Prompt and Accurate Computation of Net Present Value

Transcription

1 , pp Prompt and Accurate Computation of Net Present Value Jin Hyoung Jang Department of Accounting, Daegu University, Korea Abstract. In order to compute the net present value promptly, two different spreadsheets (Microsoft, IBM) and Texas Instruments financial calculator are tried out, and the result shows that TI s financial calculator is superior in the clarity and promptness for the users. Keywords: NPV, net present value, Excel, Lotus Symphony Spreadsheet, BA II PLUS PROFESSIONAL 1 Introduction Due to their superiority discounted cash flow methods are more widely used than nondiscounted cash flow methods [1]. The computation of net present value or the internal rate of return is essential in using the net present value method or the internal rate of return method. Among discounted methods, the net present value method is more advantageous than the internal rate of return method; this study tries to find a prompt and accurate way to calculate the net present value. 2 Advantages of the Net Present Value (NPV) Method The net present value (NPV) method has several important advantages over the rate of return (IRR) method. First, a key assumption made by the internal rate of return (IRR) method is questionable. Both methods assume that cash flows generated by a project during its useful life are immediately reinvested elsewhere. However, the two methods make different assumptions concerning the rate of return that is earned on those cash flow. The net present value method assumes the rate of return is the discount rate, whereas the internal rate of return method assumes the rate of return is the internal rate of return on the project. Specifically, if the internal rate of return of the project is high, this assumption may not be realistic [2]. Second, with certain cash flow streams it is mathematically possible to produce negative IRRs, or multiple IRRs for the cash stream (more than one discount rate that leads to a 0 NPV). For other cash flow streams, there is simply no mathematically correct IRR solution. There is no possible IRR solution when the cash flow includes only positive or only negative net cash flows. A net cash flow stream will have multiple IRRs when it includes more than one sign change. It is also possible for some net cash flow streams to produce a negative IRR value [3]. ISSN: ASTL Copyright 2013 SERSC

2 3 The Computation Theory of Net Present Value To illustrate the computation of NPV, consider Top-Spin tennis racquets, Top-Spin was one of the first major tennis-racquet producers to introduce graphite in its racquets. Top-Spin estimates that it can purchase a carbon-fiber weaving machine with a useful life of five years for a net after-tax initial investment of $379,100, which is calculated as follows: Cost of new machine $390,000 Investment in working capital Cash flow from disposing of existing machine (after-tax) (19,900) Net initial investment for new machine $379,100 In the case of Top-Spin, the purchase of the new machine is accompanied by an outlay of $9,000 for supplies and spare parts inventory. Managers estimate that by introducing carbon-fiber impregnated racquets, operating cash inflows (cash revenues minus cash operating costs) will increase by $100,000 (after tax) in the first four years and $91,000 in year 5. To simplify the analysis, suppose that all cash flows occur at the end of each year. Note that cash flow at the end of the fifth year also increases by $100,000, $91,000 in operating cash Inflows and $9,000 in working capital. Suppose the CFO at Top-Spin has set the required rate of return for the firm s investments at 8% per year [4]. The NPV of this example can be solved by the formula below. $379,100 + $100,000 ( ) + $100,000 ( ) 2 + $100,000 ( ) 3 + $100,000 ( ) 4 + $100,000 ( ) 5 = $20,171 1 This kind of computation requires a lot of time and effort if it is solved without any instruments or even by regular calculators. 2 4 NPV Computation Using Instruments 4.1 Microsoft Excel Microsoft Excel is a spreadsheet application developed by Microsoft for Microsoft Windows and Mac OS. It features calculation, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications. It has been a very widely applied spreadsheet for these platforms, especially since version 5 in 1993, and it has replaced Lotus as the industry standard for spreadsheets. Excel forms part of Microsoft Office. The NPV function syntax for NPV computation is as following [5]. 1 $20,200 showing in Horngren et al. (2012) is due to rounding. 2 The present value of $1.00 and the present value of annuity $1.00 in most textbooks can be used for the convenience of the computation. Copyright 2013 SERSC 67

3 NPV(rate,value1,[value2],...) The result of the NPV for the example above using NPV function is in $18,677. However, this amount of $18,677 is different from the amount of $20,171 computed without any help from instruments. When examined the help about the Excel s NPV function, the following remark is found. The NPV investment begins one period before the date of the value1 cash flow and ends with the last cash flow in the list. The NPV calculation is based on future cash flows. If your first cash flow occurs at the beginning of the first period, the first value must be added to the NPV result, not included in the values arguments. Following the remark in the help, the result of NPV for the example above is $20,171. This software seems not so user-friendly. Investors make investment decision based upon the amount of investment which is starting right away, the duration of investment and cash inflows from the investment. Seldom considers an investment beginning one year after from the time of decision making. If so, investment right away should become default. The examples in most textbooks do not exemplify investments beginning 1 year after from now. In order to compute IRR using IRR function, cash inflows and cash outflows are entered at the same time, but NPV computation is complicated in its procedure, and doesn t suit the ordinary people s mindset. If we do not pay considerable attention, it is easy to make mistakes. 4.2 IBM Lotus Symphony Spreadsheet IBM Lotus Symphony is a suite of applications for creating, editing, and sharing text, spreadsheet, presentations and other documents and browsing the world wide web. It is distributed as freeware. First released in 2007, the suite has a name similar to the 1980s DOS suite Lotus Symphony. IBM Lotus Symphony consists of: IBM Lotus Symphony Documents, a word processor IBM Lotus Symphony Spreadsheets, a spreadsheet program IBM Lotus Symphony Presentations, a presentation program a web browser based on Firefox 3. IBM discontinued development of Lotus Symphony in January 2012 with the final release of version 3.0.1, moving future development effort to Apache OpenOffice, and donating the source code to the Apache Software Foundation [6]. The NPV function in IBM Lotus Symphony Spreadsheet returns the present value of an investment based on a series of periodic cash flows and a discount rate. To get the net present value, subtract the cost of the project (the initial cash flow at time zero) from the returned value. The NPV function syntax for computing NPV is as following. 68 Copyright 2013 SERSC

4 NPV(Rate; Value1; Value2;...) Rate is the discount rate for a period. Value1;... are up to 30 values, which represent deposits or withdrawals. The result of NPV for the example above using Lotus Symphony Spreadsheet s NPV function is $18,677. This result is exactly same as that of Excel, therefore NPV computed again using the similar syntax of the Excel is $20, TI BA II PLUS PROFESSIONAL Calculator The BA-II Plus Professional calculator is engineered to solve calculations related to the financial field such as annuities, mortgages, leases, and various others. This TI financial calculator has the payback and discounted payback feature that offers payback and discounted values, which is ideal for investment purposes. It computes IRR and NPV. In particular, this calculator has been approved for the Chartered Financial Analyst (CFA) exam. In order to compute the NPV for the example above by this calculator, one should press input buttons as follows. CF 2ND CLR WORK /- ENTER ENTER 5 ENTER NPV 8 ENTER CTP By doing this, NPV= 20,171 3 appears on the screen promptly without any constraints. This agrees with our mindset and with solutions in management accounting textbooks and financial management textbooks. 5 Conclusions This study uses two different softwares (Microsoft Excel, IBM Lotus Symphony Spreadsheet) and TI BA II PLUS PROFESSIONAL calculator to compute the net present value. The conclusions are as following. First, a desired answer can t be obtained by the NPV function s default =NPV(rate,value1:value6), but a modified type =NPV(rate,value2:value6)+value1 can obtain a desired answer. This may confuse the users. Second, Texas Instruments financial calculator provides with an accurate and prompt answer. 3 In order to get answer of $18,677 from BA II PLUS PROFESSIONAL CALCULATOR, input 0 in CF0 column, -397,100 in C01 column, and 100,000 in C02 column. Copyright 2013 SERSC 69

5 References 1. Graham J. R., Harvey C. R.: The Theory and Practice of Corporate Finance: Evidence from the Field. Journal of Financial Economics 60, (2001) 2. Accounting For Management, 3. Business Case Analysis, 4. Horngren Charles T., Datar, Srikant M., Rajan, Madhav V.: Cost Accounting: a Managerial Emphasis, 14th ed., Prentice-Hall, New Jersey (2012) 5. Microsoft Office, 6. WIKIPEDIA, 70 Copyright 2013 SERSC