Fundamentals of Management Accounting for Decision Makers 6th edition_8 ppt

In increasing the discount rate from 20 per cent to 30 per cent, we have reduced the NPV from £24,190 (positive) to £1,880 (negative). Since the IRR is the discount rate that will give us an NPV of exactly zero, we can conclude that the IRR of Billingsgate Battery Company’s machine project is very slightly below 30 per cent. Further trials could lead us to the exact rate, but there is probably not much point, given the likely inaccuracy of the cash flow estimates. It is probably good enough, for practical pur- poses, to say that the IRR is about 30 per cent. The relationship between the NPV method discussed earlier and the IRR is shown graphically in Figure 8.4 using the information relating to the Billingsgate Battery Company. CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS 280 The relationship between the NPV and IRR methods Figure 8.4 If the discount rate were zero, the NPV would be the sum of the net cash flows. In other words, no account would be taken of the time value of money. However, if we assume increasing dis- count rates, there is a corresponding decrease in the NPV of the project. When the NPV line crosses the horizontal axis there will be a zero NPV, and the point where it crosses is the IRR. We can see that, where the discount rate is zero, the NPV will be the sum of the net cash flows. In other words, no account is taken of the time value of money. However, as the discount rate increases there is a corresponding decrease in the NPV of the pro- ject. When the NPV line crosses the horizontal axis there will be a zero NPV, and that represents the IRR. What is the internal rate of return of the Chaotic Industries project from Activity 8.2? You should use the discount table on pp. 521–522. (Hint: Remember that you already know the NPV of this project at 15 per cent (from Activity 8.12).) Since we know that, at a 15 per cent discount rate, the NPV is a relatively large negative figure, our next trial is using a lower discount rate, say 10 per cent: Activity 8.15 M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 280 We could undertake further trials in order to derive the precise IRR. If, however, we have to calculate the IRR manually, further iterations can be time-consuming. We can get an acceptable approximation to the answer fairly quickly by first calcu- lating the change in NPV arising from a 1 per cent change in the discount rate. This can be done by taking the difference between the two trials (that is, 15 per cent and 10 per cent) that we have already carried out (in Activities 8.12 and 8.15): Trial Discount factor Net present value % £000 1 15 (23.49) 2 10 (2.46) Difference 5 21.03 The change in NPV for every 1 per cent change in the discount rate will be (21.03/5) = 4.21 The reduction in the 10% discount rate required to achieve a zero NPV would there- fore be (2.46)/4.21 × 1% = 0.58% The IRR is therefore (10.00 − 0.58)% = 9.42% However, to say that the IRR is about 9 or 10 per cent is near enough for most purposes. Note that this approach assumes a straight-line relationship between the discount rate and NPV. We can see from Figure 8.4 that this assumption is not strictly correct. Over a relatively short range, however, this simplifying assumption is not usually a problem and so we can still arrive at a reasonable approximation using the approach that we took in deriving the 9.42 per cent IRR. In practice, most businesses have computer software packages that will derive a project’s IRR very quickly. Thus, in practice it is not usually necessary either to make a series of trial discount rates or to make the approximation that we have just considered. Users of the IRR method should apply the following decision rules: INTERNAL RATE OF RETURN (IRR) 281 Time Cash flows Discount factor Present value £000 (10% – from the table) £000 Immediately (150) 1.000 (150.00) 1 year’s time 30 0.909 27.27 2 years’ time 30 0.826 24.78 3 years’ time 30 0.751 22.53 4 years’ time 30 0.683 20.49 5 years’ time 30 0.621 18.63 6 years’ time 30 0.564 16.92 6 years’ time 30 0.564 16.92 NPV (2.46) This figure is close to zero NPV. However, the NPV is still negative and so the precise IRR will be a little below 10 per cent. M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 281 CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS 282 l For any project to be acceptable, it must meet a minimum IRR requirement. This is often referred to as the hurdle rate and, logically, this should be the opportunity cost of finance. l Where there are competing projects (that is, the business can choose only one of two or more viable projects), the one with the higher (or highest) IRR should be selected. IRR has certain attributes in common with NPV. All cash flows are taken into account, and their timing is logically handled. Real World 8.7 provides some idea of the IRR for one form of renewable energy. Real World 8.8 gives some examples of IRRs sought in practice. REAL WORLD 8.8 Rates of return IRR rates for investment projects can vary considerably. Here are a few examples of the expected or target returns from investment projects of large businesses. l Forth Ports plc, a port operator, concentrates on projects that generate an IRR of at least 15 per cent. l Rok plc, the builder, aims for a minimum IRR of 15% from new investments. l Hutchison Whampoa, a large telecommunications business, requires an IRR of at least 25 per cent from its telecom projects. l Airbus, the plane maker, expects an IRR of 13 per cent from the sale of its A380 super- jumbo aircraft. l Signet Group plc, the jewellery retailer, requires an IRR of 20 per cent over five years when appraising new stores. Sources: ‘FAQs, Forth Ports plc’, www.forthports.co.uk; Numis Broker Research Report www.rokgroup.com, 17 August 2006, p. 31; ‘Hutchison Whampoa’, Lex column, ft.com, 31 March 2004; ‘Airbus hikes A380 break-even target’, ft.com, 20 October 2006, ‘Risk and other factors’, Signet Group plc, www.signetgroupplc.com, 2006. REAL WORLD 8.7 The answer is blowin’ in the wind ‘Wind farms are practically guaranteed to make returns once you have a licence to operate,’ says Bernard Lambilliotte, chief investment officer at Ecofin, a financial group that runs Ecofin Water and Power Opportunities, an investment trust. ‘The risk is when you have bought the land and are seeking a licence,’ says Lambilliotte. ‘But once it is built and you are plugged into the grid it is risk-free. It will give an internal rate of return in the low to mid-teens.’ Ecofin’s largest investment is in Sechilienne, a French company that operates wind farms in northern France and generates capacity in the French overseas territories powered by sugar cane waste. Source: Batchelor, C., ‘A hot topic, but poor returns’, ft.com, 27 August 2005. FT M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 282 Problems with IRR The main disadvantage of IRR, relative to NPV, is the fact that it does not directly address the question of wealth generation. It could therefore lead to the wrong deci- sion being made. This is because IRR will always rank a project with an IRR of 25 per cent above one with an IRR of 20 per cent, assuming an opportunity cost of finance of, say, 15 per cent. Although accepting the project with the higher percentage return will often generate more wealth, this may not always be the case. This is because IRR completely ignores the scale of investment. With a 15 per cent cost of finance, £15 million invested at 20 per cent for one year will make us wealthier by £0.75 million (that is, 15 × (20 − 15)% = 0.75). With the same cost of finance, £5 million invested at 25 per cent for one year will make us only £0.5 million (that is, 5 × (25 − 15)% = 0.50). IRR does not recognise this. It should be acknowledged that it is not usual for projects to be competing where there is such a large difference in scale. Even though the problem may be rare and so, typically, IRR will give the same signal as NPV, a method that is always reliable (NPV) must be better to use than IRR. This problem with percentages is another example of the one illustrated by the Mexican road discussed in Real World 8.3. A further problem with the IRR method is that it has difficulty handling projects with unconventional cash flows. In the examples studied so far, each project has a negative cash flow arising at the start of its life and then positive cash flows thereafter. However, in some cases, a project may have both positive and negative cash flows at future points in its life. Such a pattern of cash flows can result in there being more than one IRR, or even no IRR at all. This would make the IRR method difficult to use, although it should be said that this is quite rare in practice. This is never a problem for NPV, however. When undertaking an investment appraisal, there are several practical points that we should bear in mind: l Past costs. As with all decisions, we should take account only of relevant costs in our analysis. This means that only costs that vary with the decision should be con- sidered. Thus, all past costs should be ignored as they cannot vary with the decision. In some cases, a business may incur costs (such as development costs and market research costs) before the evaluation of an opportunity to launch a new product. As those costs have already been incurred, they should be disregarded, even though the amounts may be substantial. Costs that have already been committed but not yet paid should also be disregarded. Where a business has entered into a binding contract to incur a particular cost, it becomes in effect a past cost even though payment may not be due until some point in the future. l Common future costs. It is not only past costs that do not vary with the decision; some future costs may also be the same. For example, the cost of raw materials may not vary with the decision whether to invest in a new piece of manufacturing plant or to continue to use existing plant. l Opportunity costs. Opportunity costs arising from benefits forgone must be taken into account. Thus, for example, when considering a decision concerning whether or not Some practical points SOME PRACTICAL POINTS 283 ‘ M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 283 to continue to use a machine already owned by the business, the realisable value of the machine might be an important opportunity cost. l Taxation. Owners will be interested in the after-tax returns generated from the busi- ness, and so taxation will usually be an important consideration when making an investment decision. The profits from the project will be taxed, the capital invest- ment may attract tax relief and so on. Tax is levied at significant rates. This means that, in real life, unless tax is formally taken into account, the wrong decision could easily be made. The timing of the tax outflow should also be taken into account when preparing the cash flows for the project. l Cash flows not profit flows. We have seen that for the NPV, IRR and PP methods, it is cash flows rather than profit flows that are relevant to the assessment of invest- ment projects. In an investment appraisal requiring the application of any of these methods we may be given details of the profits for the investment period. These need to be adjusted in order to derive the cash flows. We should remember that the operating profit before non-cash items (such as depreciation) is an approximation to the cash flows for the period, and so we should work back to this figure. When the data are expressed in profit rather than cash flow terms, an adjustment in respect of working capital may also be necessary. Some adjustment should be made to take account of changes in working capital. For example, launching a new product may give rise to an increase in the net investment made in trade receivables and inventories less trade payables, requiring an immediate outlay of cash. This outlay for additional working capital should be shown in the NPV calculations as part of the initial cost. However, at the end of the life of the project, the additional working capital will be released. This divestment results in an effective inflow of cash at the end of the project; it should also be taken into account at the point at which it is received. l Year-end assumption. In the examples and activities that we have considered so far in this chapter, we have assumed that cash flows arise at the end of the relevant year. This is a simplifying assumption that is used to make the calculations easier. (However, it is perfectly possible to deal more precisely with the cash flows.) As we saw earlier, this assumption is clearly unrealistic, as money will have to be paid to employees on a weekly or monthly basis and credit customers will pay within a month or two of buying the product or service. Nevertheless, it is probably not a serious distortion. We should be clear, however, that there is nothing about any of the four appraisal methods that demands that this assumption be made. l Interest payments. When using discounted cash flow techniques (NPV and IRR), inter- est payments should not be taken into account in deriving the cash flows for the period. The discount factor already takes account of the costs of financing, and so to take account of interest charges in deriving cash flows for the period would be double counting. l Other factors. Investment decision making must not be viewed as simply a mechan- ical exercise. The results derived from a particular investment appraisal method will be only one input to the decision-making process. There may be broader issues connected to the decision that have to be taken into account but which may be difficult or impossible to quantify. The reliability of the forecasts and the validity of the assumptions used in the evaluation will also have a bearing on the final decision. CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS 284 M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 284 SOME PRACTICAL POINTS 285 The directors of Manuff (Steel) Ltd are considering closing one of the business’s fac- tories. There has been a reduction in the demand for the products made at the factory in recent years, and the directors are not optimistic about the long-term prospects for these products. The factory is situated in the north of England, in an area where unemployment is high. The factory is leased, and there are still four years of the lease remaining. The direc- tors are uncertain whether the factory should be closed immediately or at the end of the period of the lease. Another business has offered to sub-lease the premises from Manuff at a rental of £40,000 a year for the remainder of the lease period. The machinery and equipment at the factory cost £1,500,000, and have a statement of financial position (balance sheet) value of £400,000. In the event of immediate closure, the machinery and equipment could be sold for £220,000. The working capital at the factory is £420,000, and could be liquidated for that amount immediately, if required. Alternatively, the working capital can be liquidated in full at the end of the lease period. Immediate closure would result in redundancy payments to employees of £180,000. If the factory continues in operation until the end of the lease period, the following operating profits (losses) are expected: Year 1 Year 2 Year 3 Year 4 £000 £000 £000 £000 Operating profit/(loss) 160 (40) 30 20 The above figures include a charge of £90,000 a year for depreciation of machinery and equipment. The residual value of the machinery and equipment at the end of the lease period is estimated at £40,000. Redundancy payments are expected to be £150,000 at the end of the lease period if the factory continues in operation. The business has an annual cost of capital of 12 per cent. Ignore taxation. (a) Determine the relevant cash flows arising from a decision to continue operations until the end of the lease period rather than to close immediately. (b) Calculate the net present value of continuing operations until the end of the lease period, rather than closing immediately. (c) What other factors might the directors take into account before making a final deci- sion on the timing of the factory closure? (d) State, with reasons, whether or not the business should continue to operate the factory until the end of the lease period. Your answer should be as follows: (a) Relevant cash flows Years 01234 £000 £000 £000 £000 £000 Operating cash flows (Note 1) 250 50 120 110 Sale of machinery (Note 2) (220) 40 Redundancy costs (Note 3) 180 (150) Sub-lease rentals (Note 4) (40) (40) (40) (40) Working capital invested (Note 5) (420) 420 (460) 210 10 80 380 Activity 8.16 ‘ M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 285 Many surveys have been conducted in the UK into the methods of investment appraisal used by businesses. They have shown the following features: l Businesses tend to use more than one method to assess each investment decision. l The discounting methods (NPV and IRR) have become increasingly popular over time, with these two becoming the most popular in recent years. l The continued popularity of PP, and to a lesser extent ARR, despite their theoretical shortcomings. Investment appraisal in practice CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS 286 Notes: 1 Each year’s operating cash flows are calculated by adding back the depreciation charge for the year to the operating profit for the year. In the case of the operating loss, the depreciation charge is deducted. 2 In the event of closure, machinery could be sold immediately. Thus an opportunity cost of £220,000 is incurred if operations continue. 3 If operations are continued, there will be a saving in immediate redundancy costs of £180,000. However, redundancy costs of £150,000 will be paid in four years’ time. 4 If operations are continued, the opportunity to sub-lease the factory will be forgone. 5 Immediate closure would mean that working capital could be liquidated. If operations continue, this opportunity is foregone. However, working capital can be liquidated in four years’ time. (b) Discount rate 12 per cent 1.000 0.893 0.797 0.712 0.636 Present vaIue (460) 187.5 8.0 57.0 241.7 Net present vaIue 34.2 (c) Other factors that may influence the decision include: l The overall strategy of the business. The business may need to set the decision within a broader context. It may be necessary to manufacture the products at the factory because they are an integral part of the business’s product range. The business may wish to avoid redundancies in an area of high unemployment for as long as possible. l Flexibility. A decision to close the factory is probably irreversible. If the factory continues, however, there may be a chance that the prospects for the factory will brighten in the future. l Creditworthiness of sub-lessee. The business should investigate the creditworthi- ness of the sub-lessee. Failure to receive the expected sub-lease payments would make the closure option far less attractive. l Accuracy of forecasts. The forecasts made by the business should be examined carefully. Inaccuracies in the forecasts or any underlying assumptions may change the expected outcomes. (d) The NPV of the decision to continue operations rather than close immediately is positive. Hence, shareholders would be better off if the directors took this course of action. The factory should therefore continue in operation rather than close down. This decision is likely to be welcomed by employees and would allow the business to main- tain its flexibility. Activity 8.16 continued M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 286 l A tendency for larger businesses to rely more heavily on discounting methods than smaller businesses. Real World 8.9 shows the results of a recent survey of UK manufacturing businesses regarding their use of investment appraisal methods. INVESTMENT APPRAISAL IN PRACTICE 287 REAL WORLD 8.9 A survey of UK business practice A survey of 83 of the UK’s largest manufacturing businesses examined the investment appraisal methods used to evaluate both strategic and non-strategic projects. Strategic projects usually aim to increase or change the competitive capabilities of a business, for example by introducing a new manufacturing process. Although a definition was provided, survey respondents were able to decide for themselves what constituted a strategic pro- ject. The results of the survey are set out below. Method Non-strategic projects Strategic projects Mean score Mean score Net present value 3.6829 3.9759 Payback 3.4268 3.6098 Internal rate of return 3.3293 3.7073 Accounting rate of return 1.9867 2.2667 Response scale: 1= never, 2 = rarely, 3 = often, 4 = mostly, 5 = always. We can see that, for both non-strategic and strategic investments, the NPV method is the most popular. As the sample consists of large businesses (nearly all with total sales revenue in excess of £100 million), a fairly sophisticated approach to evaluation might be expected. Nevertheless, for non-strategic investments, the payback method comes second in popularity. It drops to third place for strategic projects. The survey also found that 98 per cent of respondents used more than one method and 88 per cent used more than three methods of investment appraisal. Source: Based on information in Alkaraan, F. and Northcott, D., ‘Strategic capital investment decision-making: a role for emergent analysis tools? A study of practice in large UK manufacturing companies’, The British Accounting Review, No. 38, 2006, p. 159. A survey of US businesses also shows considerable support for the NPV and IRR methods. There is less support, however, for the payback method and ARR. Real World 8.10 sets out some of the main findings. REAL WORLD 8.10 A survey of US practice A survey of the chief financial officers (CFOs) of 392 US businesses examined the popularity of various methods of investment appraisal. Figure 8.5 shows the percentage of businesses surveyed that always, or almost always, used the four methods discussed in this chapter. ‘ M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 287 PP can provide a convenient, though rough and ready, assessment of the profitabil- ity of a project, in the way that it is used in Real World 8.11. CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS 288 Earlier in the chapter we discussed the theoretical limitations of the PP method. Can you explain the fact that it still seems to be a popular method of investment appraisal among businesses? A number of possible reasons may explain this finding: l PP is easy to understand and use. l It can avoid the problems of forecasting far into the future. l It gives emphasis to the early cash flows when there is greater certainty concerning the accuracy of their predicted value. l It emphasises the importance of liquidity. Where a business has liquidity problems, a short payback period for a project is likely to appear attractive. Activity 8.17 Real World 8.10 continued The use of investment appraisal methods among US businesses Figure 8.5 The IRR and NPV methods are both widely used and are much more popular than the payback and accounting rate of return methods. Nevertheless, the payback method is still used always, or almost always, by a majority of US businesses. Source: Based on information in Graham, R. and Harvey, C., ‘How do CFOs make capital budgeting and capital structure decisions?’, Journal of Applied Corporate Finance, Vol. 15, No. 1, 2002. M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 288 The popularity of PP may suggest a lack of sophistication by managers, concerning investment appraisal. This criticism is most often made against managers of smaller businesses. This point is borne out by both of the surveys discussed above, which have found that smaller businesses are much less likely to use discounted cash flow methods (NPV and IRR) than are larger ones. Other surveys have tended to reach a similar conclusion. IRR may be popular because it expresses outcomes in percentage terms rather than in absolute terms. This form of expression appears to be more acceptable to managers, despite the problems of percentage measures that we discussed earler. This may be because managers are used to using percentage figures as targets (for example, return on capital employed). Real World 8.12 shows extracts from the 2006 annual report of a well-known busi- ness: Rolls-Royce plc, the builder of engines for aircraft and other purposes. INVESTMENT APPRAISAL IN PRACTICE 289 REAL WORLD 8.11 An investment lifts off SES Global is the world’s largest commercial satellite operator. This means that it rents satellite capacity to broadcasters, governments, telecommunications groups and internet service providers. It is a risky venture that few are prepared to undertake. As a result, a handful of businesses dominates the market. Launching a satellite requires a huge initial outlay of capital, but relatively small cash outflows following the launch. Revenues only start to flow once the satellite is in orbit. A satellite launch costs around A250m. The main elements of this cost are the satellite (A120m), the launch vehicle (A80m), insurance (A40m) and ground equipment (A10m). According to Romain Bausch, president and chief executive of SES Global, it takes three years to build and launch a satellite. However, the average lifetime of a satellite is fifteen years during which time it is generating revenues. The revenues generated are such that the payback period is around four to five years. Source: Satellites need space to earn, ft.com (Burt, T.), © The Financial Times Limited, 14 July 2003. FT REAL WORLD 8.12 The use of NPV at Rolls-Royce In its 2007 annual report and accounts, Rolls-Royce plc stated: The Group continues to subject all investments to rigorous examination of risks and future cash flows to ensure that they create shareholder value. All major investments require Board approval. The Group has a portfolio of projects at different stages of their life cycles. Discounted cash flow analysis of the remaining life of projects is performed on a regular basis. Source: Rolls-Royce plc Annual Report 2007. Rolls-Royce makes clear that it uses NPV (the report refers to creating shareholder value and to discounted cash flow, which strongly imply NPV). It is interesting to note that Rolls-Royce not only assesses new projects but also reassesses existing ones. This M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 289 [...]... probability of producing a negative NPV of £200,000 and a 0.1 probability of producing a positive NPV of £3.8m Project B has a 0.6 probability of producing a positive NPV of £100,000 and a 0.4 probability of producing a positive NPV of £350,000 What is the expected net present value of each project? The expected NPV of Project A is [(0.1 × £3.8m) − (0.9 × £200,000)] = £200,000 The expected NPV of Project... become obsolete The cost of producing the software was £10,000 The client has agreed to pay a licence fee of £8,000 a year for the software if it is used in only one of its two divisions, and £12,000 a year if it is used in both of its divisions The client may use the software for either one or two years in either division but will definitely use it in at least one division in each of the two years Zeta... CAPITAL INVESTMENT DECISIONS Figure 8.9 Managing the investment decision The management of an investment project involves a sequence of five key stages The evaluation of projects using the appraisal techniques discussed earlier represents only one of these stages Stage 1: Determine investment funds available The amount of funds available for investment may be determined by the external market for funds or... manager of a business operating a fleet of vans may be able to provide information concerning the possible life of a new van based on the record of similar vans acquired in the past From the information available, probabilities may be developed for different possible lifespans However, the past may not always be a reliable guide to the future, particularly during a period of rapid change In the case of the... re-examination of the market value of the flats seems appropriate before a final decision is made M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 295 DEALING WITH RISK 295 There are two major drawbacks with the use of sensitivity analysis: l It does not give managers clear decision rules concerning acceptance or rejection of the project and so they must rely on their own judgement l It is a static form of analysis... this kind of reassessment of existing projects No doubt most other well-managed businesses do this too Project management techniques (for example, critical path analysis) should be employed wherever possible and their effectiveness reported to senior management An important part of the control process is a post-completion audit of the project This is, in essence, a review of the project’s performance... illogical conclusions – Takes almost no account of the timing of cash flows – Ignores some relevant information and may take account of some that is irrelevant – Relatively simple to use – Much inferior to NPV Payback period (PP) is the length of time that it takes for the cash outflow for the initial investment to be repaid out of resulting cash inflows l Decision rule – projects with a PP up to a defined... level of risk We now consider formal methods of dealing with risk that fall within each category 291 M08_ATRI3622_06_SE_C08.QXD 292 CHAPTER 8 5/29/09 3:31 PM Page 292 MAKING CAPITAL INVESTMENT DECISIONS Assessing the level of risk Sensitivity analysis ‘ One popular way of attempting to assess the level of risk is to carry out a sensitivity analysis on the proposed project This involves an examination of. .. attached to the project The information relating to each outcome can be presented M08_ATRI3622_06_SE_C08.QXD 5/29/09 3:31 PM Page 299 DEALING WITH RISK in the form of a diagram if required The construction of such a diagram is illustrated in Example 8.5 Example 8.5 Zeta Computing Services Ltd has recently produced some software for a client organisation The software has a life of two years and will then... expected to be sold at the end of the second year for a total of £450,000 The cost of renovation will be the subject of a binding contract with local builders if the property is bought There is, however, some uncertainty over the remaining input values The business estimates its cost of capital at 12 per cent a year (a) What is the NPV of the proposed project? (b) Assuming none of the other inputs deviates . handled. Real World 8. 7 provides some idea of the IRR for one form of renewable energy. Real World 8. 8 gives some examples of IRRs sought in practice. REAL WORLD 8. 8 Rates of return IRR rates for investment. equivalent) −20 $0.66 26. 68 2 98. 5 3.0 −10 $0.72 23.7 2 38. 6 3.3 +10 $0 .83 17.1 1 18. 9 4.4 +20 $0 .88 13.6 59.0 5.3 Capital costs Initial capital (US$m) −20 360 28. 6 261 .8 2 .8 −10 405 24.1 220.3 3.2 +10. bearing on the final decision. CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS 284 M 08_ ATRI3622_06_SE_C 08. QXD 5/29/09 3:31 PM Page 284 SOME PRACTICAL POINTS 285 The directors of Manuff (Steel) Ltd