ࡱ> VXUY 5bjbjWW .==1]8,$'~~ooo'''''''$(*'ooooo' ~ o'o'  br"'B<0 ыI'VStudent lecture notes CHAPTER 25 CAPITAL BUDGETING Capital budgeting is a process of management accounting which assists management decision making by providing .. in a project and the .. from that project, and by of the project subsequent to its implementation. The assumptions adopted No taxes No inflation Certainty in predicting future events Three methods of capital budgeting Payback method Accounting rate of return Net present value method Data A haulage company has three potential projects planned. Each will require investment in two refrigerated vehicles at a total cost of 120,000. The vehicle has a three-year life. The three projects are: (A) Expected cash inflows, after deducting all expected cash outflows, are 60,000 per annum. (B) Expected cash inflows, after deducting all expected cash outflows, are 45,000 per annum. (C) Expected cash inflows, after deducting all expected cash outflows, are 40,000 in Year 1, 70,000 in Year 2 and 80,000 in Year 3.  Payback method The payback period is the length of time required for a stream of cash inflows from a project to equal the original cash outlay. Cash flows Project AProject BProject COutlay120120120Net cash flows Year 1604540 Year 2604570 Year 3604580Payback periodWorkings Usefulness and limitations of the payback approach Concentrating on projects which give of cash flow. approach. Ignores the .. Cash flows earned should the capital sum invested plus interest. Ignores any arising after ... Accounting rate of return The accounting rate of return is calculated by taking the .. as a percentage of . Profit is not the same as cash flow. Expense associated with using a fixed asset is the reduction in the value of the asset due to depreciation. Depreciation A straight-line method of depreciation is applied, assuming a zero residual value. Annual depreciation (120,000/3 years) = 40,000 per annum deducted from cash flows to arrive at annual profit. Calculations: Accounting rate of return Cash flows Project AProject BProject COutlay (a)120,000120,000120,000Profits (cash flows minus depreciation) Year 120,0005,000nil Year 220,0005,00030,000 Year 320,0005,00040,000Average annual profit (b)Accounting rate of return ((b) ( 100/(a)) Project .... is the most desirable project. Project . is next in rank. Project ..is the least desirable. Usefulness and limitations of accounting rate of return Based on the familiar accounting measure of profit. Takes into the calculation . Ignores the . Depends on profit, including a .. accounting estimate of depreciation. Net present value method It takes into account all cash flows over the life of the project and makes allowance for the time value of money. Time value of money If 100 is invested at 10% per annum then it will grow to 110 by the end of the year. If the 100 is spent on business machinery the interest is lost. Lost opportunity of earning interest on an investment. Time value of money recognising that a project needs to compensate the business for the lost opportunity. Question You are given a written promise of 100 to be received in one years time. Interest rates are 10%. What is the price for which you could sell that promise? Answer is ... (The amount which, invested now at 10%, would grow to 100 in one years time.) Both the buyer and the seller would be equally satisfied. You are given a promise of 100 for payment in two years time. What is the price for which you could sell that promise now? Answer is (. would grow at 10% to at the end of one year and to 100 at the end of two years.) Mathematical representation as follows: The present value of a sum of 1 receivable at the end of n years when the rate of interest is r% per annum equals  EMBED Equation.2  where r =represents the annual rate of interest (discount rate), and n represents the time period when the cash flow will be received. Assuming a rate of interest of 10%: The present value of a sum of 100, due one year hence:  EMBED Equation.2 = The present value of a sum of 100, due two years hence:  EMBED Equation.2 = . A full table of discount factors is set out in the supplement at the end of Chapter 25. The column for the discount rate of 10% has the following discount factors: At end of periodPresent value of 1123 Net present value calculation The net present value of a project is equal to the present value of the .. minus the present value of the ., all discounted at the cost of capital. Calculation of net present value Using the formula approach the net present value is calculated as: 60,000+60,000+60,000(120,000(1.10)(1.10)2(1.10)3 = 54,550 + 49,590 + 45,080 - 120,000 =  Using the discount tables the net present value is calculated as follows: End of yearCash flowDiscount factorPresent value160,0000.909260,0000.826360,0000.751Less initial outlay(120,000)Net present valueThe NPV decision rule is as follows: Where the NPV of the project is . the project. Where the NPV of the project is . the project. Where the NPV of the project is .. in meeting the cost of capital but gives no surplus to its owners. If an organisation seeks to maximise the wealth of its owners, then it should accept any project which has a . net present value. Based on the above decision rule Project A will be accepted as it gives a . net present value. Project B Cash flow patterns Using the discount tables the net present value is calculated as follows: End of yearCash flowDiscount factorPresent value145,0000.909245,0000.826345,0000.751Less initial outlay(120,000)Net present value Project C Cash flow patterns Using the discount tables the net present value is calculated as: End of yearCash flowDiscount factorPresent value140,0000.909270,0000.826380,0000.751Less initial outlay(120,000)Net present value Project is the most desirable project. Project . is next in rank. Project .. would be rejected as it gives a negative net present value. Internal rate of return The internal rate of return is another method in capital budgeting which uses the time value of money but results in an answer expressed in percentage form. It is a discount rate which leads to a , where the present value of the cash inflows exactly equals the cash outflows. The internal rate of return is the discount rate at which the present value of the cash flows generated by the product is equal to the . of the capital invested, so that the net present value of the project is .. Method of calculation The calculation of the internal rate of return involves a process of repeated guessing at the discount rate until the present value of the cash flows generated is equal to the capital investment. Initial investment =  EMBED Equation.2  +  EMBED Equation.2  +  EMBED Equation.2  + +  EMBED Equation.2  Non-computerised process of estimation by use of discount tables, with the aim of arriving at a reasonably close answer. Illustration: Project A Find two values of NPV using discount rates lying either side of the actual IRR. A first guess of 20% produces a net present value which is positive. A higher discount rate of, say, 24% is used for the second guess. Calculation of net present value at 20% and at 24% End of yearCash flowsDiscount rate 20%Discount rate 24%160,0000.8330.806260,0000.6940.650360,0000.5790.524Outlay(120,000)(120,000)Net present value Locating the IRR between two discount rates of known NPV  INCLUDEPICTURE "C:\\WINDOWS\\Desktop\\WORK\\PE4409 Weetman IM\\gifs\\Ex 25-11.gif" \* MERGEFORMAT  The precise discount rate which gives a zero NPV may now be found by assuming a linear interval between 20% and 24%. The difference between the two net present values is 6,360 ( ((1,200), i.e. 7,560. The difference between the two discount rates is 4%. Using simple proportion calculations the net present value of zero lies at: 20% +  EMBED Equation.2  = 23.365% The process of estimation shown here is called .. Formula lower of the pair of discount rates +  EMBED Equation.2  Graph of net present value against discount rate showing IRR  INCLUDEPICTURE "C:\\WINDOWS\\Desktop\\WORK\\PE4409 Weetman IM\\gifs\\Ex 25-12.gif" \* MERGEFORMAT  The Internal Rate of Return decision rule Where the IRR of the project is the cost of capital, the project. Where the IRR of the project is . the cost of capital, . the project. Where the IRR of the project the cost of capital, the project is in meeting the required rate of return of those investing in the business but gives no surplus to its owners. When the net present value and the internal rate of return criteria are applied to an isolated project, they will lead to the same accept/reject decision because they both use the discounting method of calculation applied to the same cash flows. Mutually exclusive projects An organisation may need to make a choice between two projects which are mutually exclusive (perhaps because there is only sufficient demand in the market for the output of one of the projects, or because there is a limited physical capacity which will not allow both). Case example: Whisky distillery A distillery is planning to invest in a new still. There are two plans, one of which involves continuing to produce the traditional mix of output blends and the second of which involves experimentation with new blends. The second plan will produce lower cash flows in the earlier years of the life of the still but it is planned that these cash flows will overtake the traditional pattern within a short space of time. The cost of capital is 12% per annum. Two mutually exclusive projects: Cash flows, NPV and IRR ProjectInitial Cash flowsinvestmentYear 1Year 2Year 3A120,00096,00048,00012,000B120,00012,00060,000108,000 Project NPV at 12% IRRA12,52120.2%B15,41917.6% It may be seen that, looking at the net present value at the cost of capital, Project B appears the more attractive with the higher net present value. Looking at the internal rate of return, Project A appears more attractive. Profitability index The profitability index is the present value of cash flows (discounted at the cost of capital) divided by the present value of the investment intended to produce those cash flows. The project with the highest profitability index will give the highest net present value for the amount of investment funding available: Project A Profitability index = EMBED Equation  = 1.10 Project B Profitability index = EMBED Equation  = 1.13 This confirms that, of the two, Project B is preferable at a cost of capital of 12%. Sensitivity to changes in the discount rate Graph of net present value of competing projects using a range of discount rates  INCLUDEPICTURE "C:\\WINDOWS\\Desktop\\WORK\\PE4409 Weetman IM\\gifs\\Ex 25-14.gif" \* MERGEFORMAT  For both projects, the net present value . as the discount rate .. but the net present value of Project B more rapidly. The net present value of Project B is than that of Project A at all discount rates above the point M (around 14.2%). In particular Project B has a net present value than Project A at the cost of capital 12% (point N on the graph). For discount rates above 14.2%, the net present value of Project B is always .. than that of Project A. The internal rate of return for Project B is at point .. (around ..%). The internal rate of return for Project A is at point .(around %). If it is certain that the cost of capital will remain at 12%, then Project is more desirable than Project .. If there is a chance that the cost of capital will in reality be substantially higher than the 12% then it might be safer to choose Project A. Financial and Management Accounting, Third Edition Student notes 25. PAGE 1 P Weetman and P Gordon. 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