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1 ACCAspace Provided by ACCA Research Institute ACCA P4 Advanced Financial Management (AFM) 高级财务管理 ACCA Lecturer: Lily Wang ACCAspace 中国 ACCA 特许公认会计师教育平台 Copyright ACCAspace.com

2 P4 Chapter 2 Content 1 Free Cash Flow 2 NPV 3 IRR & MIRR 4 Discounted Payback Period 5 Duration 6 Capital Rationing 2

3 P4 Chapter 2 Content 7 Past Paper 8 Analysis of Comprehensive Example 3

4 Chapter Summary Investment Appraisal Free Cash Flow Economic Return Calculation of FCF Using FCF Modified IRR IRR From Accounting Infor In Investment Appraisal Multi-Period Captial Rationing From First Principles Dealing With Taxation To Value A Firm Dealing With Inflation Linear Programming Solutions PV of Dividends Formulation NPV Formulation 4

5 1.Free Cash Flow Defination: Cash that is not retained and reinvested in the business is called free cash flow. It represents cash flow availiable: to all the providers of captial of a company. to pay dividends or finance additional capital projects. Uses of free cash flow Evaluating potential investment projects Indicator of company performance e.g. Chapter 10: Corpora te failure and reconstruction Calculate the value of a firm and thus a potential share price e.g.chapter 15:Business valuation. 5

6 1.Free Cash Flow Calculating free cash flow for investment appraisal Free cash flow=revenue - Costs - Investments FCF=PBIT+Dep'n-Tax-changes in WC Operating CF-Investment in operating capital FCF to Equity=FCF-Debt int and repays+loan cash raised Use of free cash flow in investment appraisal Net Present Value Internal Rate Of Return Modified Internal Rate Of Return Discounted Payback Period Duration (Macauley Duration and Modified Duration) 6

7 2.NPV Capital investment projects are best evaluated using the n et present value(npv)technique. Some basic NPV concepts ( relevant cash flows, discounti ng, the impact of inflation, the impact of taxation) are cove red below. Relevant Cash Flows Relevant cash flows are those costs and revenues that are: future incremental You should ignore: sunk costs non-cash items committed costs apportioned overheads 7

8 2.NPV Discounting Discounted cash flow techniques: Take account of the time value of money Seek to improve shareholders' wealth Compounding: Calculates a terminal value: TV=CF(1+r) n Discounting: Calculates a present value: e.g. T 0 value PV of a single sum: CF P F(1 r n (1 r) ) n PV of a perpetuity: Perpetuity *1/ r PV of an annuity: Annuity* AF i AF is 1 (1 r) r n where Advanced annuities/perpetuities: Ignore T 0 flow Add i to the AF/Perpetuity factor Delayed annuities/perpetuities: Apply factor as normal Discount back to T 0 8

9 T 0 T 1 T 2 T 3 T 4 T 5 T 6 9

10 2.NPV The impact of inflation Inflation is a general increase in prices leading to a general decline in the real value of money. In times of inflation, the fund providers will require a return made up of two elements: Real return for the use of their funds. Additional return to compensate for inflation. Real and nominal rates are linked by the formula: (1+i)=(1+r)(1+h) r=real rate i=money/nominal interest rate h=general inflation rate 10

11 2.NPV Investment appraisal two types of inflation need considera tion: Two type of inflation Specific inflation rate General rate of inflation Impact all the individual cash flow items-each cash flow is affected by a specific rate. Impact the investors' overall required rate of return. Investors in the project need compensation for their lost purchasing power, which relates to their ability to buy a basket of all goods. Rather than any spe cific one. 11

12 2.NPV The impact of inflation methods of dealing with inflation Real method Money/Nominal method 1. Do not inflate the cash flows-leave them in real terms,i.e. in today's(t0) prices-real flows 2. Discount using the real rate REAL / real 1. Inflate each cash flow by its specific inflation rate. i.e. convert it to a money rate 2. Discount using the money rate MONEY / money BE CONSISTENT 12

13 2.NPV The impact of taxation There are two main impacts of taxation in an investment apprais al: Tax is charged on operating cashflows Tax allowable depreciation ( sometimes refered to as capital allowances or writing down allowances ) can be claimed, thus generating tax relief. 13

14 2.NPV The impact of taxation The basic rules that follow are based on the current UK slation tax legi TAD is calculated on a reducing balance basis The total TAD given over the life of an asset equates to the fall in value over the period. TAD is claimed as early as possible TAD is fiven for every year of ownership except the tear of dis posal In the year of sale or scrap a balancing allowance or charge a rises 14

15 2.NPV The impact of taxation Original cost of asset Cumulative TAD claimed Written down value of the asset Disposal value of the asset Balancing allowance or charge $ X (X) X (X) X 15

16 2.NPV Illustration:Taxation in investment appraisal A company buys an asset for $26,000.It will be used on a project for t hree years after which it will be disposed of on the final day of year 3. Tax is payable at 30% and tax allowable depreciation is available at 25% reducing balance. A Calculate the tax allowable depreciation and hence the tax saving s for each year if the proceeds on disposal of the asset are $12,500 B If net trading income from the project is $16,000 pa and the cost of capital is 8% calculate the free cash flows and hence the net present value (NPV) of the project. 16

17 2.NPV Solution Time $ Tax saving Timing $ of tax relief T 0 Initial investment 26,000 T 1 TAD@25% (6,500) 1,950 T 1 Written down value 19,500 T 2 TAD@25% (4,875) 1,463 T 2 Written down value 14,625 Sale proceeds (12,500) T 3 Balancing allowance 2, T 3 17

18 2.NPV Time T 0 T 1 T 2 T 3 Net trading inflows 16,000 16,000 16,000 Tax payable(30%) (4,800) (4,800) (4,800) Post tax operating flows 11,200 11,200 11,200 Initial investment (26,000) Scrap proceeds 12,500 Tax relief on TAD 1,950 1, Free cash flows (26,000) 13,150 12,663 24,338 Discount factor@8% 1, Present value (26,000) 12,177 10,857 19,324 NPV 16,353 18

19 3.IRR&MIRR IRR-The Basics The IRR of a project has the following features: It represents the discount rate at which the NPVof an investment is zero It can be found by linear interpolation IRR L ( N L N L N H *( H ) L) Standard projects(outflow followed by inflows) should be accepted if the IRR exceeds the cost of capital. The IRR provides a decision rule for investment appraisal, but also pr ovides information about the riskiness of a project- i.e. thesensitivity of its returns.the project will only continue to have a positive NPV whi lst the firm's cost of capital is lower than the IRR. 19

20 3.IRR&MIRR Problems with using IRR The decision rule is not always clear cut. For example, if a project has 2 IRRs(or more), it is difficult to interpret the rule which says "a ccept the project if the IRR is higher than the cost of capital" The assumptions. IRR is often mistakenly assumed to be a measu re of the reuturn from a project, which it is not. The IRR only repres ents the return from the project if funds can be reinvested at the IR R for the duration of the project. Choosing between projects.since projects can have multiple IRRs (or none at all) it is difficult to usefully compare projects using IRR. 20

21 3.IRR&MIRR MIRR MIRR measures the economic yield of the investment under the as sumption that any cash surpluses are reinvested at the firm's curre nt cost of capital. Calculation of MIRR MIRR Where [ PVR / PVI] 1/ n (1 r e ) 1 PVR=The present value of the "return phase"of the project PVI=The present value of the "investment phase"of the project r e =The firm's cost of capital 21

22 3.IRR&MIRR Example A project with the following cash flows is under consideration: $000 T 0 T 1 T 2 T 3 T 4 (20,000) 8,000 12,000 4,000 2,000 Cost of capital 8% MIRR? Solution: PVR=22,340(This is the present value of the year 1-4 cash flows) PVI=20,000 1+MIRR=(1+r e )*(PVR/PVI) 1/n =1.08*(22,340/20,000) 1/4 =1.1103, giving MIRR= 11%pa. 22

23 4.Discounted Payback Period Traditional payback period The payback period was introduced in paper F9 Payback period measures the length of time it takes for the ca sh returns from a project to cover the initial investment. The main problem with payback period is that it does not take account of the time value of money Discounted payback period Discounted payback period measures the length of time befo re the discounted cash returns from a project cover the initial investment The shorter the discounted payback period, the more attracti ve the project is. A long discounted payback period indicates that the projct is a high risk project. 23

24 4.Discounted Payback Period Example A project with the following cash flows is under consideration: $000 T 0 T 1 T 2 T 3 T 4 (20,000) 8,000 12,000 4,000 2,000 Cost of capital 8% Calculate the discounted payback period Solution Year Discounted cash flow Cumulative discounted cashflow 0 (20,000) (20,000) 1 8,000/1.08=7,407 (12,593) 2 12,000/ =10,288 (2,305) 3 4,000/ =3, DPP=2Y+(2,305/3,175)=2.73Y 24

25 5.Duration(Macauley duration) Concept of Duration Duration measures the average time to recover the present v alue of the project(if cash flows are discounted at the cost of c apital). Duration captures both the time value of money and the whol e of the cash flows of a project. Projects with higher durations carry more risk than projects wi th lower durations. If cashflows are discounted at the project's IRR, it can be use d to measure the ime to recover the initial investment 25

26 5.Duration(Macauley duration) Comparision among three techniques Payback period fail to take into account the time value of money fail to take into account cash flows beyond the project date. Discounted payback period take into account the time value of money it is possible for projects with highly negative terminal cash flows to appear attractive Duration Duration measures either the average time to recover the initial investment, or to recover the present value of the project if discounted at the cost of capital Duration captures both the time value of money and the whole of the cf of a project 26

27 5.Duration(Macauley duration) A project with the following cash flows is under consideration: $000 T 0 T 1 T 2 T 3 T 4 (20,000) 8,000 12,000 4,000 2,000 Cost of capital 8% Calaculate the project's Macauley duration Solution The Maculey duration is calculated by first calculating the discounted cas h flow for each future year, and then weighting each discounted cash flow according to its time of receipt, as follows: $000 T 0 T 1 T 2 T 3 T 4 cash flow 8,000 12,000 4,000 2,000 27

28 5.Duration(Macauley duration) $000 T 0 T 1 T 2 T 3 T 4 cash flow 8,000 12,000 4,000 2,000 DF@8% PV@8% 7,408 10,284 3,176 1,470 PV*Year 7,408 20,568 9,528 5,880 Next, the sum of the (PV*Year)figure is found, and divided by the present value of these "return phase" cash flows Sum of (PV*Year)figures=7,408+20,568+9,528,5,880=43,384 Present value of return phase cash flows=7,408+10,284+3,176+1,470=22, 338 Hence,the Macauley duration is 43,384/22,338=1.94years 28

29 5.Duration(Macauley duration) Modified Duration Macaulay Duration is the name given to the weighted average time until cash flows are received, and is measured in years. Modified Duration is the name given to the price sensitivity and is t he percentage change in price for a unit change in yield. Macaulay Duration and Modified Duration differ slightly, and there i s a simple relationship between the two: Modified Duration=Macauley Duration/(1+cost of capital) Q1 (b) June

30 6.Capital rationing Capital rationing- single period Capital rationing is where there are insufficient funds to undertak e all possible positive NPV projects to maximise shareholder wealth. independent and divisible(pi Method) independent and indivisible(trial and Error Approach) mutually exclusive(pick the one with the highest positive NPV) Past paper:slow Fashions Co (6/09) 30

31 6.Capital rationing Multi-period capital rationing A solution to a multi-period capital rationing problem cannot be fo und using PIs. This method can only deal with one limiting factor. Her e there are a number of limiting factors and linear programming techn iques must therefore be applied. However, linear programming(lp) is not expected to produce in th e exam.the linear programme is formulated in three stages: Define the unknowns Formulate the objective function Express the constraints in terms of inequalities including the nonngegativities 31

32 6.Capital rationing The impact of corporate reporting on investment appraisal Impact on shareholder wealth. e.g. the share price Impact on reported financial position e.g. gearing Performance of the firm e.g. ROCE, EPS. 32

33 Past paper Past Paper for investment appraisal DCF techniques Jonas Chemical Systems(BPP Q13) CD(BPP Q13) Slow Fashions Co (6/09) Your business (6/09) Kodiak Company (12/09) Tisa Co (6/12) Arbore Co (12/12) Neptune (6/08) Chmura Co (12/13) Blipton International (12/08) Jupiter Co (12/08) Trosoft (SFM, 12/04) Seal Island (6/10) Sleepon (SFM, 12/05) 33

34 Analysis of Example You have been conducting a detailed review of an investment project proposed by one of the divisions of your business. Your review has two aims: first to correct the proposal for any errors of principle and second, to recommend a financial measure to replace payback as one of the criteria for acceptability when a project is presented to the company's board of directors for approval. The company's current weighted average cost of capital is 10% per annum. The initial capital investment is for $150 million followed by $50 million one year later. The post tax cash flows, for this project, in $million, including the estimated tax benefit from capital allowances for tax purposes, are as follows: 34

35 Analysis of Example Company tax is charged at 30% and is paid/recovered in the year in which the liability is incurred. The company has sufficient profits elsewhere to recover capital allowances on this project, in full, in the year they are incurred. All the capital investment is eligible for a first year allowance for tax purposes of 50% followed by a writing down allowance of 25% per annum on a reducing balance basis. You notice the following points when conducting your review: 1. An interest charge of 8% per annum on a proposed $50 million loan has been included in the project's post tax cash flow before tax has been calculated. 2. Depreciation for the use of company shared assets of $4 million per annum has been charged in calculating the project post tax cash flow. 3. Activity based allocations of company indirect costs of $8 million have been included in the project's post tax cash flow. However, additional 35

36 Analysis of Example corporate infrastructure costs of $4 million per annum have been ignored which you discover would only be incurred if the project proceeds. 4. It is expected that the capital equipment will be written off and disposed of at the end of year six. The proceeds of the sale of the capital equipment are expected to be $7 million which have been included in the orecast of the project's post tax cash flow. You also notice that an estimate for site clearance of $5 million has not been included nor any tax saving recognised on the unclaimed writing down allowance on the disposal of the capital equipment. Required(:a) Prepare a corrected project evaluation using the net present value technique supported by a separate assessment of the sensitivity of the project to a $1 million change in the initial capital expenditure. (b) Estimate the discounted payback period and the duration for this project commenting on the relative advantages and disadvantages of each method. (5 marks) 36

37 Solution of Example (a) The first thing to do in this question is to determine how to correct the errors of pri nciple. (1) Interest should not be included as this is already accounted for in the discount rat e. The annual interest charge of $4 million (less tax of 30%) should be added back to the cash flow in each year. (2) Depreciation is not a cash flow and should be ignored in NPV calculations. The a nnual charge of $4million (less tax at 30%) should be added back to the cash flow in each year. (3) Indirect allocated costs are not relevant. These should be added back to the annu al cash flows (net of tax). Corporate infrastructure costs are relevant to the project an d should have been included. These costs should be deducted from annual cash flow figures (net of tax), as should the estimates for site clearance. (4) Capital allowances in year 6 should be accounted for. 37

38 Solution of Example 38

39 Solution of Example 39

40 Solution of Example 40

41 Solution of Example (b) Discounted payback and duration Discounted payback is used to determine how long it will take the project to repay its original i nvestment. As the name suggests this method uses discounted cash flows in the calculations. The discounted payback period is approximately 4.5 years. 41

42 Solution of Example Project duration is the time it takes the project to recover approximately 50% of its initial investment. It is calculated by weighting each year of the project by the percentage of the present value recovered in that year. 42

43 Solution of Example Discounted payback overcomes one of the problems of the ordinary payb ack technique that is, it uses discounted cash flows rather than ignoring t he time value of money. However the problem with payback (discounted or not) is that it ignores cash flows that occur beyond the payback period. Thu s projects that have very high initial cash flows but few (if any) in later year s may be favoured over those projects that might add greater value to the fi rm but over a longer period. The advantage of duration is that it considers the cash flows over the entir e life of the project. It measures how long it will be before the project recov ers the bulk of its present value. However it can be more difficult to underst and the concept behind duration and for this reason it may not be widely us ed. 43

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ACCA P4 习题详解. Provided by Academy of Professional Accounting (APA) Advanced Financial Management (AFM) 高级财务管理第四讲 ACCA Lecturer: Lily Wang

ACCA P4 习题详解. Provided by Academy of Professional Accounting (APA) Advanced Financial Management (AFM) 高级财务管理第四讲 ACCA Lecturer: Lily Wang Professional Accounting Education Provided by Academy of Professional Accounting (APA) ACCA P4 习题详解 Advanced Financial Management (AFM) 高级财务管理第四讲 ACCA Lecturer: Lily Wang ACCAspace 中国 ACCA 特许公认会计师教育平台