Fundamentals of Management Accounting for Decision Makers 6th edition_8 ppt

The relationship between the NPV and IRR methodsFigure 8.4 If the discount rate were zero, the NPV would be the sum of the net cash flows.. Thus, in practice it is not usually necessary

In increasing the discount rate from 20 per cent to 30 per cent, we have reduced theNPV from £24,190 (positive) to £1,880 (negative) Since the IRR is the discount ratethat will give us an NPV of exactly zero, we can conclude that the IRR of BillingsgateBattery Company’s machine project is very slightly below 30 per cent Further trialscould lead us to the exact rate, but there is probably not much point, given the likelyinaccuracy 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 showngraphically in Figure 8.4 using the information relating to the Billingsgate BatteryCompany

The relationship between the NPV and IRR methodsFigure 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 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.

dis-We can see that, where the discount rate is zero, the NPV will be the sum of the netcash 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 ject When the NPV line crosses the horizontal axis there will be a zero NPV, and thatrepresents the IRR

pro-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 negativefigure, our next trial is using a lower discount rate, say 10 per cent:

Activity 8.15

We could undertake further trials in order to derive the precise IRR If, however, wehave to calculate the IRR manually, further iterations can be time-consuming.

We can get an acceptable approximation to the answer fairly quickly by first lating the change in NPV arising from a 1 per cent change in the discount rate Thiscan be done by taking the difference between the two trials (that is, 15 per cent and

calcu-10 per cent) that we have already carried out (in Activities 8.12 and 8.15):

Trial Discount factor Net present value

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 aseries 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

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 oftwo or more viable projects), the one with the higher (or highest) IRR should beselected

IRR has certain attributes in common with NPV All cash flows are taken intoaccount, and their timing is logically handled

Real World 8.7provides some idea of the IRR for one form of renewable energy

Real World 8.8gives some examples of IRRs sought in practice

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 jumbo aircraft

super-l Signet Group plc, the jewellery retailer, requires an IRR of 20 per cent over five yearswhen 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 runsEcofin 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 internalrate of return in the low to mid-teens.’ Ecofin’s largest investment is in Sechilienne, a Frenchcompany that operates wind farms in northern France and generates capacity in the Frenchoverseas territories powered by sugar cane waste

Source: Batchelor, C., ‘A hot topic, but poor returns’, ft.com, 27 August 2005.

FT

Problems with IRR

The main disadvantage of IRR, relative to NPV, is the fact that it does not directlyaddress 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 percent 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 returnwill 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 thesame 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 bebetter to use than IRR This problem with percentages is another example of the oneillustrated by the Mexican road discussed in Real World 8.3

A further problem with the IRR method is that it has difficulty handling projectswith 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 morethan 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 forNPV, however

When undertaking an investment appraisal, there are several practical points that weshould 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 thoughthe amounts may be substantial Costs that have already been committed but notyet paid should also be disregarded Where a business has entered into a bindingcontract 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 notvary 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

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to continue to use a machine already owned by the business, the realisable value ofthe 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 aninvestment 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 meansthat, in real life, unless tax is formally taken into account, the wrong decision couldeasily be made The timing of the tax outflow should also be taken into accountwhen 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 ment projects In an investment appraisal requiring the application of any of thesemethods we may be given details of the profits for the investment period Theseneed to be adjusted in order to derive the cash flows We should remember that the

invest-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 bemade to take account of changes in working capital For example, launching a newproduct may give rise to an increase in the net investment made in trade receivablesand inventories less trade payables, requiring an immediate outlay of cash This outlay for additional working capital should be shown in the NPV calculations aspart of the initial cost However, at the end of the life of the project, the additionalworking 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 aserious distortion We should be clear, however, that there is nothing about any ofthe 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 theperiod 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 bedouble 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 issuesconnected to the decision that have to be taken into account but which may bedifficult or impossible to quantify

The reliability of the forecasts and the validity of the assumptions used in theevaluation will also have a bearing on the final decision

SOME PRACTICAL POINTS 285

The directors of Manuff (Steel) Ltd are considering closing one of the business’s tories There has been a reduction in the demand for the products made at the factory

fac-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 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.

direc-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 sion on the timing of the factory closure?

deci-(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

£000 £000 £000 £000 £000

Activity 8.16

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Many surveys have been conducted in the UK into the methods of investmentappraisal 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 overtime, with these two becoming the most popular in recent years

l The continued popularity of PP, and to a lesser extent ARR, despite their theoreticalshortcomings

Investment appraisal in practice

Notes:

1 Each year’s operating cash flows are calculated by adding back the depreciationcharge for the year to the operating profit for the year In the case of the operatingloss, the depreciation charge is deducted

2 In the event of closure, machinery could be sold immediately Thus an opportunitycost 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 operationscontinue, 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

(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 Thebusiness may wish to avoid redundancies in an area of high unemployment for aslong 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 willbrighten 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 wouldmake 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 changethe 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 ofaction The factory should therefore continue in operation rather than close down Thisdecision is likely to be welcomed by employees and would allow the business to main-tain its flexibility

Activity 8.16 continued

l A tendency for larger businesses to rely more heavily on discounting methods thansmaller businesses.

Real World 8.9shows the results of a recent survey of UK manufacturing businessesregarding 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 investmentappraisal methods used to evaluate both strategic and non-strategic projects Strategicprojects usually aim to increase or change the competitive capabilities of a business, forexample 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

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 isthe most popular As the sample consists of large businesses (nearly all with total salesrevenue in excess of £100 million), a fairly sophisticated approach to evaluation might

be expected Nevertheless, for non-strategic investments, the payback method comessecond 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 IRRmethods 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 businessessurveyed that always, or almost always, used the four methods discussed in this chapter

‘

PP can provide a convenient, though rough and ready, assessment of the ity of a project, in the way that it is used in Real World 8.11.

profitabil-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 theaccuracy of their predicted value

l It emphasises the importance of liquidity Where a business has liquidity problems, ashort 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 thanthe payback and accounting rate of return methods Nevertheless, the paybackmethod 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.

The popularity of PP may suggest a lack of sophistication by managers, concerninginvestment appraisal This criticism is most often made against managers of smallerbusinesses 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 flowmethods (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 bebecause managers are used to using percentage figures as targets (for example, return

An investment lifts off

SES Global is the world’s largest commercial satellite operator This means that it rentssatellite capacity to broadcasters, governments, telecommunications groups and internetservice providers It is a risky venture that few are prepared to undertake As a result, ahandful of businesses dominates the market

Launching a satellite requires a huge initial outlay of capital, but relatively small cashoutflows following the launch Revenues only start to flow once the satellite is in orbit Asatellite 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 takesthree 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 suchthat 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 shareholdervalue and to discounted cash flow, which strongly imply NPV) It is interesting to notethat Rolls-Royce not only assesses new projects but also reassesses existing ones This

So far, we have tended to view investment opportunities as if they are unconnected,independent entities In practice, however, successful businesses are those that set out

a clear framework for the selection of investment projects Unless this framework is inplace, it may be difficult to identify those projects that are likely to generate a positiveNPV The best investment projects are usually those that match the business’s internalstrengths (for example, skills, experience, access to finance) with the opportunitiesavailable In areas where this match does not exist, other businesses, for which the

Investment appraisal and strategic planning

Beacon Chemicals plc is considering buying some equipment to produce a chemicalnamed X14 The new equipment’s capital cost is estimated at £100,000 If its purchase isapproved now, the equipment can be bought and production can commence by the end

of this year £50,000 has already been spent on research and development work Estimates

of revenues and costs arising from the operation of the new equipment appear below

Year 1 Year 2 Year 3 Year 4 Year 5

If the equipment is bought, sales of some existing products will be lost, and this willresult in a loss of contribution of £15,000 a year over its life

The accountant has informed you that the fixed cost includes depreciation of £20,000

a year on the new equipment It also includes an allocation of £10,000 for fixed overheads

A separate study has indicated that if the new equipment were bought, additional heads, excluding depreciation, arising from producing the chemical would be £8,000 ayear Production would require additional working capital of £30,000

over-For the purposes of your initial calculations ignore taxation

Required:

(a) Deduce the relevant annual cash flows associated with buying the equipment

(b) Deduce the payback period

(c) Calculate the net present value using a discount rate of 8 per cent

(Hint: You should deal with the investment in working capital by treating it as a cash

out-flow at the start of the project and an inout-flow at the end.)

The answer to this question can be found in Appendix B at the back of the book.

Self-assessment question 8.1

must be a sensible commercial approach Businesses should not continue with existingprojects unless those projects have a positive NPV based on future cash flows Justbecause a project seemed to have a positive NPV before it started does not mean thatthis will persist in the light of changing circumstances Activity 8.16 (pp 285 –286)considered a decision on whether to close down a project

As we discussed earlier, all investments are risky This means that consideration of risk

is an important aspect of financial decision making Risk, in this context, is the extentand likelihood that what is projected to occur will not actually happen It is a particu-larly important issue in the context of investment decisions, because of

1 The relatively long timescales involved There is more time for things to go wrong

between the decision being made and the end of the project

2 The size of the investment If things go wrong, the impact can be both significant

and lasting

Various approaches to dealing with risk have been proposed These fall into two categories: assessing the level of risk and reacting to the level of risk We now considerformal methods of dealing with risk that fall within each category

Dealing with risk

DEALING WITH RISK 291

REAL WORLD 8.13

easyFit

easyJet, the UK budget airline, bought a small rival airline, GB Airways Ltd (GB) in late

2007 for £103m According to an article in the Financial Times:

GB is a good strategic fit for easyJet It operates under a British Airways franchise from Gatwick, which happens to be easyJet’s biggest base The deal makes easyJet the single largest passen- ger carrier at the UK airport There is plenty of scope for scale economies in purchasing and back office functions Moreover, easyJet should be able to boost GB’s profitability by switching the car- rier to its low-cost business model easyJet makes an estimated £4 a passenger, against GB’s

£1 Assuming easyJet can drag up GB to its own levels of profitability, the company’s value to the low-cost carrier is roughly four times its standalone worth.

The article makes the point that this looks like a good investment for easyJet, because

of the strategic fit For a business other than easyJet, the lack of strategic fit might wellhave meant that buying GB for exactly the same price of £103 million would not have been

Establishing what is the best area or areas of activity and style of approach for the

business is popularly known as strategic planning We saw in Chapter 1 that strategic

planning tries to identify the direction in which the business needs to go, in terms ofproducts, markets, financing and so on, to best place it to generate profitable invest-ment opportunities In practice, strategic plans seem to have a timespan of around fiveyears and generally tend to ask the question: where do we want our business to be infive years’ time and how can we get there?

Real World 8.13 shows how easyJet made an investment that fitted its strategicobjectives

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 the key input values affecting the project to see how changes in each input might influence the viability of the project

First, the investment is appraised, using the best estimates for each of the input factors (for example, labour cost, material cost, discount rate and so on) Assuming thatthe NPV is positive, each input value is then examined to see how far the estimatedfigure could be changed before the project becomes unviable for that reason alone Let

us suppose that the NPV for an investment in a machine to provide a particular service

is a positive value If we were to carry out a sensitivity analysis on this project, weshould consider in turn each of the key input factors:

l initial outlay for the machine;

l sales volume and selling price;

l relevant operating costs;

l life of the project; and

l financing costs (to be used as the discount rate)

We should seek to find the value that each of them could have before the NPV figurewould become negative (that is, the value for the factor at which NPV would be zero).The difference between the value for that factor at which the NPV would equal zeroand the estimated value represents the margin of safety for that particular input Theprocess is set out in Figure 8.6

A computer spreadsheet model of the project can be extremely valuable for this cise because it then becomes a very simple matter to try various values for the inputdata and to see the effect of each As a result of carrying out a sensitivity analysis, the

exer-decision maker is able to get a ‘feel’ for the project, which otherwise might not be sible Example 8.3, which illustrates a sensitivity analysis is, however, straightforwardand can be undertaken without recourse to a spreadsheet.

pos-DEALING WITH RISK 293

S Saluja (Property Developers) Ltd intends to bid at an auction, to be held today,for a manor house that has fallen into disrepair The auctioneer believes that thehouse will be sold for about £450,000 The business wishes to renovate the propertyand to divide it into flats, to be sold for £150,000 each The renovation will be in twostages and will cover a two-year period Stage 1 will cover the first year of the project

It will cost £500,000 and the six flats completed during this stage are expected to

be sold for a total of £900,000 at the end of the first year Stage 2 will cover thesecond year of the project It will cost £300,000 and the three remaining flats areexpected 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 theproperty is bought There is, however, some uncertainty over the remaining inputvalues 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 from the best estimates provided,(1) What auction price would have to be paid for the manor house to causethe project to have a zero NPV?

(2) What cost of capital would cause the project to have a zero NPV?

(3) What is the sale price of each of the flats that would cause the project to have

a zero NPV? (Each flat is projected to be sold for the same price: £150,000.)(c) Is the level of risk associated with the project high or low? Discuss your findings

Solution

(a) The NPV of the proposed project is as follows:

Cash flows Discount factor Present value

Year 1 (£900,000 − £500,000) 400,000 0.893 357,200Year 2 (£450,000 − £300,000) 150,000 0.797 119,550

(b) (1) To obtain a zero NPV, the auction price would have to be £26,750 higher

than the current estimate – that is, a total price of £476,750 This is about

6 per cent above the current estimated price

(2) As there is a positive NPV, the cost of capital that would cause the project

to have a zero NPV must be higher than 12 per cent Let us try 20 per cent

Cash flows Discount factor Present value

Year 1 (£900,000 − £500,000) 400,000 0.833 333,200Year 2 (£450,000 − £300,000) 150,000 0.694 104,100

Example 8.3

‘

As the NPV using a 20 per cent discount rate is negative,the ‘break-even’ cost

of capital lies somewhere between 12 per cent and 20 per cent A reasonableapproximation is obtained as follows:

Discount rate Net present value

(6Y × 0.893) + (3Y × 0.797) = £26,750

Y = £3,452The sale price of each flat necessary to obtain a zero NPV is therefore

£150,000 − £3,452 = £146,548This represents a fall in the estimated price of 2.3 per cent

(c) These calculations indicate that the auction price would have to be about

6 per cent above the estimated price before a zero NPV is obtained The margin

of safety is, therefore, not very high for this factor In practice this should notrepresent a real risk because the business could withdraw from the bidding ifthe price rises to an unacceptable level

The other two factors represent serious risks, because only after the project

is at a very late stage can the business be sure as to what actual cost of capitaland price per flat will prevail The calculations reveal that the price of the flatswould only have to fall by 2.3 per cent from the estimated price before theNPV is reduced to zero Hence, the margin of safety for this factor is evensmaller However, the cost of capital is less sensitive to changes and therewould have to be an increase from 12 per cent to 17.4 per cent before the pro-ject produced a zero NPV It seems from the calculations that the sale price ofthe flats is the most sensitive factor to consider A careful re-examination ofthe market value of the flats seems appropriate before a final decision is made

Example 8.3 continued

There are two major drawbacks with the use of sensitivity analysis:

l It does not give managers clear decision rules concerning acceptance or rejection ofthe project and so they must rely on their own judgement

l It is a static form of analysis Only one input is considered at a time, while the restare held constant In practice, however, it is likely that more than one input valuewill differ from the best estimates provided Even so, it would be possible to dealwith changes in various inputs simultaneously, were the project data put onto aspreadsheet model This approach, where more than one variable is altered at a time,

is known as scenario building

Real World 8.14 describes an evaluation of a mining project that incorporated sitivity analysis to test the robustness of the findings

IRR Pre-tax NPV Payback period

Sensitivity analysis was carried out on four key variables – the price of copper, the price

of gold, operating costs and capital outlay costs – to help assess the riskiness of the project This was done by assessing the IRR, NPV and PP, making various assumptionsregarding the prices of copper and gold and about the percentage change in both theoperating and the capital costs The following table sets out the findings

Average spot*

copper price US$/lb

Expected net present value

Another means of assessing risk is through the use of statistical probabilities It may bepossible to identify a range of feasible values for each of the items of input data and toassign a probability of occurrence to each of these values Using this information, wecan derive an expected net present value (ENPV), which is, in effect, a weighted aver-age of the possible outcomes where the probabilities are used as weights To illustratethis method, let us consider Example 8.4

* The spot price is the price for immediate delivery of the mineral.

In its report, the business stated:

This project is most sensitive to percentage changes in the copper price which have the largest impact, whereas movements in the gold price have the least The impact of changes in operating costs is more significant than capital costs.

Source: Adapted from ‘Eureka Mining PLC – drilling report’, www.citywire.co.uk, 26 July 2006.

C Piperis (Properties) Ltd has the opportunity to acquire a lease on a block of flatsthat has only two years remaining before it expires The cost of the lease would

be £100,000 The occupancy rate of the block of flats is currently around 70 percent and the flats are let almost exclusively to naval personnel There is a largenaval base located nearby, and there is little other demand for the flats The occup-ancy rate of the flats will change in the remaining two years of the lease, depend-ing on the outcome of a defence review The navy is currently considering threeoptions for the naval base These are:

l Option 1 Increase the size of the base by closing down a base in another region

and transferring the personnel to the one located near the flats

l Option 2 Close down the naval base near to the flats and leave only a skeleton

staff there for maintenance purposes The personnel would be moved to a base

in another region

l Option 3 Leave the base open but reduce staffing levels by 20 per cent.

Example 8.4

The expected NPV approach has the advantage of producing a single numerical come and of having a clear decision rule to apply If the expected NPV is positive, weshould invest; if it is negative, we should not.

out-However, the approach produces an average figure, and it may not be possible forthis figure actually to result This point was illustrated in Example 8.4 where theexpected annual cash flow (£61,200) does not correspond to any of the stated options.Perhaps more importantly, using an average figure can obscure the underlying riskassociated with the project Simply deriving the ENPV, as in Example 8.4, can be mis-leading Without some idea of the individual possible outcomes and their probability

DEALING WITH RISK 297

The directors of Piperis have estimated the following net cash flows for each ofthe two years under each option and the probability of their occurrence:

of the possible options will arise) The business has a cost of capital of 10 per cent

Should the business purchase the lease on the block of flats?

Solution

To calculate the expected NPV of the proposed investment, we must first late the weighted average of the expected outcomes for each year, using the prob-abilities as weights, by multiplying each cash flow by its probability of occurrence

calcu-Thus, the expected annual net cash flows will be:

Cash flows Probability Expected

Having derived the expected annual cash flows, we can now discount theseusing a rate of 10 per cent to reflect the cost of capital:

cash flows rate present value

We can see that the expected NPV is positive Hence, the wealth of shareholders

is expected to increase by purchasing the lease

of occurring, the decision maker is in the dark In Example 8.4, were either of Options

2 or 3 to occur, the investment would be adverse (wealth-destroying) It is 40 per centprobable that one of these two options will occur, so this is a significant risk Onlyshould Option 1 arise (60 per cent probable) would investing in the flats represent agood decision Of course, in advance of making the investment, which option willactually occur is not known None of this should be taken to mean that the investment

in the flats should not be made, simply that the decision maker is better placed to make

a judgement where information on the possible outcomes is available Activity 8.18further illustrates this point

Qingdao Manufacturing Ltd is considering two competing projects Details are as follows:

l Project A has a 0.9 probability of producing a negative NPV of £200,000 and a 0.1 probability of producing a positive NPV of £3.8m.

l 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)] = £200,000The expected NPV of Project B is

[(0.6 × £100,000) + (0.4 × £350,000)] = £200,000

Activity 8.18

Although the expected NPV of each project in Activity 8.18 is identical, this does notmean that the business will be indifferent about which project to undertake We cansee from the information provided that Project A has a high probability of making

a loss whereas Project B is not expected to make a loss under either possible outcome

If we assume that the shareholders dislike risk – which is usually the case – they willprefer the directors to take on Project B as this provides the same level of expectedreturn as Project A but for a lower level of risk

It can be argued that the problem identified above may not be significant where thebusiness is engaged in several similar projects This is because a worse than expectedoutcome on one project may well be balanced by a better than expected outcome

on another project However, in practice, investment projects may be unique eventsand this argument will not then apply Also, where the project is large in relation toother projects undertaken, the argument loses its force There is also the problem that

a factor that might cause one project to have an adverse outcome could also haveadverse effects on other projects For example, a large, unexpected increase in the price

of oil may have a simultaneous adverse effect on all of the investment projects of a particular business

Where the expected NPV approach is being used, it is probably a good idea to makeknown to managers the different possible outcomes and the probability attached to

each outcome By so doing, the managers will be able to gain an insight to the downside risk attached to the project The information relating to each outcome can be presented