cima f3 notes - financial strategy - chapter 7

8/17/2019 CIMA F3 Notes - Financial Strategy - Chapter 7

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CIMA F3 Course Notes

Chapter 7

Investment AppraisalTechniques


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1. Investment decisions

A financial strategy is one key element of a business strategy as a whole. Ithas three key constituents:

Financing decisions

Businesses need funding to invest in capital (e.g. equipment, machinery,buildings etc, to pay e!penses and working capital (e.g. salaries,inventories, utilities etc.

"inancing decisions relate to the decisions about where this money comesfrom, and is primarily about balancing:

• equity (i.e. from owners#shareholders• debt (from lenders such as banks

• retained earnings.

Investment decisions

$nce raised the money needs to be invested, and investment decisions helpthe organisation decide where to invest this money to repay debt (andinterest payments and achieve a good rate of return for shareholders.

%trategic options are generated as part of the business strategy settingprocess. As part of the evaluation of the strategic options, investmentdecisions can be made using techniques such as:

• &et present value (&'

• Internal rate of return (I))

• 'ayback period

• )eturn on capital employed ()$*+

Dividend decisions

Assuming investments were well made, funds can be returned toshareholders in the form of dividend payments.

he directors have to balance the payment of dividends with retention ofcash in the business to allow for future investment and growth.

his chapter deals in detail with the second of these three elements,investment decisions.


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. !elevant costing

-hen undertaking investment decisions, on crucial factor is to ensure theuse of relevant costs.

)elevant costs are F"T"!#$ CA%&$ and INC!#M#NTA' costs directl( arisingas the result o) an investment decision. his includes the following costtypes:

Future cash )lo*s

)elevant cash flows are always related to the future and there must be anactual cash flow associated with it.

"or instance the purchase of materials on a construction proect are a

future, relevant cash flow as without the proect we would not bepurchasing the material.

/sing material that the company already has stored is not a relevant cashflow as this occurred in the past and the purchase was not made with thisproect in mind. his is a sun+ cost (see below and should be ignored fordecision making purposes, as whether we undertake this proect or notthere are no additional costs to the business 0 so the original cost of this isirrelevant to the decision being made.

If this material however has a resale value, that is a relevant cash flow as ifwe proceed with the proect we will not be able to realise that resale value.he relevant cost when assessing this decision is therefore the resale value.

Incremental costs

Any increase or decrease in future cashflows as a result of a decision, is arelevant cost.

"or instance, staff are not always a relevant cost. "ull1time employed staffworking on a proect would be paid whether a particular proect was in

place or not. 2owever hiring temporary staff to work on a specific proect isan incremental relevant cost of this proect, so it must be included.

,pportunit( costs

$pportunity cost is the benefit sacrificed (lost contribution by choosing onedecision over another.


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#-ample

A company has a production line for a 'roduct. )evenues are 34 per

product, costs of labour 35 and costs of materials 35.67. hat gives us acontribution of 38.67.

he company are offered a special proect which will mean moving 9 skilledstaff who can not be replaced and who are paid 386 per hour from theproduction line A to the proect thereby losing 8,777 units, what is theopportunity cost of this

%olution

he staff are being paid whichever production line they are working and sothere is no change in future cashflow and this cashflow is not relevant tothe decision.

2owever, 8777 units will not be produced so revenues of 8,777 ! 34 will belost, while the materials for these units will not be purchased saving 8,777 !35.67. he opportunity cost (and relevant cost of using the labour herethen is 34,777 1 35,677 ; 39,677.

Avoidale costs

A cost which can be avoided is relevant as it is affected by the decisionbeing made. If this cost was unavoidable and therefore fi!ed, it would notbe relevant to the decision making process.

If a company would incur )


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Committed costs

A committed cost is a "uture *ash flow but one which will irrespective ofthe decision being made and so is not relevant to the decision makingprocess.

)ental costs are often an e!ample of committed costs. If a company is tiedinto a > year rental lease and is choosing which 8> month proect to pursue,the rental cost is not relevant as it will be incurred irrespective of thedecision.

Allocated costs

*osts are often allocated from another part of the business, for instance,for the use of central services. As these costs are incurred by the business as

a whole irrespective of whether a proect proceeds or not, they are notrelevant to the decision on that proect.

If we consider a financial institution which needs to keep staff up to datewith the latest legislation and this training is compulsory and allocated toeach department, this cost will be incurred irrespective of the proectsundertaken by an individual department and therefore is not relevant fortheir internal decision making processes.

Depreciation and Amortisation

As relevant costs only deal with cash flows, depreciation and amortisationare also considered irrelevant costs.

!elevant Cost #-ample

Investment appraisal using relevant costing normally combines a range ofthese different relevant costs. 2ere?s an e!ample.

#-ample

A company has 67 units of material B which it bought one year ago but wassurplus to use at the time. he cost of purchasing the material was [email protected], the company has taken on a ob which requires 867 units of thismaterial. he current purchase price is 3>7 per unit, the resale value is 387per unit, or it could be used in another product saving 34 per unit.*alculate the relevant cost of this ob:


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%olution

he cost of purchasing 67 units (3@67 one year ago is not relevant, it is asunk or past cost that has no bearing on the decision making process goingforward.

he relevant cost of the material we already own is the higher of resalevalue and contribution from alternate use. I.e. what would we do if wedidn?t use it here -ould we sell it (here for 387 or use it for alternativeuses (saving 34 here -hichever is the higher is what we would do, so istherefore the relevant cost of using this material . In this case then therelevant cost is 387 per unit.

he relevant cost of this ob would therefore be ;

(877 ! 3>7 (67 ! 387 ; 3>,677

3. Net /resent 0alue N/02

&et 'resent alue (&' is a proect appraisal technique which usesrelevant net cash )lo*s generated by a proect over its total lifetime to

calculate a proect?s net contribution to an organisation.

+ffectively it calculates an organisations change in *ealth if it undertakesa particular proect. A positive &' is an increase in the total value of thecompany from doing the proect, while a negative &' is the decrease intotal value of the company from doing the proect. *learly then, anyproect with a positive &' should be undertaken.

Discounting and the time value o) mone(

he same amount of money received in 8 year?s time are not as valuable asmonies received now. $ne of a number of reasons why this is true is that in8 year not as much could be purchased with the same funds due to inflation.Another way of thinking about this is that those funds invested now, wouldbe worth more in 8 year as they would have earned interest in that year.

his effect is called the time value o) mone(.

&' takes account of the time value of money by discounting? futurecashflows so the further they are away the less value they have.


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Civen that the company needs to achieve a percentage return equivalent tothe cost of capital to satisfy investors, the effective rate used is the cost ofcapital. "or e!ample, if the cost of capital is 87D. 3887 received in 8 year?stime has a present value of 3887#7.87 ; 3877, or in other words the investorwould need 3887 in 8 year to give then their 87D return on 3877 now

aking account of the time value of money and all relevant cash flows (bothincoming and outgoing means &' is considered a superior proect appraisaltechnique to others such as A)), payback and I)) (see later.

The timing o) cash )lo*s

-hen completing &' calculations it is vital therefore that the timing ofcashflows is clearly recorded as amounts received at later times need to

have a greater discounting factor applied to them.

It is vital therefore that a standardised approach is used in thesecalculations including a standard &' proforma.

Eou will need to memorise the following proforma for &' calculations:

Year 0 Year 1 Year 2 Year 3 Year 4

Sales Receipts X X X

Costs (X) (X) (X)

Sales less costs X X X

Taxation (X) (X) (X) (X)

Capital expenditure (X)

Scrap Value X

Working Capital (X) X

Tax benefit of tax dep'n X X X X

(X) X X X (X)

Discount factors@

post-tax cost of capital X X X X X

Present value (X) X X X (X)

here are some assumptions which are typically made when completing an

&' proforma:

Cash out)lo*s that occur at the eginning o) a pro4ect occur no*, whichis Eear 7, therefore all outflows are already at their nominal value.

Cash out)lo*s or in)lo*s that occur during an( particular (ear are alltreated as if they occurred at the end o) that )inancial (ear. "or instancerevenue will be earned over a full 8> month period, but for the purpose of&' calculations we treat revenue as if it occurred all in month 8>. hisassumption is used to keep calculations straightforward.

If you are speci)icall( told that a cash out)lo* or in)lo* occurs at thestart o) a (ear$ include it as the end o) the previous (ear. "or instance a


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cashflow received at that start of Eear > is deemed to have occurred at theend of Eear 8 and should be included in Eear 8 cash flows in yourcalculation. Again this is an understood assumption that ensures consistenttreatment of inflows # outflows across different &' calculations.

#-ample 1 5 6asic N/0

#-ample

%atoshi 'lc. is a Fapanese clothing brand who have a store in central Gondonwhich has been highly successful. hey now want to e!pand to other citiesacross the /H. hey have a company policy of acquiring all of their storelocations. he following cash flows are forecast:


Land and buildings 4,225.00-

Fittings and equipment 910.00-

Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

*alculate the &' of this proect where cost of capital is 8>D

%olution

%tart by completing a table over a number of years, in this case the same asin the question above.

&e!t use discount tables (given to you by *IA in the e!am look up therelevant discount factors to use. Gook at the present value table under 8>Dand then copy in the relevant figures.

hen multiply the net cashflows by the discount factors to find the presentvalue in each year.

"inally, add up all years of present values to find the &et 'resent alue.

2ere?s what this should then look like:




Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Discount Factor @ 12% 1.00 0.893 0.797 0.712 0.636

PV of Future Cash Flows 5,135.00- 2,089.62 2,590.25 2,591.68 2,480.40

Net Present Value 4,616.95


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he &' of the proect is positive. his means it gives investors a returnabove the 8>D cost of capital, and so it should be undertaken.

It?s also worth noting that effectively this is saying that doing this proectincreases the total value of the company J9,K8K.L6. If the stock market was

efficient, as soon as the announcement of the proect was made to themarket, the total market capitalisation.

#-ample 5 N/0 including relevant costs and scrap value.

#-ample

/sing the same e!ample we can add in additional factors to demonstrateother concepts you will need to be familiar with when completing &'calculations. he following question introduces a range of other costs (someof which are relevant and some which are not and scrap value.

Get?s take a look:


Land and buildings 4,225.00

Fittings and equipment 910.00

Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-

Marketing 220.00- 325.00- 260.00- 260.00-

Office overheads 165.00- 165.00- 165.00- 165.00-

(a) The cost of land and buildings includes £100,000 which has been spent on legal fees.

(b) 55% of office overhead is a charge made for head office services.

(C) Satoshi expects to be able to sell the new stores at the end of year 4 for £4,000,000

which includes £75,000 for fixtures and fittings.

*alculate the &' of this proect where cost of capital is 8>D.

%olution

he above e!ample contains details which require you to identify relevantand irrelevant costs. 2ere we have a sunk # past cost in the legal fees andan allocated overhead charge which is also irrelevant to this proect.

In addition we are told that %atoshi is considering selling the new stores atthe end of year 9 and this additional factor has also been included in thesolution below.


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Sunk cost - Legal Fees 100.00

Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-Marketing 220.00- 325.00- 260.00- 260.00-

Office overheads, only 45%

of this cost is relevant 74.25- 74.25- 74.25- 74.25-

Resale / Scrap Value 4,000.00

Net Cash Flows 5,035.00- 1,070.75 1,420.75 1,355.75 5,485.75

Discount Factor @ 12% 1.000 0.893 0.797 0.712 0.636

PV of Future Cash Flows 5,035.00- 956.18 1,132.34 965.29 3,488.94

Net Present Value 1,507.75

he &' of the proect is positive and should be undertaken.

As you will notice the inclusion of the sale of the shops is verystraightforward. A lot of the work with &' calculations is about beingmethodical, ensuring that you cover all of the criteria and working througheach factor carefully. -hile parts of an &' calculation can become quiteinvolved there are also a lot of easy marks available.

.

N/0 and 8or+ing Capital

'roects obviously require capital and you can be asked as part of an &'calculation to build in working capital requirements.

As we are only dealing with relevant cash flows, the full amount of workingcapital is recorded in Eear 7 of your calculation and then only theincremental amounts are recorded in subsequent years. At the end of theproect the full amount invested will be released.

9ear : *or+ing capital requirements

Eou will often find that working capital requirements are given as a D ofturnover. In the e!ample below >7D of turnover is needed as workingcapital. In year 8 >7D ! 5,5>7 ; KK9 is needed. As working capital is requiredat the start of a particular year this will be recorded in the previous year inyour &' calculation, so in this case it is recorded as Eear 7 working capital


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Time Year 0 Year 1 Year 2 Year 3 Year 4

Turnover 3,320.00 3,600.00 4,000.00 4,700.00

Working Capital 664.00- 720.00- 800.00- 940.00-

Relevant Cash Flow 664.00- 56.00- 80.00- 140.00- 940.00

Mid;pro4ect *or+ing capital requirements

It is only relevant cash flows which go into your &' calculation.*onsequently it is the incremental amount from one year to the ne!t whichis recorded mid1proect. he amount input in Eear 8 for e!ample istherefore (1@>7 1KK9 ; 16K.

Final (ear *or+ing capital requirements

In the last year of the proect the full amount of working capital invested isreleased. In the above e!ample year 715 cashflows are added up to get L97which is treated as an inflow in that final year.


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Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-Marketing 220.00- 325.00- 260.00- 260.00-




(c) Satoshi expects to be able to sell the new stores at the end of year 4 for £4,000,000


(d) Working capital requirements are forecast to be 10% of revenue at the start of each year.

(e) Corporation tax is charged at 30% and is collected 1 year in arrears.

%olution

In the solution below ta! has been added e!actly as the question instructed0 calculated at 57D of net cashflows, and shown 8 year later. )elevantworking capital cash flows have also been included.

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5



Sunk cost - Legal Fees 100.00 Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-

Marketing 220.00- 325.00- 260.00- 260.00-


of this cost is relevant 74.25- 74.25- 74.25- 74.25-

1,070.75 1,420.75 1,355.75 1,485.75

30% Tax 1 year in arrears 321.23- 426.23- 406.73- 445.73-


Working Capital (W1) 234.00- 91.00- 39.00- 26.00- 390.00

Net Cash Flows 5,269.00- 979.75 1,060.53 903.53 5,469.03 445.73-

Discount Factor @ 12% 1.000 0.893 0.797 0.712 0.636 0.567

PV of Future Cash Flows 5,269.00- 874.92 845.24 643.31 3,478.30 252.73-

Net Present Value 572.76

Working Capital (W1) Year 0 Year 1 Year 2 Year 3 Year 4

Turnover 2,340.00 3,250.00 3,640.00 3,900.00

Working Capital 234.00- 325.00- 364.00- 390.00-

(10% of turnover)Relevant Cash Flows 234.00- 91.00- 39.00- 26.00- 390.00


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Ta- ene)it allo*ed ( capital allo*ances

A capital allo*ance is a sum of money that a business can deduct from theta! on its profits. his is an allowed ta! saving against specific purchaseditems. he value of this saving is given at government advised rates.

Eou will be given the capital allowance rates and the items that these ratesapply to in your e!am question.

ypically rates will be >6D writing down allowances but do not assume this,make sure to check the question detail, and these will be against a specificitem listed in your question for instance plant and machinery.

=8riting do*n allo*ances refers to the annual amount claimed each yearwhich is taken off the total asset value for the following year?s balance. "ore!ample, a 3977 asset with a >6D allowance, it has a first year writing downallowance of 3877, leaving a balance of 3577 to claim against in thefollowing year.

Items allowed for capital allowances include motor vehicles, equipment,furniture, computers, plant and machinery and building improvements.

#-ample

he value of the plant and machinery is 38,777,777 and the capitalallowance rate >6D. he machine is sold for 3877,777 in year 9. *alculatethe annual capital allowances.

%olution

Eear 8 *apital Allowance: 38,777,777 M >6D ; 3>67,777.

At the end of each year calculate the balance which has yet to be

claimed against for ta!.

&ew balance ; 38,777,777 1 3>67,777 ; 3@67,777

Eear > *apital Allowance: 3@67,777 M >6D ; 384@,677

&ew balance ; 3@67,777 1 384@,677 ; 36K>,677

Eear 5 *apital Allowance: 36K>,677 M >6D ; 3897,K>6

&ew balance ; 36K>,677 1 3897,K>6 ; 39>8,4@6


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In the final year of holding an asset all the remaining balance can becharged for ta! less any scrap value this is the alancing allo*ance.

Eear 9 Balancing Allowance: *urrent balance 1 scrap value

39>8,4@613877,777 ; 35>8,4@6

In this scenario the capital allowances would therefore beEear 8 : 3>67,777Eear > : 384@,677Eear 5 : 3897,K>6Eear 9 : 35>8,4@6

he annual capital allowances are then multiplied by the ta! rate, whichhere we will assume is 57D, to give the actual annual ta! savings which gointo your &' calculation.

Eear 8 : 3>67,777 ! 57D ; 3@6,777Eear > : 384@,677 ! 57D ; 36K,>67Eear 5 : 3897,K>6 ! 57D ; 39>,844Eear 9 : 35>8,4@6 ! 57D ; 3LK,6K5

-hen inputting these values into your calculation treat them for timing(which year they should be input on the same basis as you have beendirected to treat your ta!.

#-ample 5 N/0 *ith capital allo*ances

#-ample




Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-

Marketing 220.00- 325.00- 260.00- 260.00-






(d) Working capital requirements are forecast to be 10% of revenue at the start of each year.

(e) Corporation tax is charged at 30% and is collected 1 year in arrears.

(f) Capital Allowances will be claimed on fixtures and fittings at 25% on a reducing balace basis


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%olution

*apital allowances have been calculated based on the 3L87k cost of fi!tureand fittings, at a written down allowance of >6D and against a corporation

ta! charge of 57D

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5




Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-

Marketing 220.00- 325.00- 260.00- 260.00-


of this cost is relevant 74.25- 74.25- 74.25- 74.25-Cash Flows 1,070.75 1,420.75 1,355.75 1,485.75

30% Tax 1 year in arrears 321.23- 426.23- 406.73- 445.73-

Tax saved (W1 Cap Allow) 68.25 51.19 38.39 92.40


Working Capital (W2) 234.00- 91.00- 39.00- 26.00- 390.00

Net Cash Flows 5,269.00- 979.75 1,128.78 954.71 5,507.42 353.33-

Discount Factor @ 12% 1.000 0.893 0.797 0.712 0.636 0.567

PV of Future Cash Flows 5,269.00- 874.92 899.63 679.76 3,502.72 200.34-

Net Present Value 688.02

Capital Allowances (W1) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Claims 227.50 170.63 127.97 308

Balancing allowance Cost £910k - scrap value - claims to date 308

Tax Saved 68.25 51.19 38.39 92.40

Working Capital (W2) Year 0 Year 1 Year 2 Year 3 Year 4

Turnover 2,340.00 3,250.00 3,640.00 3,900.00

Working Capital 234.00- 325.00- 364.00- 390.00-

(10% of turnover)Relevant Cash Flows 234.00- 91.00- 39.00- 26.00- 390.00

he scenarios given in the previous e!amples have looked at the varyingaspects of the &' calculation that you need to know.

he following scenario looks at bringing inflation into an &' calculation,something which is often tested and is an easy way of adding additionalrequirements to an &' scenario.


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>. N/0 *ith in)lation

Cash)lo*s *ith in)lation

If cash flows have inflation, then in the e!am you may be required to inflate

cash flows so they represent the actual cash that will be paid in that year.Eou may be given cashflows in N)eal termsO, known as real cash )lo*s. hismeans that no inflation has been applied to them. +.g. 3877 received inyear 9 in real terms, means that it would cost you 3877 at today?s prices.

hat, of course is not what you would actually pay in 9 years time. heactual amount you would pay would need to have inflation added on 0 this isknown as the nominal cash )lo*. It is these nominal cashflows that weshould show in our &'.

Cost o) capital *ith in)lation

Another issue can be the use of real and nominal cost of capital figures.he real cost o) capital is the return investors require on real cashflows i.e.before inflation is applied. hat?s not the cost of capital we usually want touse in &'s though as typically we use nominal cash flows so need thenominal cost o) capital, so you may have to convert the real cost of capitalto a nominal cost of capital.

o calculate a nominal cost of capital when you are given a real cost ofcapital you must use the fisher equation.

1 ? real cost o) capital2 - 1 ? general in)lation rate2 @ 1 ? nominal cost o) capital2

$) in algebraic form

(8 r ! (8 i ; (8 n

#-ample

he real cost of capital is 4D, and general inflation rate is 5D. -hat is the

nominal cost of capital (that should be used in a typical &' calculation

%olution

(8 r ! (8 i ; (8 n

(8.74 ! (8.75 ; 8.88>9

&ominal cost of capital ; 88.>9D


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#-ample 5 N/0 *ith in)lation

/sing our previous e!ample, we will now add elements of inflation to it 0see part (g.

#-ample

%atoshi 'lc.%atoshi 'lc. is a Fapanese clothing brand who have a store in central Gondonwhich has been highly successful. hey now want to e!pand to other citiesacross the /H. hey have a company policy of acquiring all of their storelocations. he following cash flows are forecast:


Land and buildings 4,225.00 Fittings and equipment 910.00

Gross revenue 2,340.00 3,250.00 3,640.00 3,900.00

Direct costs 975.00- 1,430.00- 1,950.00- 2,080.00-

Marketing 220.00- 325.00- 260.00- 260.00-






(d) Working capital requirements are forecast to be 10% of revenue at the start of each year.(e) Corporation tax is charged at 30% and is collected 1 year in arrears.

(f) Capital Allowances will be claimed on fixtures and fittings at 25% on a reducing balace basis

(g) Satoshi Plc's real cost of capital is 7.7%p.a. Inflation of 4% has not been accounted for

in the above information

%olution

As you will notice when working through the following solution that we must

first convert the cashflows to nominal terms by adding on inflation of 9D.-e must also work out the nominal cost of capital to use to undertake ourdiscounting (working 5.


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Time Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Sales 2,340.00 3,250.00 3,640.00 3,900.00

Direct Cost 975.00- 1,430.00- 1,950.00- 2,080.00-

Marketing 220.00- 325.00- 260.00- 260.00-


REAL cash flows 1,071.00 1,421.00 1,356.00 1,486.00

2.00 3.00 4.00

4% inflation x1.04 x1.04 x1.04 x1.04

Nominal Cash Flows 1,113.84 1,537.52 1,525.50 1,738.62

30% Tax 334.15- 461.26- 457.65- 521.59-

Tax Saved (W1) 68.25 51.19 38.39 92.40

Resale Value 4,000.00

Working capital (W2) 234.00- 104.00- 55.85- 44.90- 439.00

Land and Buildings 4,225.00-



Net 5,269.00- 1,009.84 1,215.77 1,070.53 5,758.36 429.19-

Discount Facto 12% (W4) 1.000 0.893 0.797 0.712 0.636 0.568

PV 5,269.00- 901.79 968.97 762.22 3,662.32 243.78-

NPV 782.51

Capital Allowances (W1) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Claims 227.50 170.63 127.97 308.00

Balancing allowance Cost £910k - scrap value - claims to date 308.00

Tax Saved 68.25 51.19 38.39 92.40

Working Capital (W2) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

10% of turnover 234.00 325.00 364.00 390.00

Adjuted for inflation 234.00 338.00 393.85 438.75

Cash Flow 234.00- 104.00- 55.85- 44.90- 439.00

Cost of capital calculation (W3)

(1 + real rate) x (1 + inflation) = ( 1 + nominal rate)

( 1 + 0.077) x ( 1 + 0.04) = ( 1 + 0.12)


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7. Internal !ate o) !eturn I!!2

he Internal )ate of )eturn calculation provides the cost of capital at whichthe net present value of all cash flows from a proect is 7. his is a breakeven cost of capital.

If the I)) is above the current cost of capital then the returns are higherthan those required by shareholders and so the proect should be accepted.

I!! Calculation:

he I)) calculation is done using the following formula:

IRR = A + (NPVa / NPVa – NPVb) x (B-A)

Where A is the first discount rate used to calculate NPVaand B is the second discount rate used to calculate NPVb

Here’s the process you’ll need to use – see the lecture example below for theway this is done:

1. To calculate a projects IRR you first need to calculate an NPV at a givencost of capital that you choose (often 10% is a good starting point).

2. You then need to calculate a second NPV value using a different cost ofcapital. If the first NPV calculated was positive use a higher discount rate(e.g. 15%), if negative use a lower rate (e.g. 5%)

3. Complete the calculation using the formula:

a. When completing the IRR calculation the cost of capital used foryour first calculation is input as A and the resulting NPV asNPVa,

b. The cost of capital used for the second calculation is input as B

and the resulting NPV as NPVb,

The following lecture example demonstrates how the IRR calculation works inpractice.

'ecture #-ample 5 Fitness %olutions

Fitness solutions are considering expanding their business by procuring asecond gym in a neighbouring town. The SAS Gym will cost £525,000 to

purchase and a further £75,000 for refurbishment and new equipment. Cash


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flow projections for this project show the following profits over the coming 5years.

Year Net Cash Flow (£)1 105,0002 117,000

3 120,0004 150,0005 180,000

While equipment at the gym is expected to have a low re-sale value by theend of year 5, it is forecast that the whole business could be sold for£525,000,

The current estimated cost of capital for the project is 12%.

Calculate both an NPV and IRR for this scenario

%olution

%tep 1 Calculate an NPV using an arbitrary percentage cost of capital. Herewe’ll use 12%.


£'000 £'000 £'000 £'000 £'000 £'000

Capital Expenditure 600.00-

Net cash flow 105.00 117.00 120.00 150.00 180.00

Sale of business 525.00

Discount factor @ 12% 1.00 0.89 0.80 0.71 0.64 0.57

Present Value 600.00- 93.77 93.25 85.44 95.40 399.74

NPV 167.59

%tep Repeat using a different percentage cost of capital. As the NPV on thefirst NPV was positive, when calculating the IRR we should now choose asecond cost of capital that is higher than 12%, so lets choose 20%.


£'000 £'000 £'000 £'000 £'000 £'000


Net cash flow 105.00 117.00 120.00 150.00 180.00


Discount factor @ 20% 1.00 0.83 0.69 0.58 0.48 0.40

Present Value 600.00- 87.47 81.20 69.48 72.30 283.41

NPV 6.15-

The second NPV calculation at the higher cost of capital has given amarginally negative NPV value. That’s ideal as the formula works best whenthis is the case.

%tep 3 We now need to input these results into the IRR calculation.


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a. When completing the IRR calculation the cost of capital used foryour first calculation is input as A (12%) and the resulting NPVas NPVa (167.6),

b. The cost of capital used for the second calculation is input as B

(20%) and the resulting NPV as NPVb (6.15)

IRR = 12% + (167.6 / 167.6 + 6.1) x (20% -12%) = 19.7%

Advantages o) the I!!

• The IRR calculation does ta+e account o) the time value o) mone(.

• The IRR also considers all cash )lo*s.

• It gives a percentage measure that is easil( understandale to bothfinancial and non-financial managers

• There is no need to +no* an e-act cost o) capital (which can be veryhard to calculate in practise).

Disadvantages o) the I!!

As it is a % measure it is not suitale )or choosing et*een pro4ects o)di))erent siBes.

e.g. Project A has an IRR of 10%. It is a large project

Project B has an IRR of 15%. It is a small project.

Project A although it has the smaller IRR, as it’s a large project may actuallybe more beneficial to the company as it’s a larger project in the same way that10% of £100 = £10 while 15% of £50 is just £7.50.

In other unusual circumstances the IRR can conflict with the NPV decisionand when this occurs, the NPV is considered the superior tool for projectassessment.

. Modi)ied I!! ased on terminal value

Gooking at the above e!ample for "itness %olutions. If their actual cost ofcapital is 8>D there is a significant gap from this value to the I)) result of8L.@D. his causes a problem with the I)) calculation, making the 8L.@Dunrealistic. his is because the I)) calculation assuming the cash flows earlyin the proect are reinvested at the high I)) rate distorts their proects realbreak even cost of capital.

Gooking at the following calculation:


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£'000 £'000 £'000 £'000 £'000 £'000


Net cash flow 105.00 117.00 120.00 150.00 180.00 Sale of business 525.00

he I)) calculation assumes net cash flow in Eear 8 of 3876,777 isreinvested at 8L.@D, but the reality is if the company?s cost of capital is ust8>D it will only be able to reinvest this in other proects at ust 8>D.

-e can therefore adust the I)) to a odified I)) which more accuratelyreflects this problem.

8. *alculate the interest rate multiplier for 9 years at the cost of capital,

here 8>D giving 8.8> ! 8.8> ! 8.8> ! 8.8> ; 8.6@56. hen repeat for 5 years,> years and 8 year.

4 3 2 1

Cash flows reinvested @12% x1.12 x1.12 x1.12 x1.12

Interest rate multiplier 1.57 1.40 1.25 1.12 1.00

Amount when reinvested 165.22 164.38 150.53 168.00 705.00

>. ultiply this multiplier by that years cashflow. +.g. 8.6@56 ! 876 ; 8K6.>>

5. he total cash outflow in year 7 is 13K77,777 and this is compared to the

forecast inflow in year 6 from reinvesting the cash flows. his is the total ofthe inflated cash flows from year 8 to 6 which equals 38,565,8>7

Total return = 1,353,120 / 600,000 = 2.255

The MIRR is the 5th square route of 2.255 = 1.1766

MIRR = 1.1766 - 1

MIRR = 17.7%

he I)) of 8@.@D will therefore be a better measure than the I)) of 8L.@Dbecause its assumption that the reinvestment of cash flows is at thecompany cost of capital and not at the I)) rate itself.


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. /a(ac+ period

his is the length of time it will take for an investment to be paid back.he longer the payback period, the greater the risk as a greater period oftime is being allowed for problems to arise.

'ayback period ; cost of proect # Annual *ash flows.

If a proect costs 3677k and net cash flows are forecast to be 3877kannually, the payback period will be:

677 # 877 ; 6 years.

here are two immediate problems with this method of proect evaluation.he first is that is does not consider any cash flows after the paybackperiod.

A proect may payback quickly but if further investigation then shows thatafter its payback period cash flows will all but dry1up, this needs to beknown.

he second issues is that it does not take into account the time value ofmoney.

he second issue we can overcome by using the discounted paybackmethod. his means that we do an &' calculation using a discount factorand then complete the payback calculation.

-e can demonstrate this by calculating payback period for the proect"itness solutions is considering:


£'000 £'000 £'000 £'000 £'000 £'000


Net cash flow 105.00 117.00 120.00 150.00 180.00


Discount factor @ 12% 1.00 0.89 0.80 0.71 0.64 0.57 Present Value 600.00- 93.77 93.25 85.44 95.40 399.74

NPV 167.59

If we look again at the &' of the proect we calculated we could do asimple payback calculation using the *apital e!penditure info and the netcash flows that follow:


£'000 £'000 £'000 £'000 £'000 £'000


Net cash flow 105.00 117.00 120.00 150.00 180.00


Remaining outstanding balance 495.00- 378.00- 258.00- 108.00-


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he payback for this proect is 9 years 874 # (847 6>6 ; 9.86

his particular scenario does not account for the time value of cash flows.o do this we would complete the same calculation using the discounted

cash inflows.


£'000 £'000 £'000 £'000 £'000 £'000


Net cash flow 105.00 117.00 120.00 150.00 180.00


Discount factor @ 12% 1.00 0.89 0.80 0.71 0.64 0.57

Present Value 600.00- 93.77 93.25 85.44 95.40 399.74

Remaining outstanding balance 506.24- 412.99- 327.55- 232.15-

he payback for this proect is 9 years >5>.86 # 5LL.@9 ; 9.64


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cima f3 notes - financial strategy - chapter 7

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