Advanced Capital Budgeting Decisions PDF

CHAPTER 3 ADVANCED CAPITAL BUDGETING DECISIONS LEARNING OUTCOMES After going through the chapter student shall be able to understand  Current trends in Capital Budgeting  Dealing with Risk in Investment...

CHAPTER 3 ADVANCED CAPITAL BUDGETING DECISIONS LEARNING OUTCOMES After going through the chapter student shall be able to understand  Current trends in Capital Budgeting  Dealing with Risk in Investment Decisions  Internal and External Factors affecting capital budgeting decision  Methods of incorporating risk in Capital Budgeting  Adjusted Present Value  Optimum Replacement Cycle 1. CURRENT TRENDS IN CAPITAL BUDGETING While discussing the capital budgeting or investment evaluation techniques at Intermediate Level, we have assumed that the investment proposals do not involve any risk and cash flows of the project are known with certainty. This assumption was taken to simplify the understanding of the capital budgeting techniques. However, in practice, this assumption is not correct. In-fact, investment projects are exposed to various types of factors some of which are as follows: (i) Inflation (ii) Change in technology (iii) Change in Government Policies Now let us discuss the impact of each factor in a detailed manner. © The Institute of Chartered Accountants of India  2.2 3.2 ADVANCED FINANCIAL MANAGEMENT 1.1 Impact of Inflation on Capital Budgeting Decisions Adjustment for inflation is a necessity for capital investment appraisal. This is because inflation will raise the revenues & costs of the project. The net revenues after adjustment for inflation shall be equal to net revenues in current terms. The considerations, which cause distortion, are: (1) Depreciation charges are based on historical costs. Tax benefits accruing from depreciation charges do not keep parity with inflation. As annual after-tax cash inflow of a project is equal to (R – C – D) (1 – T) + D = (R – C) (1 – T) + DT Where, R  Revenue from project C  Costs (apart from depreciation) relating to the project D  Depreciation charges T  Tax Rate Here (R – C) (1 – T) tends to move in line with inflation as inflation influences revenues & costs similarly. DT does not depend on inflation as depreciation charges are based on historical costs. The effect of inflation is to reduce the actual rate of return. Example: Initial outlay of a project – ` 80,000 Expected life – 4 years Salvage value – Nil Annual revenues – ` 60,000 Annual costs other than depreciation – ` 20,000 Tax Rate – 50% Depreciation on straight-line basis presuming as if there is no inflation. Year 1 2 3 4 Revenues ` 60,000 ` 60,000 ` 60,000 ` 60,000 Costs other than depreciation ` 20,000 ` 20,000 ` 20,000 ` 20,000 Depreciation ` 20,000 ` 20,000 ` 20,000 ` 20,000 Taxable profit ` 20,000 ` 20,000 ` 20,000 ` 20,000 Tax ` 10,000 ` 10,000 ` 10,000 ` 10,000 Profit after tax ` 10,000 ` 10,000 ` 10,000 ` 10,000 Net cash inflow ` 30,000 ` 30,000 ` 30,000 ` 30,000 © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.3 2.3 If there is inflation @ 10% applicable to revenues & cost of project. Year 1 2 3 4 Revenues ` 66,000 ` 72,600 ` 79,860 ` 87,846 Costs other than depreciation ` 22,000 ` 24,200 ` 26,620 ` 29,282 Depreciation ` 20,000 ` 20,000 ` 20,000 ` 20,000 Taxable profit ` 24,000 ` 28,400 ` 33,240 ` 38,564 Tax ` 12,000 ` 14,200 ` 16,620 ` 19,282 Profit after tax ` 12,000 ` 14,200 ` 16,620 ` 19,282 Net cash inflow ` 32,000 ` 34,200 ` 36,620 ` 39,282 The actual net cash flow stream after deflating for inflation rate of 10%. Real Net Cash Flow ` 29,091 ` 28,264 ` 27,513 ` 26,830 So actual net cash flows are less than net cash flow if there is no inflation. (2) Costs of capital considered for investment appraisals contain a premium for anticipated inflation. Due to inflation investors require the nominal rate of return to be equal to: Required Rate of Return in real terms plus Rate of Inflation. Formula RN = RR + P RN Required rate of return in nominal terms. RR Required rate of return in real terms. P  Anticipated inflation rate. If cost of capital (required rate of return) contains a premium for anticipated inflation, the inflation factor has to be reflected in the projected cash flows. If there is no inflation, then it has to be discounted at required rate of return in real terms. Illustration 1 Determine NPV of the project with the following information: Initial Outlay of project ` 40,000 Annual revenues (Without inflation) ` 30,000 Annual costs excluding depreciation (Without inflation) ` 10,000 Useful life 4 years Salvage value Nil Tax Rate 50% © The Institute of Chartered Accountants of India  2.4 3.4 ADVANCED FINANCIAL MANAGEMENT Cost of Capital (Including inflation premium of 10%) 12% Solution Annual Cash Flow of project is (` 30,000 – ` 10,000) (1 – 0.50) + ` 10,000 x 0.50 = ` 15,000 It would be inconsistent to discount these real cash flows at 12% (nominal rate of return). There are two alternatives: (i) Either to restate the cash flow in nominal term and discount at 12% or (ii) Restate the discount rate in real terms and use this to discount the real cash flows. NPV using (i) approach Since inflation rate is 10% a year, real cash flows may be stated in nominal cash flows as follows: Nominal Cash Flow = (1 + Inflation Rate) Real Cash Flows Year Real Cash Flows Nominal Cash flows 1 15000 15,000 × 1.10 = 16,500 2 15,000 15,000 × (1.10)2 = 18,150 3 15,000 15,000 × (1.10.)3 = 19,965 4 15,000 15,000 × (1.10)4 = 21,962 NPV using nominal discounting rate 12% 16,500 18,150 19,965 21,962 + + + - 40,000 (1.12) (1.12)2 (1.12)3 (1.12) 4 = ` 14,732 + ` 14,469 + ` 14,211+ ` 13,957 – ` 40,000 = ` 17,369 (Approx) NPV using (ii) approach To compute NPV using (ii) approach, we shall need real discount rate, which shall be computed as follows: 1+ Nominal Discount Rate Real Discount Rate= −1 1 + Inflation Rate 1+ 0.12 Real Discount Rate= − 1 = 0.0182 i.e. 1.8%. 1 + 0.10 n NPV = ∑ cft − Io t =1 Where t = Time Period © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.5 2.5 cft = Annual Cash Flow Io = Initial Outlay Accordingly NPV of the project 15,000 15,000 15,000 15,000 + 2 + 3 + - 40,000 (1.0182) (1.0182) (1.0182) (1.0182)4 = ` 14,732 + ` 14,469 + ` 14,210+ ` 13,956 – ` 40,000 = ` 57,367 – ` 40,000 = `17,367(Approx) NPV based on consideration that inflation rate for revenue and cost are different shall be computed as follows: N.P.V. = nΣt=1 [{Rt (1+ir) - CttΣr=1(1+ic)} (1-T) + DtT] / (1+k)t - I0 Rt revenues for the year ‘t’ with no inflation. ir annual inflation rate in revenues for ‘r th ’ year. Ct costs for year ‘t’ with no inflation. ic annual inflation rate of costs for year ‘r’. T  tax rate. Dt depreciation charge for year ‘t’. I0 initial outlay. k  cost of capital (with inflation premium). Illustration 2 XYZ Ltd. requires ` 8,00,000 for an unit. Useful life of project - 4 years. Salvage value - Nil. Depreciation Charge ` 2,00,000 p.a. Expected revenues & costs (excluding depreciation) ignoring inflation. Year 1 2 3 4 Revenues ` 6,00,000 ` 7,00,000 ` 8,00,000 ` 8,00,000 Costs ` 3,00,000 ` 4,00,000 ` 4,00,000 ` 4,00,000 Tax Rate 60% cost of capital 10% (including inflation premium). Calculate NPV of the project if inflation rates for revenues & costs are as follows: Year Revenues Costs 1 10% 12% © The Institute of Chartered Accountants of India  2.6 3.6 ADVANCED FINANCIAL MANAGEMENT 2 9% 10% 3 8% 9% 4 7% 8% Solution Computation of Annual Cash Flow (i) Inflation adjusted Revenues Year Revenues (`) Revenues (Inflation Adjusted) (`) 1 6,00,000 6,00,000(1.10) = 6,60,000 2 7,00,000 7,00,000(1.10)(1.09) = 8,39,300 3 8,00,000 8,00,000(1.10)(1.09)(1.08) = 10,35,936 4 8,00,000 8,00,000(1.10)(1.09)(1.08)(1.07) = 11,08,452 (ii) Inflation adjusted Costs Year Revenues (`) Revenues (Inflation Adjusted) (`) 1 3,00,000 3,00,000(1.12) = 3,36,000 2 4,00,000 4,00,000(1.12)(1.10) = 4,92,800 3 4,00,000 4,00,000(1.12)(1.10)(1.09) = 5,37,172 4 4,00,000 4,00,000(1.12)(1.10)(1.09)(1.08) = 5,80,124 (iii) Tax Benefit on Depreciation = ` 2,00,000 x 0.60 = ` 1,20,000 (iv) Net Profit after Tax Year Revenues Costs Net Profit Tax Net after (Inflation (Inflation (`) (`) Profit Adjusted) Adjusted) (3) = (1) - (2) (4) = 60% (`) (`)(1) (`)(2) of (3) (3) - (4) 1 6,60,000 3,36,000 3,24,000 1,94,400 1,29,600 2 8,39,300 4,92,800 3,46,500 2,07,900 1,38,600 3 10,35,936 5,37,172 4,98,764 2,99,258 1,99,506 4 11,08,452 5,80,124 5,28,328 3,16,997 2,11,331 (iv) Present Value of Cash Inflows Year Net after Tax Benefit on Cash Inflow PVF@ PV Profit Depreciation 10% (`) (`) (`) (`) © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.7 2.7 1 1,29,600 1,20,000 2,49,600 0.909 2,26,886 2 1,38,600 1,20,000 2,58,600 0.826 2,13,604 3 1,99,506 1,20,000 3,19,506 0.751 2,39,949 4 2,11,331 1,20,000 3,31,331 0.683 2,26,299 9,06,738 NPV = ` 9,06,738 – ` 8,00,000 = ` 1,06,738 1.2 Impact of change in technology on Capital Budgeting Decisions Generally it has been observed that those making capital Budgeting decision evaluates the proposals in monetary terms i.e. quantitative values and normally fails to consider critical factors i.e. qualitative factor that can affect the future cash flows one of such factor is technology. It is important to note that here we are not simply talking about decision to replace existing machinery with new machine having improved technology rather we are talking about the impact of technology change on capital budgeting. Now the question arises why it is important to analyze the impacts of change in technology it is because of following reason:  Change in technology can significantly alter production process.  Changes can also yield benefits such as improved quality, delivery time greater flexibility, etc.  Changed technology can also result in reduction in cost of capital  Improved cash inflows can be achieved through technological changes.  There may be need to incur additional cost in the form of additional capital expenditure.  The sale volume can be impacted as the anticipated life cycle of the product can be shortened because of change in consumer preference. Now next question arises how to incorporate impact in capital budgeting decision. For this purpose it is very necessary that once the project has been launched it should be reviewed on continuous basis and if required it need to be revised in light of changes in the technology. The various ways in which the impact of change in technology can be incorporated in capital Budgeting decisions are as follows. 1. At the time of making Capital Budgeting decisions the risk of change in technology should be considered using various techniques such as sensitivity analysis, Scenario Analysis, Simulation Analysis etc. (discussed later in this chapter) 2. Once project has been launched analyze the impact of change in technology both positive or negative and revise estimates in monetary terms. 3. If continuation of project is proving to be unviable then look for abandonment option and evaluate the same (discussed later). © The Institute of Chartered Accountants of India  2.8 3.8 ADVANCED FINANCIAL MANAGEMENT 4. Suitably adjusting the discounting rate. 1.3 Impact of change in Government Policies on Capital Budgeting Decisions Government Policies are important external factors that impacts the capital budgeting decision because directly or indirectly they affect the future cash flows of the firm that forms the basis of capital budgeting decisions. It might be possible that Government Policy may not affect us, but it may affect our supplier, buyers, customers, service providers etc. The impact of changes in these policies can be positive as well as negative. What is more important is that the impact of such should be analysed and if required the estimation should be revised adequately. If required, the firm should consider the option to abandon the project (discussed in later chapter of study material). The change in Government Policy can be analysed under two headings: i. Impact of change of Policies on Domestic Capital Budgeting Decision. ii. Impact of change of Policies on International Capital Budgeting Decision. While some Government policies are changed after a longer period, say five to ten years, some change from quarter to a year. The impact of each policy may vary from each other. For example, the policies such as New Industrial Policy 1991, might had drastically impacted the Capital Budgeting decisions of various firms in the beginning period of 1990s due to opening of the doors of the Indian Economy for the Global world. However, such types of policies normally come out after a longer period. On the other hand, there are some policies of the Government that are announced/ reviewed within a period of one year. Some of these are as follows:  Fiscal policy: The use of government spending, taxation and borrowing to influence both the pattern of economic activity and level of growth of aggregate demand, output and employment.  Monetary Policy: Monetary policy refers to the use of monetary policy instruments which are at the disposal of the central bank to regulate the availability, cost and use of money and credit to promote economic growth, price stability, optimum levels of output and employment, balance of payments equilibrium, stable currency or any other goal of government's economic policy. Generally, the change in monetary policy depends on the economic status of the nation. In India, the monetary policy includes decisions on open market operations, variation in reserve requirements, selective credit controls, supply of currency, bank rates (Repo Rates) and other rates. Since in India members of Monetary Policy Committee (MPC) are required to meet at least four times in a year generally changes in the policies related to above mentioned matters takes at least two to three times in a year. © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.9 2.9 Now let us discuss how changes in Government Policies affect the Capital Budgeting decision under two broad heads: 1.3.1 Impact of changes in Government Policies on Domestic Capital Budgeting Decision. (a) Since the change in interest rate are decided by Government through its Monetary Policy. This can affect the Cost of Capital because the Cost of Debt is normally dependent on the bank rate of interest as they are considered as one of the important factors to compute YTM. Though this rate change may not much affect Capital Budgeting decision because they are financed from long term source of finance but they may impact working capital decisions to a great extent. The main reason behind is that the Bank Overdraft as one of the important constituents of Working Capital and it may lead to change in cash flow estimation. Hence, it is important that though small change in Bank Interest can be ignored but a major change say about 100 basis points or so can impact cash flows of the firm and may call for revision of estimations. (b) Another important change (Government Policy) is related to Fiscal Policy, Since Fiscal Policy forms the basis of Tax Rate and Annual Cash Flows are dependent on Rate of Depreciation of Tax Rate, any drastic change in any of these two items may call for revision of estimated cash flows. 1.3.2 Impact of changes in Government Policies on International Capital Budgeting Decision. (a) In International Capital Budgeting Decisions, the foreign exchange rate play a very important role. As mentioned above the change in bank rate and money supply is decided as per Monetary Policy, the change in any of these two impacts the rate of Foreign Exchange and it may call for revision of estimates. (b) Change in Tax Rates relating to Foreign Income or changes in provisions of Double Tax Avoiding Agreement (DTAA) as decided in Fiscal Policy may call revision of estimates. Thus, from above discussion it can be concluded that while estimating future cash inflows change in the policies be forecasted and a proper provision should be incorporated in the expected cash flows. 2. DEALING WITH RISK IN INVESTMENT DECISIONS While discussing the capital budgeting or investment evaluation techniques at Intermediate Level in the paper of Financial Management, we have assumed that the investment proposals do not involve any risk and cash flows of the project are known with certainty. This assumption was taken to simplify the understanding of the capital budgeting techniques. However, in practice, this assumption is not correct. In-fact, investment projects are exposed to various degrees of risk. © The Institute of Chartered Accountants of India  2.10 3.10 ADVANCED FINANCIAL MANAGEMENT There can be three types of decision making: (i) Decision making under certainty: When cash flows are certain. (ii) Decision making involving risk: When cash flows involves risk and probability can be assigned. (iii) Decision making under uncertainty: When the cash flows are uncertain and probability cannot be assigned. 2.1 Risk and Uncertainty Risk is the variability in terms of actual returns comparing with the estimated returns. Most common techniques of risk measurement are Standard Deviation and Coefficient of Variation. There is a thin difference between risk and uncertainty. In case of risk, probability distribution of cash flow is known. When no information is known to formulate probability distribution of cash flows, the situation is referred as uncertainty. However, these two terms are used interchangeably. 2.2 Reasons for adjustment of Risk in Capital Budgeting decisions Main reasons for considering risk in capital budgeting decisions are as follows: 1. There is an opportunity cost involved while investing in a project for the level of risk. Adjustment of risk is necessary to help make the decision as to whether the returns out of the project are proportionate with the risks borne and whether it is worth investing in the project over the other investment options available. 2. Risk adjustment is required to know the real value of the Cash Inflows. Higher risk will lead to higher risk premium and also expectation of higher return. 3. INTERNAL AND EXTERNAL FACTORS AFFECTING CAPITAL BUDGETING DECISION Risk arises from different factors, depending on the type of investment being considered, as well as the circumstances and the industry in which the organisation is operating. Accordingly it these factors can be divided following two broad categories: 3.1 Internal Factors These factors are internal to the company, and they can further be divided into following categories: 3.1.1 Project-specific risk Risks which are related to a particular project and affects the project’s cash flows. It includes completion of the project in scheduled time, error of estimation in resources and allocation, estimation of cash flows etc. For example, a nuclear power project of a power generation company has different risks than hydel projects. © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.11 2.11 3.1.2 Company-specific risk Risk which arise due to company specific factors like downgrading of credit rating, changes in key managerial persons, cases for violation of intellectual property rights (IPR) and other laws and regulations, dispute with workers etc. All these factors affect the cash flows of an entity and access to funds for capital investments. For example, two banks have different exposure to default risk. 3.2 External Factors These factors are external to the company, and they can further be divided into following categories: 3.2.1 Industry-specific risk These are the risks which effect the whole industry in which the company operates. These risks include regulatory restrictions on industry, changes in technologies etc. For example, regulatory restriction imposed on leather and breweries industries. 3.2.2 Market risk The risk which arise due to market related conditions like entry of substitute, changes in demand conditions, availability and access to resources etc. For example, a thermal power project gets affected if the coal mines are unable to supply coal requirements of a thermal power company etc. 3.2.3 Competition risk These are risks related with competition in the market in which a company operates. These risks are risk of entry of rival, product dynamism and change in taste and preference of consumers etc. 3.2.4 Risk due to Economic conditions These are the risks which are related with macro-economic conditions like changes in monetary policies by central banks, changes in fiscal policies like introduction of new taxes and cess, inflation, changes in GDP, changes in savings and net disposable income etc. 3.2.5 International risk These are risk which are related with conditions which are caused by global economic conditions like restriction on free trade, restrictions on market access, recessions, bilateral agreements, political and geographical conditions etc. For example, restriction on outsourcing of jobs to overseas markets. 4. METHODS OF INCORPORATING RISK IN CAPITAL BUDGETING Techniques of risk analysis in capital budgeting can be classified as below: © The Institute of Chartered Accountants of India  2.12 3.12 ADVANCED FINANCIAL MANAGEMENT Probability Statistical Variance or Standard Techniques Deviation Coefficient of Variation Techniques of Risk Risk-adjusted discount Conventional rate Analysis techniques Certainty Equivalent Sensitivity analysis Scenario analysis Others techniques Simulation analysis Decision Tree 4.1 Statistical Techniques 4.1.1 Probability Probability is a measure about the chances that an event will occur. When an event is certain to occur, probability will be 1 and when there is no chance of happening an event, probability will be 0. Example: Assumption Cash Flows (`) Probability Best guess 3,00,000 0.3 High guess 2,00,000 0.6 Low guess 1,20,000 0.1 In the above example chances that cash flow will be ` 3,00,000, ` 2,00,000 and ` 1,00,000 are 30%, 60% and 10% respectively. (i) Expected Net Cash Flows Expected Net Cash flows are calculated as the sum of the likely Cash flows of the Project multiplied by the probability of cash flows. Expected Cash flows are calculated as below: E(R)/ENCF = ∑ni=1 NCFi × Pi © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.13 2.13 Where, E(R)/ENCF = Expected Net Cash flows Pi = Probability of Cash flows NCFi = Net Cash flows Example: Assumption Cash Flows (`) Probability Expected cash flow (`) (1) (2) (3) (2×3) Best guess 3,00,000 0.3 3,00,000 × 0.3 = 90,000 High guess 2,00,000 0.6 2,00,000 × 0.6 = 1,20,000 Low guess 1,20,000 0.1 1,20,000 × 0.1 = 12,000 Expected Net cash flow (ENCF) 2,22,000 (ii) Expected Net Present Value Expected net present value = n ENCF ENPV = ∑ t t=1 (1+k ) Where, ENPV = Expected Net Present Value ENCF = Expected Net Cash Flows(including both inflows and outflows) t = Period k = Discount rate. (a) Expected Net Present Value - Single period Let us understand the calculation of Expected Net Present Value (ENPV) for a single period through an illustration as follows: Illustration 3 Possible net cash flows of Projects A and B at the end of first year and their probabilities are given below. Discount rate is 10 per cent. For both the projects, initial investment is ` 10,000. Calculate the expected net present value for each project. State which project is preferable? Possible Project A Project B Event Cash Flow (`) Probability Cash Flow (`) Probability A 8,000 0.10 24,000 0.10 B 10,000 0.20 20,000 0.15 © The Institute of Chartered Accountants of India  2.14 3.14 ADVANCED FINANCIAL MANAGEMENT C 12,000 0.40 16,000 0.50 D 14,000 0.20 12,000 0.15 E 16,000 0.10 8 ,000 0.10 Solution Calculation of Expected Value for Project A and Project B Project A Project B Possible Cash Probability Expected Cash Probability Expected Event Flow Value Flow Value (`) (`) (`) (`) A 8,000 0.10 800 24,000 0.10 2,400 B 10,000 0.20 2,000 20,000 0.15 3,000 C 12,000 0.40 4,800 16,000 0.50 8,000 D 14,000 0.20 2,800 12,000 0.15 1,800 E 16,000 0.10 1,600 8,000 0.10 800 ENCF 12,000 16,000 The Net Present Value for Project A is (0.909 × ` 12,000 – ` 10,000) = ` 908 The Net Present Value for Project B is (0.909 × ` 16,000 – ` 10,000) = ` 4,544. (b) Expected Net Present Value- Multiple period Let us understand the calculation of Expected Net Present Value (ENPV) for multiple periods through an illustration as follows: Illustration 4 Probabilities for net cash flows for 3 years of a project are as follows: Year 1 Year 2 Year 3 Cash Flow Probability Cash Flow Probability Cash Flow Probability (`) (`) (`) 2,000 0.1 2,000 0.2 2,000 0.3 4,000 0.2 4,000 0.3 4,000 0.4 6,000 0.3 6,000 0.4 6,000 0.2 8,000 0.4 8,000 0.1 8,000 0.1 © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.15 2.15 Calculate the expected net present value of the project using 10 per cent discount rate if the Initial Investment of the project is ` 10,000. Solution Calculation of Expected Value Year 1 Year 2 Year 3 Cash Prob. Expected Cash Prob. Expected Cash Prob. Expected Flow Value Flow Value Flow Value (`) (`) (`) (`) (`) (`) 2,000 0.1 200 2,000 0.2 400 2,000 0.3 600 4,000 0.2 800 4,000 0.3 1200 4,000 0.4 1,600 6,000 0.3 1,800 6,000 0.4 2400 6,000 0.2 1,200 8,000 0.4 3,200 8,000 0.1 800 8,000 0.1 800 ENCF 6,000 4,800 4,200 The present value of the expected value of cash flow at 10 per cent discount rate has been determined as follows: ENCF1 ENCF2 ENCF3 Present Value of cash flow = + + (1+k)1 (1+k)2 (1+k)3 6,000 4,800 4,200 = + + (1.1) (1.1)2 (1.1)3 = (6,000 × 0.909) + (4,800 × 0.826) + (4,200 × 0.751) = ` 12,573 Expected Net Present value = Present Value of cash flow - Initial Investment = ` 12,573 – ` 10,000 = ` 2,573. 4.1.2 Variance Variance is a measurement of the degree of dispersion between numbers in a data set from its average. In very simple words, variance is the measurement of difference between the average of the data set from every number of the data set. Variance is calculated as below: 2 Variance(σ2 ) = ∑nj= 1 NCFj − ENCF Pj Where, NCFj = Net Cash Flow ENCF = Expected Net Cash Flow Pj = Probability © The Institute of Chartered Accountants of India  2.16 3.16 ADVANCED FINANCIAL MANAGEMENT Variance measures the uncertainty of a value from its average. Thus, variance helps an organization to understand the level of risk it might face on investing in a project. A variance value of zero would indicate that the cash flows that would be generated over the life of the project would be same. This might happen in a case where the company has entered into a contract of providing services in return of a specific sum. A large variance indicates that there will be a large variability between the cash flows of the different years. This can happen in a case where the project being undertaken is very innovative and would require a certain time frame to market the product and enable to develop a customer base and generate revenues. A small variance would indicate that the cash flows would be somewhat stable throughout the life of the project. This is possible in case of products which already have an established market. 4.1.3 Standard Deviation Standard Deviation (SD) is a degree of variation of individual items of a set of data from its average. The square root of variance is called Standard Deviation. For Capital Budgeting decisions, Standard Deviation is used to calculate the risk associated with the estimated cash flows from the project. Importance of Variance and Standard Deviation in Capital Budgeting: For making capital budgeting decisions, these two concepts are important to measure the volatility in estimated cash flows and profitability in an investment proposal. Both the concepts measures the difference between the expected cash flows and estimated cash flows (mean or average). Variance measures the range of variability (difference) in cash flows data while Standard deviation determines risk in an investment proposal. An investment proposal in which expected cash flows are close to the estimated net cash flow are seen as less risky and has the potential to make profit. Standard deviation and Variance are two different statistical concepts but are closely interrelated. Standard deviation is calculated as square root of variance, hence, variance is prerequisite for calculation of SD. Illustration 5 Calculate Variance and Standard Deviation of Project A and Project B on the basis of following information: Possible Project A Project B Event Cash Flow (`) Probability Cash Flow (`) Probability A 8,000 0.10 24,000 0.10 B 10,000 0.20 20,000 0.15 C 12,000 0.40 16,000 0.50 D 14,000 0.20 12,000 0.15 E 16,000 0.10 8,000 0.10 © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.17 2.17 Solution Calculation of Expected Value for Project A and Project B Project A Project B Possible Cash Flow Probability Expected Cash Flow Probability Expected Event (`) Value (`) (`) Value (`) A 8,000 0.10 800 24,000 0.10 2,400 B 10,000 0.20 2,000 20,000 0.15 3,000 C 12,000 0.40 4,800 16,000 0.50 8,000 D 14,000 0.20 2,800 12,000 0.15 1,800 E 16,000 0.10 1,600 8,000 0.10 800 ENCF 12,000 16,000 Project A: Variance (σ2) = (8,000 – 12,000)2 × (0.1) + (10,000 – 12,000)2 × (0.2) + (12,000 – 12000)2 × (0.4) + (14,000 – 12,000)2 × (0.2) + (16000 – 12,000)2 × (0.1) = 16,00,000 + 8,00,000 + 0 + 8,00,000 + 16,00,000 = 48,00,000 Standard Deviation (σ) = Variance(σ 2 ) = 48,00,000 = 2,190.90 Project B: Variance(σ2) = (24,000 – 16,000)2 × (0.1) + (20,000 – 16,000)2 × (0.15) + (16,000 – 16,000)2 × (0.5) + (12,000 – 16,000)2 × (0.15) + (8,000 – 16,000)2 × (0.1) = 64,00,000 + 24,00,000 + 0 + 24,00,000 + 64,00,000 = 1,76,00,000 Standard Deviation (σ) = Variance(σ 2 ) = 1,76,00,000 = 4195.23 4.1.4 The Coefficient of Variation The standard deviation is a useful measure of calculating the risk associated with the estimated cash inflows from an Investment. However, in Capital Budgeting decisions, the management is several times faced with choosing between many investments' avenues. Under such situations, it becomes difficult for the management to compare the risk associated with different projects using Standard Deviation as each project has different estimated cash flow values. In such cases, the Coefficient of Variation becomes useful. The Coefficient of Variation calculates the risk borne for every percent of expected return. It is calculated as: © The Institute of Chartered Accountants of India  2.18 3.18 ADVANCED FINANCIAL MANAGEMENT Stanadrd Deviation Coefficient of variation = Expected Return/ Expected Cash Flow The Coefficient of Variation enables the management to calculate the risk borne by the concern for every unit of estimated return from a particular investment. Simply put, the investment avenue which has a lower ratio of standard deviation to expected return will provide a better risk – return trade off. Thus, when a selection has to be made between two projects, the management would select a project which has a lower Coefficient of Variation. Illustration 6 Calculate Coefficient of Variation of Project A and Project B based on the following information: Possible Project A Project B Event Cash Flow (`) Probability Cash Flow (`) Probability A 10000 0.10 26,000 0.10 B 12,000 0.20 22,000 0.15 C 14,000 0.40 18,000 0.50 D 16,000 0.20 14,000 0.15 E 18,000 0.10 10,000 0.10 Solution Calculation of Expected Value for Project A and Project B Project A Project B Possible Cash Flow Probability Expected Cash Probability Expected Event (`) Value Flow Value (`) (`) (`) A 10,000 0.10 1,000 26,000 0.10 2,600 B 12,000 0.20 2,400 22,000 0.15 3,300 C 14,000 0.40 5,600 18,000 0.50 9,000 D 16,000 0.20 3,200 14,000 0.15 2,100 E 18,000 0.10 1,800 10,000 0.10 1,000 ENCF 14,000 18,000 Project A Variance (σ2) = (10,000 – 14,000)2 × (0.1) + (12,000 – 14,000)2 × (0.2) + (14,000 – 14000)2 × (0.4) © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.19 2.19 + (16,000 – 14,000)2 × (0.2) + (18000 – 14,000)2 × (0.1) = 16,00,000 + 8,00,000 + 0 + 8,00,000 + 16,00,000 = 48,00,000 Standard Deviation (σ) = Variance(σ 2 ) = 48,00,000 = 2,190.90 Project B: Variance(σ2) = (26,000 – 18,000)2 × (0.1) + (22,000 – 18,000)2 × (0.15) + (18,000 – 18,000)2 × (0.5) + (14,000 – 18,000)2 × (0.15) + (10,000 – 18,000)2 × (0.1) = 64,00,000 + 24,00,000 + 0 + 24,00,000 + 64,00,000 = 1,76,00,000 Standard Deviation (σ) = Variance(σ 2 ) = 1,76,00,000 = 4195.23 Projects Coefficient of variation Risk Expected Value A 2190.90 Less Less = 0.1565 14000 B 4195.23 More More = 0.2331 18000 In project A, risk per rupee of cash flow is ` 0.16 while in project B, it is ` 0.23. Therefore, Project A is better than Project B. 4.2 Conventional Techniques 4.2.1 Risk Adjusted Discount Rate The use of risk adjusted discount rate (RADR) is based on the concept that investors demand higher returns from the risky projects. The required rate of return on any investment should include compensation for delaying consumption plus compensation for inflation equal to risk free rate of return, plus compensation for any kind of risk taken. If the risk associated with any investment project is higher than risk involved in a similar kind of project, discount rate is adjusted upward in order to compensate this additional risk borne. Under this method, NPV is calculated as follows: n NCF NPV = ∑ t -I t =1 (1+k ) Where, NCFt = Net cash flow k = Risk adjusted discount rate (RADR) I = Initial Investment t = Period A risk adjusted discount rate is a sum of risk-free rate and risk premium. The Risk Premium depends on the perception of risk by the investor of a particular investment and risk aversion of the Investor. © The Institute of Chartered Accountants of India  2.20 3.20 ADVANCED FINANCIAL MANAGEMENT So, Risk adjusted discount rate (RADR) = Risk free rate + Risk premium Risk Free Rate: It is the rate of return on Investments that bear no risk. For e.g., Government securities yield a return of 6% and bear no risk. In such case, 6% is the risk-free rate. Risk Premium: It is the rate of return over and above the risk free rate, expected by the Investors as a reward for bearing extra risk. For high risk projects, the risk premium will be high and for low risk projects, the risk premium would be lower. Illustration 7 An enterprise is investing ` 100 lakhs in a project. The risk-free rate of return is 7%. Risk premium expected by the Management is 7%. The life of the project is 5 years. Following are the cash flows that are estimated over the life of the project: Year Cash flows (` in lakhs) 1 25 2 60 3 75 4 80 5 65 Calculate Net Present Value of the project based on Risk free rate and also on the basis of Risks adjusted discount rate. Solution The Present Value of the Cash Flows for all the years by discounting the cash flow at 7% is calculated as below: Year Cash flows Discounting Factor Present value of Cash Flows (` in lakhs) @ 7% (` In Lakhs) 1 25 0.935 23.38 2 60 0.873 52.38 3 75 0.816 61.20 4 80 0.763 61.04 5 65 0.713 46.35 Total of Present value of Cash flows 244.34 Less: Initial investment 100.00 Net Present Value (NPV) 144.34 Now, when the risk-free rate is 7% and the risk premium expected by the Management is 7%, then © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.21 2.21 risk adjusted discount rate is 7% + 7% = 14%. Discounting the above cash flows using the Risk Adjusted Discount Rate would be as below: Year Cash flows Discounting Present Value of Cash Flows (` in Lakhs) Factor @ 14% (` in lakhs) 1 25 0.877 21.93 2 60 0.769 46.14 3 75 0.675 50.63 4 80 0.592 47.36 5 65 0.519 33.74 Total of Present value of Cash flows 199.79 Less: Initial investment 100.00 Net present value (NPV) 99.79 Advantages of Risk-adjusted discount rate (1) It is easy to understand. (2) It incorporates risk premium in the discounting factor. Limitations of Risk-adjusted discount rate (1) Difficulty in finding risk premium and risk-adjusted discount rate. (2) Though NPV can be calculated but it is not possible to calculate Standard Deviation of a given project. 4.2.2 Certainty Equivalent (CE) As per CIMA terminology, “Certainty Equivalent is an approach dealing with risk in a capital budgeting context. It involves expressing risky future cash flows in terms of the certain cashflow which would be considered, by the decision maker, as their equivalent, that is the decision maker would be indifferent between the risky amount and the (lower) riskless amount considered to be its equivalent.” The certainty equivalent is a guaranteed return that the management would accept rather than accepting a higher but uncertain return. This approach allows the decision maker to incorporate his or her utility function into the analysis. In this approach a set of risk less cash flow is generated in place of the original cash flows. Steps in the Certainty Equivalent (CE) approach Step 1: Remove risks by substituting equivalent certain cash flows from risky cash flows. This can be done by multiplying each risky cash flow by the appropriate α t value (CE coefficient) © The Institute of Chartered Accountants of India  2.22 3.22 ADVANCED FINANCIAL MANAGEMENT Certain cash flow α1 = Risky or expected cash flow t Suppose on tossing out a coin, if it comes head, you will win ` 10,000 and if it comes out to be tail, you will win nothing. Thus, you have 50% chance of winning and expected value is ` 5,000 (` 10,000 × 0.50). In such case, if you are indifferent at receiving ` 3,000 for a certain amount and not playing then ` 3,000 will be certainty equivalent and 0.3 (i.e. ` 3,000/` 10,000) will be certainty equivalent coefficient. Step 2: Discounted value of cash flow is obtained by applying risk less rate of interest. Since you have already accounted for risk in the numerator using CE coefficient, using the cost of capital to discount cash flows will tantamount to double counting of risk. Step 3: After that, normal capital budgeting method is applied except in case of IRR method, where IRR is compared with risk free rate of interest rather than the firm’s required rate of return. Certainty Equivalent Coefficient transforms expected values of uncertain flows into their Certainty Equivalents. It is important to note that the value of Certainty Equivalent Coefficient lies between 0 & 1. Certainty Equivalent Coefficient 1 indicates that the cash flow is certain or management is risk neutral. In industrial situation, cash flows are generally uncertain and managements are usually risk averse. Under this method, NPV is calculated as follows: n α𝑡𝑡 × NCFt NPV = -I (1 + k)t t=1 Where, αt = Risk-adjustment factor or the certainly equivalent coefficient NCFt = Forecasts of net cash flow for year ‘t’ without risk-adjustment k = Risk free rate assumed to be constant for all periods I = Initial Investment Illustration 8 If Investment proposal costs ` 45,00,000 and risk free rate is 5%, calculate net present value under certainty equivalent technique. Year Expected cash flow (`) Certainty Equivalent coefficient 1 10,00,000 0.90 2 15,00,000 0.85 3 20,00,000 0.82 4 25,00,000 0.78 © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.23 2.23 Solution 10,00,000×(0.90) 15,00,000×(0.85) 20,00,000×(0.82) 25,00,000×(0.78) NPV = + + + - 45,00,000 (1.05) (1.05)2 (1.05)3 (1.05)4 = ` 5,34,570 Advantages of Certainty Equivalent Method 1. The certainty equivalent method is simple and easy to understand and apply. 2. It can easily be calculated for different risk levels applicable to different cash flows. For example, if in a particular year, a higher risk is associated with the cash flow, it can be easily adjusted and the NPV can be recalculated accordingly. Disadvantages of Certainty Equivalent Method 1. There is no objective or mathematical method to estimate certainty equivalents. Certainty Equivalents are subjective and vary as per each individual’s estimate. 2. Certainty equivalents are decided by the management based on their perception of risk. However, the risk perception of the shareholders who are the money lenders for the project is ignored. Hence, it is not used often in corporate decision making. Risk-adjusted Discount Rate Vs. Certainty-Equivalent Certainty Equivalent Method is superior to Risk Adjusted Discount Rate Method as it does not assume that risk increases with time at constant rate. Each year's Certainty Equivalent Coefficient is based on level of risk impacting its cash flow. Despite its soundness, it is not preferable like Risk Adjusted Discount Rate Method. It is difficult to specify a series of Certainty Equivalent Coefficients but simple to adjust discount rates. 4.3 Other Techniques 4.3.1 Sensitivity Analysis As per CIMA terminology, “Sensitivity Analysis a modelling and risk assessment procedure in which changes are made to significant variables in order to determine the effect of these changes on the planned outcome. Particular attention is thereafter paid to variables identified as being of special significance”. Sensitivity analysis put in simple terms is a modelling technique which is used in Capital Budgeting decisions, to study the impact of changes in the variables on the outcome of the project. In a project, several variables like weighted average cost of capital, consumer demand, price of the product, cost price per unit etc. operate simultaneously. The changes in these variables impact the outcome of the project. Therefore, it becomes very difficult to assess, change in which variable impacts the project outcome in a significant way. In Sensitivity Analysis, the project outcome is studied after taking into account change in only one variable. The more sensitive is the NPV (or IRR), the more critical is that variable. So, Sensitivity analysis is a way of finding impact on the project’s NPV (or IRR) for a given change in one of the variables. © The Institute of Chartered Accountants of India  2.24 3.24 ADVANCED FINANCIAL MANAGEMENT Steps involved in Sensitivity Analysis Sensitivity Analysis is conducted by following the steps as below: 1. Finding variables, which have an influence on the NPV (or IRR) of the project. 2. Establishing mathematical relationship between the variables. 3. Analysing the effect of the change in each of the variables on the NPV (or IRR) of the project. Illustration 9 X Ltd. is considering its new project with the following details: Sr. No. Particulars Figures 1 Initial capital cost ` 400 Cr. 2 Annual unit sales 5 Cr. 3 Selling price per unit ` 100 4 Variable cost per unit ` 50 5 Fixed costs per year ` 50 Cr. 6 Discount Rate 6% Required: 1. Calculate the NPV of the project. 2. Compute the impact on the project’s NPV considering a 2.5 per cent adverse variance in each variable. Which variable is having maximum effect? Consider Life of the project as 3 years. Solution 1. Calculation of Net Cash Inflow per year Particulars Amount (`) A Selling price per unit 100 B Variable cost per unit 50 C Contribution per unit (A - B) 50 D Number of units sold per year 5 Cr. E Total Contribution (C × D) ` 250 Cr. F Fixed cost per year ` 50 Cr. G Net cash inflow per year (E - F) ` 200 Cr. © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.25 2.25 Calculation of Net Present Value (NPV) of the Project Year Year Cash Flow PV factor @ 6% Present Value (PV) (` in Cr.) (` in Cr.) 0 (400.00) 1.000 (400.00) 1 200.00 0.943 188.60 2 200.00 0.890 178.00 3 200.00 0.840 168.00 Net Present Value 134.60 Here, NPV represent the most likely outcomes and not the actual outcomes. The actual outcome can be lower or higher than the expected outcome. 2. Sensitivity Analysis considering 2.5 % Adverse Variance in each variable Particulars Base Initial Selling Variable Fixed Cost Units capital Price per Cost Per Per Unit sold per cost Unit Unit increased year increased Reduced increased to reduced to ` 410 to ` 97.5 to ` 51.25 ` 51.25 to 4.875 crore crore (`) (`) (`) (`) (`) (`) A Selling price per 100 100 97.5 100 100 100 unit B Variable cost per 50 50 50 51.25 50 50 unit C Contribution per unit 50 50 47.5 48.75 50 50 (A - B) (` in Cr.) (` in Cr.) (` in Cr.) (` in Cr.) (` in Cr.) (` in Cr.) D Number of units 5 5 5 5 5 4.875 sold per year (units in Crores) E Total Contribution 250 250 237.5 243.75 250 243.75 (C × D) F Fixed cost per year 50 50 50 50 51.25 50 © The Institute of Chartered Accountants of India  2.26 3.26 ADVANCED FINANCIAL MANAGEMENT G Net Cash Inflow per 200 200 187.5 193.75 198.75 193.75 year (E - F) H PV of Net cash 534.60 534.60 501.19 517.89 531.26 517.89 Inflow per year (G × 2.673) I Initial capital cost 400 410 400 400 400 400 J NPV (H - I) 134.60 124.60 101.19 117.89 131.26 117.89 K Percentage Change - -7.43% -24.82% -12.41% -2.48% -12.41% in NPV The above table shows that by changing one variable at a time by 2.5% (adverse) while keeping the others constant, the impact in percentage terms on the NPV of the project can be calculated. Thus, the change in selling price has the maximum effect on the NPV by 24.82%. Advantages of Sensitivity Analysis: Following are the main advantages of Sensitivity Analysis: (1) Critical Issues: This analysis identifies critical factors that impinge on a project’s success or failure. (2) Simplicity: It is a simple technique. Disadvantage of Sensitivity Analysis Following are the main disadvantages of Sensitivity Analysis: (1) Assumption of Independence: This analysis assumes that all variables are independent i.e. they are not related to each other, which is unlikely in real life. (2) Ignore probability: This analysis does not look to the probability of changes in the variables. 4.3.2 Scenario Analysis Although sensitivity analysis is probably the most widely used risk analysis technique, it does have limitations. Therefore, we need to extend sensitivity analysis to deal with the probability distributions of the inputs. In addition, it would be useful to vary more than one variable at a time so we could see the combined effects of changes in the variables. Scenario analysis provides answer to these situations of extensions. This analysis brings in the probabilities of changes in key variables and also allows us to change more than one variable at a time. This analysis begins with base case or most likely set of values for the input variables. Then, go for worst case scenario (low unit sales, low sale price, high variable cost, etc.) and best case scenario © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.27 2.27 (high unit sales, high sale price, low variable cost, etc.). Alternatively, Scenarios analysis is possible where some factors are changed positively and some factors are changed negatively. So, in a nutshell Scenario analysis examine the risk of investment, to analyse the impact of alternative combinations of variables, on the project’s NPV (or IRR). Illustration 10 XYZ Ltd. is considering a project “A” with an initial outlay of ` 14,00,000 and the possible three cash inflow attached with the project as follows: Particulars Year 1 Year 2 Year 3 Worst case 450 400 700 Most likely 550 450 800 Best case 650 500 900 Assuming the cost of capital as 9%, determine NPV in each scenario. If XYZ Ltd is certain about the most likely result in first two years but uncertain about the third year’s cash flow, analyze what will be the NPV expecting worst scenario in the third year. Solution The possible outcomes will be as follows: Year PVF Worst Case Most likely Best case @ 9% Cash PV Cash PV Cash PV Flow Flow Flow (` ‘000) (` ‘000) (` ‘000) (` ‘000) (` ‘000) (` ‘000) 0 1 (1,400) (1,400) (1,400) (1,400) (1,400) (1,400) 1 0.917 450 412.65 550 504.35 650 596.05 2 0.842 400 336.80 450 378.90 500 421.00 3 0.772 700 540.40 800 617.60 900 694.80 NPV -110.15 100.85 311.85 If XYZ Ltd. is certain about the most likely result in first two years but uncertain about the third year’s cash flow, then, NPV expecting worst case scenario is expected in the third year will be as follows: ` 5,50,000 ` 4,50,000 ` 7,00,000 = − ` 14,00,000 + + + (1+0.09) (1+0.09)2 (1+0.09)3 = − ` 14,00,000 + ` 5,04,587 + ` 3,78,756 + ` 5,40,528 = ` 23,871 © The Institute of Chartered Accountants of India  2.28 3.28 ADVANCED FINANCIAL MANAGEMENT Scenario Analysis Vs Sensitivity Analysis  Sensitivity analysis and Scenario analysis both help to understand the impact of the change in input variable on the outcome of the project. However, there are certain basic differences between the two.  Sensitivity analysis calculates the impact of the change of a single input variable on the outcome of the project viz., NPV or IRR. The sensitivity analysis thus enables to identify that single critical variable which can impact the outcome in a huge way and the range of outcomes of the project given the change in the input variable.  Scenario analysis, on the other hand, is based on a scenario. The scenario may be recession or a boom wherein depending on the scenario, all input variables change. Scenario Analysis calculates the outcome of the project considering this scenario where the variables have changed simultaneously. Similarly, the outcome of the project would also be considered for the normal and recessionary situation. The variability in the outcome under the three different scenarios would help the management to assess the risk a project carries. Higher deviation in the outcome can be assessed as higher risk and lower to medium deviation can be assessed accordingly.  Scenario analysis is far more complex than sensitivity analysis because in scenario analysis all inputs are changed simultaneously, considering the situation in hand while in sensitivity analysis, only one input is changed and others are kept constant. 4.3.3 Simulation Analysis (Monte Carlo) Simulation is the exact replica of the actual situation. To simulate an actual situation, a model shall be prepared. The simulation Analysis is a technique, in which infinite calculations are made to obtain the possible outcomes and probabilities for any given action. Monte Carlo simulation ties together sensitivities and probability distributions. The method came out of the work of first nuclear bomb and was so named because it was based on mathematics of Casino gambling. Fundamental appeal of this analysis is that it provides decision makers with a probability distribution of NPVs rather than a single point estimates of the expected NPV. This analysis starts with carrying out a simulation exercise to model the investment project. It involves identifying the key factors affecting the project and their inter relationships. It involves modelling of cash flows to reveal the key factors influencing both cash receipt and payments and their inter relationship. This analysis specifies a range for a probability distribution of potential outcomes for each of model’s assumptions. 4.3.3.1 Steps for Simulation Analysis: 1. Modelling the project: The model shows the relationship of NPV with parameters and exogenous variables. (Parameters are input variables specified by decision maker and held © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.29 2.29 constant over all simulation runs. Exogenous variables are input variables, which are stochastic in nature and outside the control of the decision maker). 2. Specify values of parameters and probability distributions of exogenous variables. 3. Select a value at random from probability distribution of each of the exogenous variables. 4. Determine NPV corresponding to the randomly generated value of exogenous variables and pre-specified parameter variables. 5. Repeat steps (3) & (4) a large number of times to get a large number of simulated NPVs. 6. Plot probability distribution of NPVs and compute a mean and Standard Deviation of returns to gauge the project’s level of risk. Example: Uncertainty associated with two aspects of the project: Annual Net Cash Flow & Life of the project. NPV model for the project is n ∑ [CFt /(1 + i) t ] - I t =1 Where i Risk free interest rate, I initial investment are parameters, CF = Annual Cash Flow With i = 10%, I = ` 1,30,000, CFt & n stochastic exogenous variables with the following distribution will be as under: Annual Cash Flow Project Life Value (`) Probability Value (Year) Probability 10,000 0.02 3 0.05 15,000 0.03 4 0.10 20,000 0.15 5 0.30 25,000 0.15 6 0.25 30,000 0.30 7 0.15 35,000 0.20 8 0.10 40,000 0.15 9 0.03 10 0.02 Ten manual simulation runs are performed for the project. To perform this operation, values are generated at random for the two exogenous variables viz., Annual Cash Flow and Project Life. For this purpose, we take following steps (1) set up correspondence between values of exogenous variables and random numbers (2) choose some random number generating device. Correspondence between Values of Exogenous Variables and two Digit Random Numbers: © The Institute of Chartered Accountants of India  2.30 3.30 ADVANCED FINANCIAL MANAGEMENT Annual Cash Flow Project Life Value Probability Cumulative Two Value Probability Cumulative Two (`) Probability Digit (Year) Probability Digit Random Random No. No. 10,000 0.02 0.02 00 – 01 3 0.05 0.05 00 – 04 15,000 0.03 0.05 02 – 04 4 0.10 0.15 05 – 14 20,000 0.15 0.20 05 – 19 5 0.30 0.45 15 – 44 25,000 0.15 0.35 20 – 34 6 0.25 0.70 45 – 69 30,000 0.30 0.65 35 – 64 7 0.15 0.85 70 – 84 35,000 0.20 0.85 65 – 84 8 0.10 0.95 85 – 94 40,000 0.15 1.00 85 - 99 9 0.03 0.98 95 – 97 10 0.02 1.00 98 - 99 Random Number 53479 81115 98036 12217 59526 97344 70328 58116 91964 26240 66023 38277 74523 71118 84892 99776 75723 03172 43112 83086 30176 48979 92153 38416 42436 81874 83339 14988 99937 13213 19839 90630 71863 95053 55532 09337 33435 53869 52769 18801 31151 58295 40823 41330 21093 67619 52515 03037 81699 17106 For random numbers, we can begin from any-where taking at random from the table and read any pair of adjacent columns, column/row wise. For the first simulation run we need two digit random numbers (1) For Annual Cash Flow (2) For Project Life. The numbers are 53 & 97 and corresponding value of Annual Cash Flow and Project Life are ` 3,000 and 9 years respectively. Simulation Results Annual Cash Flow Project Life Run Random Corres. Value Random Corres. Value PVAF NPV No. of Annual No. of Project @ 10% (1)x(2) – Cash Flow (1) Life (2) 1,30,000 © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.31 2.31 1 53 30,000 97 9 5.759 42,770 2 66 35,000 99 10 6.145 85,075 3 30 25,000 81 7 4.868 (8,300) 4 19 20,000 09 4 3.170 (66,600) 5 31 25,000 67 6 4.355 (21,125) 6 81 35,000 70 7 4.868 40,380 7 38 30,000 75 7 4.868 16,040 8 48 30,000 83 7 4.868 16,040 9 90 40,000 33 5 3.791 21,640 10 58 30,000 52 6 4.355 650 4.3.3.2. Advantages of Simulation Analysis: Strength lies in Variability. (1) We can predict all type of bad market situation beforehand. (2) Handle problems characterised by: (a) numerous exogenous variables following any kind of distribution. (b) complex inter-relationships among parameters, exogenous variables and endogenous variables. Such problems defy capabilities of analytical methods. (c) compels decision maker to explicitly consider the inter-dependencies and uncertainties featuring the project. 4.3.3.3 Shortcomings (1) Difficult to model the project and specify probability distribution of exogenous variables. (2) Simulation is inherently imprecise. Provides rough approximation of probability distribution of NPV Due to its imprecision, simulation probability distribution may be misleading when a tail of distribution is critical. (3) Realistic simulation model being likely to be complex would probably be constructed by management expert and not by the decision maker. Decision maker lacking understanding of the model may not use it. (4) Determine NPV in simulation run, risk free discount rate is used. It is done to avoid pre- judging risk, which is reflected in the dispersion of the distribution of N.P.V. This derived measure of NPV takes a different meaning from its original value, and, therefore, is difficult to interpret. © The Institute of Chartered Accountants of India  2.32 3.32 ADVANCED FINANCIAL MANAGEMENT 4.3.4. Decision Tree Analysis Till now we have discussed simple accept-or-reject decisions which view current investments in isolation of subsequent decisions. However, practically investment decisions may have implications for future or further investment decisions and may also impact future decision and events. Such situation can be handled by taking a sequence of decisions over a period. The technique to handle this type of sequential decisions is done through “Decision Tree” technique. Basically, decision tree is a graphic display of the relationship between a present decision and future events, future decision, and their consequences. This approach assumes that there are only two types of situations that a finance manager has to face. The first situation is where the manager has control or power to determine what happens next. This is known as “Decision”, as he can do what he desires to do. The second situation is where finance manager has no control over what happens next. This is known as “Event”. Since the outcome of the events is not known, a probability distribution needs to be assigned to the various outcomes or consequences. It should, however, be noted when a finance manager faced with a decision situation, he is assumed to act rationally. For example, in a commercial business, he will choose the most profitable course of action and in non-profit organization, the lowest cost may be rational choice. Steps involved in Decision Tree analysis: Step 1- Define Investment: Decision tree analysis can be applied to a variety of business decision- making scenarios. Normally it includes following types of decisions. Whether or not to launch a new product, if so, whether this launch should be local, national, or international. Whether extra production requirement should be met by extending the factory or by outsourcing it to an external supplier. Whether to dig for oil or not if so, upto what height and continue to dig even after finding no oil upto a certain depth. Step 2- Identification of Decision Alternatives: It is very essential to clearly identity decision alternatives. For example if a company is planning to introduce a new product, it may be local launch, national launch or international launch. Step 3- Drawing a Decision Tree: After identifying decision alternatives, at the relevant data such as the projected cash flows, probability distribution expected present value etc. should be put in diagrammatic form called decision tree. While drawing a decision tree, it should be noted that NPVs etc. should be placed on the branches of decision tree, coming out of the decisions identified. While drawing a decision tree, it should be noted that the:- © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.33 2.33 The decision point (traditionally represented by square) is the option available for manager to take or not to take - in other words action at these points. The event or chance or outcome (traditionally represented by circle) which are dependent on chance process, along with the probabilities thereof, and monetary value associated with them. This diagram is drawn from left to right. Step 4- Evaluating the Alternatives: After drawing out the decision the next step is the evaluation of alternatives. The various alternatives can be evaluated as follows: (i) This procedure is carried out from the last decision in the sequence (extreme right) and goes on working back to the first (left) for each of the possible decision. (ii) At each final stage decision point, select the alternative which has the highest NPV and truncate the other alternatives. Each decision point is assigned a value equal to the NPV of the alternative selected at the decision point. (iii) Proceed backward in the same manner calculating the NPV at chance or event or outcome points ( ) selecting the decisions alternative which has highest NPV at various decision points [ ] rejecting the inferior decision option, assigning NPV to the decision point, till the first decision point is reached. In Capital Budgeting, the decision taker has to identify and find out the various alternatives available to an investment decision. By drawing a decision tree, the alternatives are highlighted through a diagram, giving the range of possible outcomes. The stages set for drawing a decision tree is based on the following rules. 1. It begins with a decision point, also known as decision node, represented by a rectangle while the outcome point, also known as chance node, denoted by a circle. 2. Decision alternatives are shown by a straight line starting from the decision node. 3. The Decision Tree Diagram is drawn from left to right. Rectangles and circles have to be sequentially numbered. 4. Values and Probabilities for each branch are to be incorporated next. The Value of each circle and each rectangle is computed by evaluating from right to left. This procedure is carried out from the last decision in the sequence and goes on working back to the first for each of the possible decisions. The following rules have been set for such evaluation. (a) The expected monetary value (EMV) at the chance node with branches emanating from a circle is the aggregate of the expected values of the various branches that emanate from the chance node. © The Institute of Chartered Accountants of India  2.34 3.34 ADVANCED FINANCIAL MANAGEMENT (b) The expected value at a decision node with branches emanating from a rectangle is the highest amongst the expected values of the various branches that emanate from the decision node. X 1 Decision node 22 Y 2 and 3 Chance node Z 1 X,Y and Z Possible Outcomes 33 Illustration 11 L & R Limited wishes to develop new virus-cleaner software. The cost of the pilot project would be ` 2,40,000. Presently, the chances of the product being successfully launched on a commercial scale are rated at 50%. In case it does succeed. L&R can invest a sum of ` 20 lacs to market the product. Such an effort can generate perpetually, an annual net after tax cash income of ` 4 lacs. Even if the commercial launch fails, they can make an investment of a smaller amount of ` 12 lacs with the hope of gaining perpetually a sum of ` 1 lac. Evaluate the proposal, adopting decision tree approach. The discount rate is 10%. Solution Decision tree diagram is given below: Evaluation At Decision Point C: The choice is between investing ` 20 lacs for a perpetual benefit of ` 4 lacs and not to invest. The preferred choice is to invest, since the capitalized value of benefit of ` 4 lacs (at 10%) adjusted for the investment of ` 20 lacs, yields a net benefit of ` 20 lacs. © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.35 2.35 At Decision Point D: The choice is between investing ` 12 lacs, for a similar perpetual benefit of ` 1 lac. and not to invest. Here the invested amount is greater than capitalized value of benefit at ` 10 lacs. There is a negative benefit of ` 2 lacs. Therefore, it would not be prudent to invest. At Outcome Point B: Evaluation of EMV is as under (` in lacs). Outcome Amount (`) Probability Result (`) Success 20.00 0.50 10.00 Failure 0.00 0.50 00.00 Net result 10.00 EMV at B is, therefore, `10 lacs. At A: Decision is to be taken based on preferences between two alternatives. The first is to test, by investing ` 2,40,000 and reap a benefit of ` 10 lacs. The second is not to test, and thereby losing the opportunity of a possible gain. The preferred choice is, therefore, investing a sum of ` 2,40,000 and undertaking the test. 5. REPLACEMENT DECISION Capital budgeting refers to the process we use to make decisions concerning investments in the long-term assets of the firm. The general idea is that the capital, or long-term funds, raised by the firms are used to invest in assets that will enable the firm to generate revenues several years into the future. Often the funds raised to invest in such assets are not unrestricted, or infinitely available; thus the firm must budget how these funds are invested. Among various capital budgeting decision, Replacement decision is one of the most important classifications of capital budgeting. The replacement decision can be divided into following two types of decisions: 5.1 Replacement of Existing Machine This is a decision concerning whether an existing asset should be replaced by a newer version of the same machine or even a different type of machine that has the same functionality as the existing machine. Such replacements are generally made to maintain existing levels of operations, although profitability might change due to changes in expenses (that is, the new machine might be either more expensive or cheaper to operate than the existing machine). Evaluation of replacement projects is slightly more complicated comparing expansion projects because an existing asset is being replaced. When identifying the cash flows for replacement projects, keep in mind that the cash flows associated with the existing (replaced) asset will no longer exist if the new asset is purchased. Therefore, we must not only determine the cash flows that the new asset will generate, but we must also determine the effect of eliminating the cash flows generated by the replaced asset. For example, if a new asset that will produce cash sales equal to ` 100,000 per year is purchased to replace an existing asset that is generating cash sales equal to ` 75,000, then the incremental, or marginal, cash flow related to sales is ` 25,000. Likewise, if the © The Institute of Chartered Accountants of India  2.36 3.36 ADVANCED FINANCIAL MANAGEMENT asset that is replaced can be sold for ` 350,000, then the purchase price of the new asset effectively is ` 350,000 less than its invoice price. In other words, for replacement decisions, we must determine the overall net effect of purchasing a new asset to replace an existing asset—the cash flows associated with the old asset will be replaced with the cash flows associated with the new asset. Two items that you must remember to include when determining the incremental cash flows are depreciation — not because it is a cash flow, but because it affects cash flows through taxes and taxes — both of which generally change when an older asset is replaced with a newer asset. Therefore analysis of replacement decision follows certain steps: Step I. Net cash outflow (assumed at current time /[Present value of cost]): a. (Book value of old equipment - market value of old equipment) × Tax Rate = Tax payable/ savings from sale b. Cost of new equipment – [Tax payable/savings from sale + market value of old equipment] = Net cash outflow Step II. Estimate change in cash flow per year, if replacement decision is implemented. Change in cash flow = [(Change in sales ± Change in operating costs) – Change in depreciation] (1 – tax rate) + Change in depreciation Step III. Present value of benefits = Present value of yearly cash flows + Present value of estimated salvage of new system Step IV. Net present value = Present value of benefits – Present value of costs Step V. Decision rule. Accept when present value of benefits > present value of costs. Reject when the opposite is true. Illustration 12 A Company named Roby’s cube decided to replace the existing Computer system of their organisation. Original cost of old system was ` 25,000 and it was installed 5 years ago. Current market value of old system is ` 5,000. Depreciation of the old system was charged with life of 10 years with Estimated Salvage value as Nil. Depreciation of the new system will be charged with life over 5 years. Present cost of the new system is ` 50,000. Estimated Salvage value of the new system is ` 1,000. Estimated cost savings with new system is ` 5,000 per year. Increase in sales with new system is assumed at 10% per year based on original total sales of ` 10,00,00. Company follows straight line method of depreciation. Cost of capital of the company is 10% whereas tax rate is 30%. Solution Step I. Net cash outflow (assumed at current time) [Present values of cost]: a. (Book value of old system – market value of old system) × Tax Rate © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.37 2.37 = Tax payable/savings from sale = [(` 25,000 – 5 × ` 2,500) – ` 5,000] × 0.30 = ` 7,500 × 0.30 = ` 2,250 b. Cost of new system – [Tax payable/savings from sale + Market value of old system] = Net cash outflow Or, ` 50,000 – [` 2,250 + ` 5,000] = `42,750 Step II. Estimated change in cash flows per year if replacement decision is implemented. Change in cash flow = [(Change in sales ± Change in operating costs)-Change in depreciation)] (1- tax rate) + Change in depreciation = [` 1,00,000 × 0.1 + ` 5,000 – (` 49,000/5 – ` 25,000/10)] (1-0.30) + (` 49,000/5 – ` 25000/10)] = ` 12,690 Step III. Present value of benefits = Present value of yearly cash flows + Present value of estimated salvage of new system = ` 12,690 × PVIFA (10%, 5) + ` 1,000 × PVIF (10%, 5) = ` 48,723 Step IV. Net present value = Present value of benefits - Present value of costs = ` 48,723 – ` 42,750 = ` 5,973 Step V. Decision rule: Since NPV is positive we should accept the proposal to replace the machine. 5.2 Optimum Replacement Cycle Case discussed above is a simple example replacement decision based on NPV. This decision was based on assumption that the projects do not form part of continuous replacement cycle. However, sometimes, project may involve continuous replacement cycle. In such cases NPV decision rules needs modification. To determine optimal replacement cycle, concept of Equivalent Annual Cost (EAC), discussed at Intermediate (IPC) Level is used. The formula to compute EAC is as follows: PV of Cash Outflow PVAF This decision is based on assumption that as the machine (asset) becomes older its efficiency decreases and leading to increase in operating cost and reduction in resale value. © The Institute of Chartered Accountants of India  2.38 3.38 ADVANCED FINANCIAL MANAGEMENT Illustration 13 X Ltd. is a taxi operator. Each taxi cost to company ` 4,00,000 and has a useful life of 3 years. The taxi’s operating cost for each of 3 years and salvage value at the end of year is as follows: Year 1 Year 2 Year 3 Operating Cost ` 1,80,000 ` 2,10,000 ` 2,38,000 Resale Value ` 2,80,000 ` 2,30,000 ` 1,68,000 You are required to determine the optimal replacement period of taxi if cost of capital of X Ltd. is 10%. Solution NPV if taxi is kept for 1 Year = – ` 4,00,000 - ` 1,80,000 (0.909) + ` 2,80,000 (0.909) = – ` 3,09,100 NPV if taxi is kept for 2 Year = – ` 4,00,000 – ` 1,80,000 x 0.909 + ` 20,000 x 0.826 = – ` 5,47,100 NPV if taxi is kept for 3 Year = – ` 4,00,000 – ` 1,80,000 x 0.909 – ` 2,10,000 x 0.826 – ` 70,000 x 0.751 = – ` 7,89,650 Since above NPV figures relate to different periods, there are not comparable. to make them comparable we shall use concept of EAC as follows: EAC of 1 year 3,09,100 = ` 3,40,044 0.909 EAC of 2 year 5,47,100 = ` 3,15,331 1.735 EAC of 3 year 7,89,650 = ` 3,17,639 2.486 Since lowest EAC incur if taxi for 2 year; Hence the optimum replacement cycle to replace taxi in 2 years. © The Institute of Chartered Accountants of India  ADVANCED CAPITAL BUDGETING DECISIONS 3.39 2.39 6. ADJUSTED PRESENT VALUE As we are well aware that to evaluate a capital project we discount the expected cash flows by overall Cost of Capital i.e. WACC. Further, as discussed earlier to incorporate risk in the evaluation of any project we can adjust the same discount rate. However instead of adjusting the cost of capital we can use an alternative approach called Adjusted Present Value (APV) Method. This approach separates the investment decision and financing decision. Following formula is used to evaluate a project as per this appr