YIELD rate or YIELD rate of return for a project. Illustrative Example 7: Assume a project has a cost of $20,000 and is expected to produce annual net cash inflows of $3,834 for the next 10 years. The net present value calculation for this project can be formulated as follows: ACCG404 – Lecture 12 Capital Budgeting - 10 - Solution to Illustrative Example 7: For projects that involve a uniform cash flow over the life of the project, the IRR is to be calculated, using the following steps: Step 1: Calculate the Annuity PV factor via: = = = Step 2: Original Investment ÷ Annual cash flow 20,000 / 3,834 5.2165 Check the 5.2165 along the Annuity PV for the 10 year line and read of the interest rate from the table, as this represents the IRR. Present value of ANNUITY of $1 Period 1 2 3 4 5 6 7 8 9 4% 0.962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 8.111 8.760 9.385 9.986 5% 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 6% 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 7% 0.935 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8% 0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 10% 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 12% 0.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 14% 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 16% 0.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 10 11 12 13 5.216 5.453 5.660 5.842 Illustrative Example 8 A project promises the following after tax net cash flows: Year 1 Year 2 CASH FLOWS 5,000 4,200 Year 3 3,700 The project will require an initial investment of $10,000 with a zero salvage value. Required: Calculate the projects internal rate of return. FOR UNEVEN CASH FLOWS use Microsoft Excel to calculate the IRR. (See notes on Excel for instructions). Solution to Illustrative Example 8: After Tax Cash Flows Internal Rate of Return Year 0 -$10,000 Year 1 $5,000 Year 2 $4,200 Year 3 $3,700 14.72% ACCG404 – Lecture 12 Capital Budgeting - 11 - Appendix to Lecture 12 Capital Budgeting using Microsoft Excel In this section the following Capital Budgeting functions included in the Excel spreadsheet program will be covered: 1. Capital Project Evaluation techniques 1.1 1.2 1.3 Internal Rate of Return Net Present Value Determining After Tax Cash Flows 1. Capital Project Evaluation techniques Microsoft Excel provides a number of inbuilt functions that facilitate project evaluation using capital budgeting techniques. The functions to be used in this section are as follows: (i) Internal Rate of Return (IRR) which is a discounted cash flow technique where the answer derived is the discount rate (or interest rate) that equates the PRESENT VALUE of the cash OUTFLOWS to the PRESENT VALUE of the cash INFLOWS giving a Net Present Value of zero. (ii) Net Present Value (NPV) which is also a discounted cash flow technique used to evaluate the acceptability of a project based on the discounting of the cash outflows and inflows generated by a project and using a predetermined discount (interest) rate which is indicative of the firm’s Cost of Capital. ACCG404 – Lecture 12 Capital Budgeting - 12 - 1.1 Internal Rate of Return The internal rate of return function needs to have specified: =IRR ( Range of Cash Flows ) and will calculate the interest rate at which the present value of cash inflows equals the present value of cash outflows equating them to zero. The operation of the IRR command will be illustrated using the following example: Formula and Data Entry 1 2 3 Year 4 5 6 7 8 9 10 11 IRR = A Internal Rate of return Cash flow 0 1 2 3 4 5 -$140,000 35,000 37,000 45,000 38,000 32,000 =IRR(B4:B9) B Solutions Display A B 1 Internal Rate of return 2 3 Year Cash flow 4 0 -$140,000 5 1 35,000 6 2 37,000 7 3 45,000 8 4 38,000 9 32,000 5 10 11 IRR = 10.57% The answer displayed at cell B11 may initially be displayed as 11%. This is because the default display for PERCENTAGES is NO decimal places. To increase the number of decimal points displayed point and click on the Decimal Point increase icon as displayed in the formatting toolbar. When using the IRR function it is necessary to specify the Range of Cash Outflows and Cash Inflows in the chronological order in which they occur in a contiguous range of cells. ACCG404 – Lecture 12 Capital Budgeting - 13 - 1.2 Net Present Value The Net Present Value function needs to have specified: =NPV (Interest, Cash flows) + Initial Investment and will determine the PRESENT VALUE of a series of expected future cash flows at a constant interest rate. The operation of the =NPV command is as follows: Formula and Data Entry 1 2 3 Year 4 5 6 7 8 9 10 11 Interest Rate 12 13 Net Present Value 14 A Net Present Value B C 0 1 2 3 4 5 Cash Outflows -140,000 Cash Inflows 35,000 37,000 45,000 38,000 32,000 10% =NPV(B11,C5:C9)+B4 Solutions Display 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A Net Present Value Year 0 1 2 3 4 5 Interest Rate Net Present Value B C Cash Outflows -140,000 Cash Inflows 35,000 37,000 45,000 38,000 32,000 10% $2,029.85 The formula used to calculate the NPV in cell B13 comprises: ACCG404 – Lecture 12 Capital Budgeting - 14 - (i) (ii) (iii) Interest Rate, at cell B11 Cash Inflows for years 1 to 5 at cells C5:C9, and to obtain the Net Present Value it will be necessary to deduct the Initial Cash Outflow which is a negative amount, hence its addition as +B4. 1.3 Determining After Tax Cash Flows When evaluating capital projects the first step is to determine the After Tax ANNUAL Cash Flows relevant to the project which is usually a result of the following calculations : Annual Cash Inflows before Depreciation and Tax Less Depreciation $100,000 The cash flows generated by the project before allowing for depreciation and tax $-10,000 Depreciation is deducted to obtain the net profit. There is no cash flow associated with depreciation. $90,000 The net profit before tax is the amount used to calculate the tax liability. $-36,000 Taxation is charged on the net profit before tax. $54,000 This is the annual net profit figure after tax. As depreciation is a non-cash charge $10,000 against profits, it needs to be added back to determine the net annual cash inflow of the project. This amount is used to evaluate the $64,000 project’s feasibility. The net cash inflows are compared to the cash outflows to determine the acceptability of the project. Net Profit Before Tax Less Taxation at 40% Net Profit after Tax Add Back Depreciation NET CASH INFLOW An alternate method to calculate the annual cash inflow is to use NET PROFIT AFTER TAX and add back DEPRECIATION. ACCG404 – Lecture 12 Capital Budgeting - 15 - Practice Exercise The Mojon Company has the opportunity to expand business operations by acquiring new plant and equipment. Projections of cash flows and operating characteristics are as follows: Initial Cost of Asset Useful life of asset Salvage Value $80,000 5 years $0 Depreciation is 20% per annum, straight line method. Cash inflows (before depreciation and taxation) are as follows: Year Cash Inflow 1 $20,000 2 $30,000 3 $35,000 4 $30,000 5 $25,000 The taxation rate is 39% per annum. Required: Using the Microsoft Excel spreadsheet program, calculate: (a) the “net cash flows” after depreciation and tax (b) Internal Rate Of Return (c) Net Present Value (NPV) assuming the Company’s cost of capital is 12%. Solution to Practice Exercise 8: A B Formula Display: C D E F G 1 Capital Budgeting Techniques 2 3 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 4 Initial Cost of Project -80000 5 6 7 Cash Inflows before Depn & Tax 20000 30000 35000 30000 25000 8 9 Less Depreciation (20% Straight Line) 20% =$B$9*$B$4 =$B$9*$B$4 =$B$9*$B$4 =$B$9*$B$4 =$B$9*$B$4 10 Net Profit Before Tax =C7+C9 =D7+D9 =E7+E9 =F7+F9 =G7+G9 11 12 Less Taxation -39% =C10*$B$12 =D10*$B$12 =E10*$B$12 =F10*$B$12 =G10*$B$12 13 Net Profit after Tax =C10+C12 =D10+D12 =E10+E12 =F10+F12 =G10+G12 14 15 Add Back Depreciation =C9 =D9 =E9 =F9 =G9 16 NET CASH INFLOW after Depreciatioun & Tax =C13+C15 =D13+D15 =E13+E15 =F13+F15 =G13+G15 17 NET CASH FLOWS – SUMMARY DATA 18 Annual Cash Inflows / (Outflows) =B4 =C16 =D16 =E16 =F16 =G16 19 20 Internal Rate of Return (IRR) =IRR(B18:G18) 21 22 Net Present Value at 12% =NPV(B23,C18:G18)+B18 23 Cost of Capital (discount rate) 12% ACCG404 – Lecture 12 Capital Budgeting - 16 - Practice Exercise: Solutions Display 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A Capital Budgeting Techniques B C D E F G Initial Cost of Project Year 0 Year 1 - 80,000 Year 2 Year 3 Year 4 Year 5 Cash Inflows before Depn & Tax Less Depreciation (20% Straight Line) Net Profit Before Tax Less Taxation Net Profit after Tax 20% 20,000 16,000 4,000 -39% - 1,560 2,440 16,000 18,440 18,440 30,000 16,000 14,000 - 5,460 8,540 16,000 24,540 24,540 35,000 16,000 19,000 - 7,410 11,590 16,000 27,590 27,590 30,000 16,000 14,000 - 5,460 8,540 16,000 24,540 24,540 25,000 16,000 9,000 - 3,510 5,490 16,000 21,490 21,490 Add Back Depreciation Net Cash Inflow (after Tax & Depreciation) NET CASH FLOWS – SUMMARY DATA Annual Cash Inflows / (Outflows) - 80,000.00 Internal Rate of Return (IRR) Net Present Value at 12% Cost of Capital (discount rate) 13.68% $3,455.06 12% Homework Exercises Question 1: A company is considering an investment in a new piece of equipment that will cost $140,000. The equipment should yield the following after tax cash inflow for each of the five years of the predicted economic life of the equipment. Year 1 2 3 4 5 Required: (a) (b) (b) Cash Inflow $ 40,000 $ 45,000 $ 38,000 $ 32,000 $ 24,000 The Payback Period the net present value of the project assuming a cost of capital of 8 per cent. calculate the internal rate of return. ACCG404 – Lecture 12 Capital Budgeting - 17 - Question 2: The McGraw Company is considering a proposal to purchase new plant and equipment to be used in the manufacture of a new product line. The expected cash flow details are as follows: Cost of equipment Life of project Depreciation Tax Rate $400,000 5 years 20% of prime cost (ie. $90,000 per annum) 30% Expected Cash Inflows before depreciation and taxation are as follows: Cash Inflows Year 1 $130,000 Year 2 $140,000 Year 3 $150,000 Year 4 $140,000 Year 5 $130,000 Required: Assuming tax is paid in the year incurred, calculate: (a) The after tax cash flows resulting from the project. (b) Payback Period (c) The Accounting rate of Return (d) Calculate the Internal Rate of Return for the project. (e) Assuming a cost of capital of 12%, calculate the Net Present Value. Question 3: The Stettson Company has the opportunity to expand business operations by acquiring new plant and equipment. Projections of cash flows and operating characteristics are as follows: Initial Cost of Asset Useful life of asset $90,000 5 years Depreciation is 30% per annum, prime cost method. Gross cash inflows (before depreciation and taxation) are as follows: Year 1 2 3 4 5 Gross Cash flows 30,000 45,000 48,000 35,000 30,000 The taxation rate is 30% per annum and is paid for in the year the income is earned. Required: (i) (ii) (iii) (iv) (v) Using Microsoft Excel spreadsheet program, calculate : The cash flows associated with this project. Accounting Rate of Return Payback period the Internal Rate of Return (IRR) the Net Present Value assuming a cost of capital equal to 12%. ACCG404 – Lecture 12 Capital Budgeting - 18 - Question 4: (Internal Rate of Return) A company is considering a capital project which will require the purchase of a machine at an outlay cost of $140,000. Although the machine is expected to have a productive life and have positive net cash flows (before tax) of $50,000 per year for a period of 6 years, the firm can depreciate the asset for tax purposes over a 4 year period at the rate of 25% using the prime cost method. The company's tax rate is 30 per cent and is paid at the end of the year the income is earned. Required: (a) (b) (c) (d) Calculate the net cash flows after tax for the project. Compute the payback period. Compute the accounting rate of return. Compute the net present value of the project using: (i) a 12% after tax cost of capital, and (ii) a 14% after tax cost of capital. Calculate the projects internal rate of return. (e) Question 5: A company is interested in purchasing a machine that will cost $160,000 and generate annual cash operating cost savings of $50,000 for the next 6 years. The minimum required rate of return is 16% after taxes, and the tax rate is 30%. The machine will be depreciated over 4 years using the prime cost method. The equipment will have a zero salvage value at the end of 6 years. Tax effects are treated at the end of the year of income. REQUIRED: Calculate: (i) The cash flows associated with this project. (ii) Payback period (iii) The Accounting Rate of return (iv) Internal Rate of Return (IRR) (v) Net Present Value assuming a cost of capital equal to 12%. ACCG404 – Lecture 12 Capital Budgeting - 19 - Present Value Tables Present value of $1 Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4% 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 0.475 0.456 5% 0.952 0.907 0.864 0.823 0.784 0.746 0.711 0.677 0.645 0.614 0.585 0.557 0.530 0.505 0.481 0.458 0.436 0.416 0.396 0.377 6% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.456 7% 0.935 0.873 0.816 0.763 0.713 0.666 0.623 0.582 0.544 0.508 0.475 0.444 0.415 0.388 0.362 0.339 0.317 0.296 0.277 0.456 8% 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215 10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104 14% 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 16% 0.862 0.743 0.641 0.552 0.476 0.410 0.354 0.305 0.263 0.227 0.195 0.168 0.145 0.125 0.108 0.093 0.080 0.069 0.060 0.051 Present value of ANNUITY of $1 Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4% 0.962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 8.111 8.760 9.385 9.986 10.563 11.118 11.652 12.166 12.659 13.134 13.590 5% 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 6% 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9.712 10.106 10.477 10.828 11.158 11.470 7% 0.935 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 12.166 9.763 10.059 10.336 10.594 8% 0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 10% 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 7.367 7.606 7.824 8.022 8.201 8.365 8.514 12% 0.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 7.469 14% 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 6.550 6.623 16% 0.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.668 5.749 5.818 5.877 5.929

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At the conclusion of this lecture, students should be able to understand the concepts and techniques used to evaluate capital projects, referred to as long term projects, in that they have a useful life extending over 2 or more years.

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