Chapter 1 Discounted Cash Flow Techniques
ACCA P4
Advanced Financial Management
Education Class 1
Session 1 & 2
Chapter 1
Patrick Lui
hklui2007@.hk
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Chapter 1 Discounted Cash Flow Techniques
|LEARNING OBJECTIVES |
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|1. Evaluate the potential valued added to an organization arising from a specified capital investment project or portfolio using the |
|NPV model. Project modeling should include explicit treatment of: |
|a. Inflation and specific price variation |
|b. Taxation including capital allowances and tax exhaustion |
|c. Single period capital rationing and multi-period capital rationing. Multi-period capital rationing to include the formulation of |
|programming methods and the interpretation of their output. |
|d. Probability analysis and sensitivity analysis when adjusting fro risk and uncertainty in investment appraisal |
|e. Risk adjusted discount rates |
|2. Outline the application of Monte Carlo simulation to investment appraisal. |
|3. Establish the potential economic return (using IRR and MIRR) and advise on a project’s return margin. |
[pic]
1. Net Present Value with Inflation and Taxation
1.1 NPV and shareholder wealth maximization
1.1.1 All acceptable investment project should have positive NPV.
1.1.2 The market value of the company, theoretically at least, increases by the amount of the NPV.
1.1.3 The share price of the company should theoretically increase as well.
1.1.4 Objective of maximizing the wealth of shareholders is usually substituted by the objective of maximizing the share price of a company.
1.2 The effect of inflation
1.2.1 It is important to adapt investment appraisal methods to cope with the phenomenon of price movement. Future rates of inflation are unlikely to be precisely forecasted; nevertheless, we will assume in the analysis that follows that we can anticipate inflation with reasonable accuracy.
1.2.2 Two types of inflation can be distinguished.
(a) Specific inflation refers to the price changes of an individual good or service.
(b) General inflation is the reduced purchasing power of money and is measured by an overall price index which follows the price changes of a ‘basket’ of goods and services through time.
Even if there was no general inflation, specific items and sectors might experience price rises.
[pic]
1.2.3 Inflation creates two problems for project appraisal.
(a) The estimation of future cash flows is made more troublesome. The project appraiser will have to estimate the degree to which future cash flows will be inflated.
(b) The rate of return required by the firm’s security holders, such as shareholders, will rise if inflation rises. Thus, inflation has an impact on the discount rate used in investment evaluation.
1.3 Real and money interest rate
1.3.1 The money (nominal or market) interest rate incorporates inflation. When the nominal rate of interest is higher than the rate of inflation, there is a positive real rate. When the rate of inflation is higher than the nominal rate of interest, the real rate of interest will be negative.
|1.3.2 |Fisher’s (1930) Equation (Dec 08) |
| |The generalized relationship between real rates of interest and nominal rate of interest is expressed as follow under |
| |Fisher’s equation: |
| | |
| |(1 + i) = (1 + r) (1 + h) |
| | |
| |Where h = inflation rate |
| |r = real interest rate |
| |i = nominal interest rate |
|Example 1 |
|$1,000 is invested in an account that pays 10% interest pa. Inflation is currently 7% pa. Find the real return on the investment. |
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|Solution: |
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|Real return = $1,000 × 1.1/1.07 = $1.028. A return of 2.8%. |
1.3.3 Real rate or nominal rate? The rule is as follows:
(a) We use the nominal rate if cash flows are expressed in actual numbers of dollars that will be received or paid at various future rates.
(b) We use the real rate if cash flows are expressed in constant price terms.
1.4 Allowing for taxation
1.4.1 In investment appraisal, tax is often assumed to be payable one year in arrears, but you should read the question details carefully.
1.4.2 Typical assumptions which may be stated in questions are as follows.
(a) An assumption about the timing of payments will have to be made.
(i) Half the tax is payable in the same year in which the profits are earned and half in the following year.
(ii) Tax is payable in the year following the one in which the taxable profits are made. Thus, if a project increase taxable profits by $10,000 in year 2, there will be a tax payment, assuming tax at (say) 30%, of $3,000 in year 3.
(iii) Tax is payable in the same year that the profits arise.
(b) Net cash flows from a project should be considered as the taxable profits arising from the project.
1.5 Capital allowances (tax-allowable depreciation, or writing down allowances (WDAs) or depreciation allowances)
1.5.1 Capital allowance is used to reduce taxable profits, and the consequent reduction in a tax payment should be treated as a cash saving from the acceptance of a project.
1.5.2 There are two assumptions about the time when capital allowance start to be claim.
(a) It can be assumed that the first claim occurs at the start of the project (at year 0).
(b) Alternatively it can be assumed that the first claim occurs later in the first year.
|Question 1 |
|A company is considering whether or not to purchase an item of machinery costing $40,000 in 2015. It would have a life of four years, |
|after which it would be sold for $5,000. The machinery would create annual cost savings of $14,000. |
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|The machinery would attract tax-allowable depreciation of 25% on the reducing balance basis which could be claimed against taxable |
|profits of the current year, which is soon to end. A balancing allowance or charge would arise on disposal. The tax rate is 30%. Tax |
|is payable half in the current year, half one year in arrears. The after-tax cost of capital is 8%. |
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|Tax-allowable depreciation is first claimed against year 0 profits. |
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|Should the machinery be purchased? |
|Solution: |
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1.6 Tax exhaustion
1.6.1 In most tax systems, capital expenditure is set off against tax liabilities so as to reduce the taxes a company pays and to encourage investment.
1.6.2 The effect of capital allowances can be from the definition of after-tax earnings
After-tax earnings = Earnings before tax – tax liability
Where tax liability = Tax rate × (Earnings before tax – capital allowances)
1.6.2 There will be circumstances when the capital allowances in a particular year will equal or exceed before tax earnings. In such a case the company will pay no tax.
1.6.3 In most tax systems unused capital allowances can be carried forward indefinitely, so that the capital allowance that is set off against the tax liability in any one year includes not only the writing down allowance for the particular year but also any unused allowances from previous years.
|Question 2 |
|Suppose that a company has invested $10 million in a plant. The first year allowance is 40 percent, whereas the remaining amount is |
|written down over a period of four years. The tax rate is 30 percent. Earnings before tax over a five year period are as follows: |
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|Year 1 |
|Year 2 |
|Year 3 |
|Year 4 |
|Year 5 |
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|$m |
|$m |
|$m |
|$m |
|$m |
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|3 |
|2.5 |
|3.5 |
|3.8 |
|4.2 |
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|(a) Calculate the tax liability every year and the after-tax earnings. |
|(b) Calculate the impact on earnings if the first year allowance is 60 percent. |
|Solution: |
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2. Capital Rationing
2.1 Meaning of capital rationing
2.1.1 In order to invest in all projects with a positive NPV a company must be able to raise funds as and when it needs them: this is only possible in a perfect capital market.
2.1.2 In practice capital markets are not perfect and the capital available for investment is likely to be limited or rationed. The causes of capital rationing may be external (hard capital rationing) or internal (soft capital rationing).
2.2 Soft and hard capital rationing
2.2.1 Capital rationing occurs when funds are not available to finance all wealth-enhancing projects. There are two types of capital rationing:
(a) Soft capital rationing – is internal management-imposed limits on investment expenditure. Such limits may be linked to the firm’s financial control policy.
(b) Hard capital rationing – relates to capital from external sources. Agencies (e.g. shareholders and bank) external to the firm will not supply unlimited amounts of investment capital, even though positive NPV projects are identified.
2.2.2 Soft capital rationing may arise for one of the following reasons.
(a) Management may be reluctant to issue additional share capital because of concern that this may lead to outsiders gaining control of the business.
(b) Management may be unwilling to issue additional share capital if it will lead to a dilution of earnings per share.
(c) Management may not want to raise additional debt capital because they do not wish to be committed to large fixed interest payments.
(d) Management may wish to limit investment to a level that can be financed solely from retained earnings.
(e) Capital expenditure budgets may restrict spending.
(f) Managers may prefer slower organic growth in order to remain in control of the growth process and so avoid rapid growth.
(g) Managers may want to make capital investments compete for funds in order to week out weaker or marginal projects.
2.2.3 Hard capital rationing may arise for one of the following reasons.
(a) Raising money through the stock market may not be possible if share prices are depressed.
(b) There may be restrictions on bank lending due to government control.
(c) Lending institutions may consider an organization to be too risky to be granted further loan facilities.
(d) The costs associated with making small issues of capital may be too great.
2.3 Relaxation of capital constraints
2.3.1 If an organization adopts a policy that restricts funds available for investment (soft capital rationing), the policy may be less than optimal. The organization may reject projects with a positive NPV and forgo opportunities that would have enhanced the market value of the organization.
2.3.2 A company may be able to limit the effects of hard capital rationing and exploit new opportunities.
(a) It may seek joint venture partners with which to share projects.
(b) As an alternative to direct investment in a project, the company may be able to consider a licensing or franchising agreement with another enterprise, under which the licensor/franchisor company would receive royalties.
(c) It may be possible to contract out parts of a project to reduce the initial capital outlay required.
(d) The company may seek new alternative sources of capital, for example:
(i) Venture capital
(ii) Debt finance secured on the assets of the project
(iii) Sale and leaseback of property or equipment
(iv) Grant aid
(v) More effective capital management
2.4 Single period capital rationing
(Jun 09)
2.4.1 The simplest and most straightforward form of rationing occurs when limits are placed on finance availability for only one year.
2.4.2 There are two possibilities with this single-period rationing situation.
(a) Divisible projects – The nature of the proposed projects is such that it is possible to undertake a fraction of a total project. For instance, if a project is established to expand a retail shop by opening a further 100 shops, it would be possible to take only 30% (that is 30 shops) or any other fraction of the overall project.
(b) Indivisible projects – with some projects it is impossible to take a fraction. The choice is between undertaking the whole of the investment or none of it (for instance, a project to build a ship, or a bridge or an oil platform).
2.4.3 When capital rationing occurs in a single period, projects are ranked in terms of profitability index.
|2.4.4 |Profitability Index (PI) |
| |Profitability index is the ratio of the PV of the project’s future cash flows (not including the capital investment) |
| |divided by the present value of the total capital investment. |
| | |
| |PI = |
| |PV of future cash flows |
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| |Initial investment |
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|Example 2 |
|Suppose that ABC Co is considering four projects, W, X, Y and Z. Relevant details are as follows. |
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|Project |
|Investment required |
|PV of cash inflows |
|NPV |
|PI |
|Ranking as per NPV |
|Ranking as per PI |
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|$ |
|$ |
|$ |
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|W |
|(10,000) |
|11,240 |
|1,240 |
|1.12 |
|3 |
|1 |
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|X |
|(20,000) |
|20,991 |
|991 |
|1.05 |
|4 |
|4 |
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|Y |
|(30,000) |
|32,230 |
|2,230 |
|1.07 |
|2 |
|3 |
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|Z |
|(40,000) |
|43,801 |
|3,801 |
|1.10 |
|1 |
|2 |
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|Without capital rationing all four projects would be viable investments. Suppose, however, that only $60,000 was available for capital |
|investment. Let us look at the resulting NPV if we select projects in the order of ranking per NPV. |
|By NPV: |
|Project |
|Priority |
|Outlay |
|NPV |
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|Z |
|1st |
|40,000 |
|3,801 |
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|Y (balance)* |
|2nd |
|20,000 |
|1,487 |
|(2/3 of $2,230) |
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|60,000 |
|5,288 |
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|By PI: |
|Project |
|Priority |
|Outlay |
|NPV |
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|W |
|1st |
|10,000 |
|1,240 |
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|Z |
|2nd |
|40,000 |
|3,801 |
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|Y |
|3rd |
|10,000 |
|743 |
|(1/3 of $2,230) |
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|60,000 |
|5,784 |
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|* Projects are divisible. By spending the balancing $20,000 on project Y, two thirds of the full investment would be made to earn two |
|thirds of the NPV. |
2.5 Single period rationing with non-divisible projects
2.5.1 If the projects are not divisible then the method shown above may not result in the optimal solution. Another complication which arises is that there is likely to be a small amount of unused capital with each combination of projects. The best way to deal with this situation is to use trial and error and test the NPV available from different combinations of projects. This can be a laborious process if there are a large number of projects available.
|Example 3 |
|ABC Co has capital of $95,000 available for investment in the forthcoming period. The directors decide to consider projects P, Q and R |
|only. They wish to invest only in whole projects, but surplus can be invested. Which combination of projects will produce the highest |
|NPV at a cost of capital of 20%? |
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|Project |
|Investment required |
|PV of inflows at 20% |
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|$000 |
|$000 |
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|P |
|40 |
|56.5 |
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|Q |
|50 |
|67.0 |
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|R |
|30 |
|48.8 |
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|Solution: |
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|The investment combinations we need to consider are the various possible pairs of projects P, Q and R. |
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|Projects |
|Required investment |
|PV of inflows |
|NPV from projects |
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|$000 |
|$000 |
|$000 |
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|P and Q |
|90 |
|123.5 |
|33.5 |
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|P and R |
|70 |
|105.3 |
|35.3 |
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|Q and R |
|80 |
|115.8 |
|35.8 |
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|The highest NPV will be achieved by undertaking projects Q and R and investing the unused funds of $15,000 externally. |
2.6 Multi-period capital rationing
(Dec 12)
2.6.1 A situation where there is a shortage of funds in more than one period is known as multi-period capital rationing. This makes the analysis more complicated because we have multiple limitations and multiple outputs. In such a situation we must employ a linear programming model to identify the profit maximizing mix of investments.
2.6.2 In the exam you will not be expected to produce a solution to a linear programming problem. However, you need to know how to formulate the model and explain the results of the model.
|Example 4 |
|The board of ABC Inc has approved the following investment expenditure over the next three years. |
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|Year 1 |
|Year 2 |
|Year 3 |
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|$16,000 |
|$14,000 |
|$17,000 |
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|You have identified four investment opportunities which require different amounts of investment each year, details of which are given |
|below. |
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|Required investment |
|Project NPV |
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|Project |
|Year 1 |
|Year 2 |
|Year 3 |
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|Project 1 |
|7,000 |
|10,000 |
|4,000 |
|8,000 |
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|Project 2 |
|9,000 |
|0 |
|12,000 |
|11,000 |
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|Project 3 |
|0 |
|6,000 |
|8,000 |
|6,000 |
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|Project 4 |
|5,000 |
|6,000 |
|7,000 |
|4,000 |
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|Which combination of projects will result in the highest overall NPV whilst remaining within the annual investment constraints? |
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|The problem can be formulated as a linear programming problem as follows. |
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|Let Y1 be investment in project 1 |
|Y2 be investment in project 2 |
|Y3 be investment in project 3 |
|Y4 be investment in project 4 |
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|Objective function |
|Maximise Y1 × 8,000 + Y2 × 11,000 + Y3 × 6,000 + Y4 × 4,000 |
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|Subject to the three annual investment constraints : |
|Y1 × 7,000 + Y2 × 9,000 + Y3 × 0 + Y4 × 5,000 ≦ 16,000 (Year 1 constraint) |
|Y1 × 10,000 + Y2 × 0 + Y3 × 6,000 + Y4 × 6,000 ≦ 14,000 (Year 2 constraint) |
|Y1 × 4,000 + Y2 × 12,000 + Y3 × 8,000 + Y4 × 7,000 ≦ 17,000 (Year 3 constraint) |
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|When the objective function and constraints are fed into a computer programme, the results are: |
|Y1 = 1, Y2 = 1, Y3 = 0, Y4 = 0 |
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|This means that Project 1 and Project 2 will be selected and Project 3 and Project 4 will not. The NPV of the investment scheme will be|
|equal to $19,000. |
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|Note that the solution: |
|Y1 = 0, Y2 = 0, Y3 = 1, Y4 = 1 |
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|also satisfies the constraints. However this is not the optimal solution since the combined NPV of projects 3 and 4 is $10,000 which is|
|lower than the value derived above. |
3. Risk and Uncertainty
3.1 Meaning of risk and uncertainty
3.1.1 Investment appraisal faces the following problems:
(a) all decisions are based on forecasts;
(b) all forecasts are subject to uncertainty;
(c) this uncertainty needs to be reflected in the financial evaluation.
3.1.2 The decision maker must distinguish between:
(a) Risk – can be quantifiable and be applied to a situation where there are several possible outcomes and, on the basis of past relevant experience, probabilities can be assigned to the various outcomes that could prevail.
(b) Uncertainty – is unquantifiable and can be applied to a situation where there are several possible outcomes but there is little past experience to enable the probability of the possible outcomes to be predicted.
3.1.3 If risk and uncertainty were not considered, managers might make mistake of placing too much confidence in the results of investment appraisal, or they may fail to monitor investment projects in order to ensure that expected results are in fact being achieved.
3.1.4 Assessment of project risk can also indicate projects that might be rejected as being too risky compared with existing business operations, or projects that might be worthy of reconsideration if ways of reducing project risk could be found in order to make project outcomes more acceptable.
3.2 Probability and expected value (EV)
(Dec 14)
3.2.1 This approach involves assigning probabilities to each outcome of an investment project, or assigning probabilities to different values of project variables.
3.2.2 The range of NPVs that can result from an investment project is then calculated, together with the joint probability of each outcome. The NPVs and their joint probabilities can be used to calculate the mean or average NPV (the expected NPV or ENPV) which could arise if the investment project could be repeated a large number of times.
3.2.3 Other useful information that could be provided by the probability analysis includes the worst outcome, the best outcome and the most likely outcome. Managers could then make a decision on the investment that took account more explicitly of its risk profile.
|3.2.4 |Expected value |
| |The EV is the weighted average of all possible outcomes, with the weightings based on the probability estimates. |
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| |The formula for calculating an EV is: |
| |EV = [pic] |
| |Where: p = the probability of an outcome |
| |x = the value of an outcome |
3.3 Sensitivity analysis
(Jun 09, Dec 12)
3.3.1 It assesses the sensitivity of project NPV to changes in project variables.
3.3.2 It calculates the relative change in a project variable required to make the NPV zero, or the relative change in NPV for a fixed change in a project variable. For example, what if demand fell by 10% compared to our original forecasts? Would the project still be viable?
3.3.3 Only one variable is considered at a time.
3.3.4 These show where assumptions may need to be checked and where managers could focus their attention in order to increase the likelihood that the project will deliver its calculated benefits.
3.3.5 However, since sensitivity analysis does not incorporate probabilities, it cannot be described as a way of incorporating risk into investment appraisal, although it is often described as such.
|3.3.6 |Decision rule |
| |(a) A simple approach to deciding which variables the NPV is particularly sensitive is to, the following formula can be |
| |applied: |
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| |Sensitivity |
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| |NPV |
| |% |
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| |PV of project variable |
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| |(b) The lower the percentage, the more sensitive is NPV to that project variable as the variable would need to change by a|
| |smaller amount to make the project non-viable. |
|Example 5 |
|ABC Co is considering a project with the following cash flows. |
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|Year |
|Initial investment |
|($000) |
|Variable costs |
|($000) |
|Cash inflows |
|($000) |
|Net cash flows |
|($000) |
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|0 |
|7,000 |
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|1 |
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|(2,000) |
|6,500 |
|4,500 |
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|2 |
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|(2,000) |
|6,500 |
|4,500 |
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|Cash flows arise from selling 650,000 units at $10 per unit. ABC Co has a cost of capital of 8%. |
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|Required: |
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|Measure the sensitivity of the project to changes in variables. |
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|Solution: |
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|The PVs of the cash flow are as follows. |
|Year |
|Discount factor 8% |
|PV of initial investment |
|PV of variable costs |
|PV of cash inflows |
|PV of net cash flow |
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|$000 |
|$000 |
|$000 |
|$000 |
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|0 |
|1.000 |
|(7,000) |
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|(7,000) |
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|1 |
|0.926 |
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|(1,852) |
|6,019 |
|4,167 |
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|2 |
|0.857 |
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|(1,714) |
|5,571 |
|3,857 |
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|(7,000) |
|(3,566) |
|11,590 |
|1,024 |
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|NPV = 1,024 |
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|The project has a positive NPV and would appear to be worthwhile. The sensitivity of each project variable is as follows. |
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|(a) Initial investment |
|Sensitivity = 1,024 / 7,000 × 100% = 14.6% |
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|(b) Sales volume |
|Sensitivity = 1,024 / (11,590 – 3,566) × 100% = 12.8% |
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|(c) Selling price |
|Sensitivity = 1,024 / 11,590 × 100% = 8.8% |
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|(d) Variable costs |
|Sensitivity = 1,024 / 3,566 × 100% = 28.7% |
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|(e) Cost of capital. We need to calculate the IRR of the project. |
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|Year |
|Net cash flow |
|Discount factor 15% |
|PV |
|Discount factor 20% |
|PV |
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|$000 |
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|$000 |
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|$000 |
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|0 |
|(7,000) |
|1 |
|(7,000) |
|1 |
|(7,000) |
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|1 |
|4,500 |
|0.870 |
|3,915 |
|0.833 |
|3,749 |
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|2 |
|4,500 |
|0.756 |
|3,402 |
|0.694 |
|3,123 |
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|317 |
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|(128) |
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|IRR = 0.15 + [pic] = 18.56% |
|The cost of capital can therefore increase by 132% before the NPV becomes negative. |
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|The elements to which the NPV appears to be most sensitive are the selling price followed by the sales volume. Management should thus |
|pay particular attention to these factors so that they can be carefully monitored. |
3.4 Duration (Macauley duration)
(Jun 09, Jun 11, Pilot 13, Jun 14)
3.4.1 Duration measures the average time to recover the present value of the project (if cash flows are discounted at the cost of capital).
3.4.2 Projects with higher durations carry more risk than projects with lower durations.
|Example 6 – Macauley duration |
|A project with the following cash flows is under consideration: |
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|Year 0 |
|Year 1 |
|Year 2 |
|Year 3 |
|Year 4 |
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|$000 |
|$000 |
|$000 |
|$000 |
|$000 |
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|(20,000) |
|8,000 |
|12,000 |
|4,000 |
|2,000 |
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|Cost of capital is 8%. |
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|Required: |
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|Calculate the project’s Macauley duration. |
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|Solution: |
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|The Macauley duration is calculated by first calculating the discounted cash flow for each future year, and then weighting each |
|discounted cash flow according to its time of receipt, as follows: |
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|Year 1 |
|Year 2 |
|Year 3 |
|Year 4 |
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|$000 |
|$000 |
|$000 |
|$000 |
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|Cash flow |
|8,000 |
|12,000 |
|4,000 |
|2,000 |
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|DF @ 8% |
|0.926 |
|0.857 |
|0.794 |
|0.735 |
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|PV |
|7,408 |
|10,284 |
|3,176 |
|1,470 |
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|× 1 |
|× 2 |
|× 3 |
|× 4 |
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|PV × Year |
|7,408 |
|20,568 |
|9,528 |
|5,880 |
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|Next, the sum of the (PV × Year) figures is found, and divided by the present value of these “return phase” cash flows. |
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|Sum of (PV × Year) figures = 7,408 + 20,568 + 9,528 + 5,880 = 43,384 |
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|PV of return phase cash flows = 7,408 + 10,284 + 3,176 + 1,470 = 22,338 |
| |
|Hence, the Macauley duration = 43,384 ÷ 22,338 = 1.94 years. |
|Question 3 |
|A project with the following cash flows is under consideration: |
| |
|Year |
|0 |
|1 |
|2 |
|3 |
|4 |
|5 |
|6 |
| |
| |
|$m |
|$m |
|$m |
|$m |
|$m |
|$m |
|$m |
| |
|Net cash flow |
|(127) |
|(37) |
|52 |
|76 |
|69 |
|44 |
|29 |
| |
| |
|Cost of capital is 10%. |
| |
|Required: |
| |
|Calculate the project’s Macauley duration. |
|Solution: |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|Question 4 |
|Arbore Co is a large listed company with many autonomous departments operating as investment centres. It sets investment limits for |
|each department based on a three-year cycle. Projects selected by departments would have to fall within the investment limits set for |
|each of the three years. All departments would be required to maintain a capital investment monitoring system, and report on their |
|findings annually to Arbore Co’s board of directors. |
| |
|The Durvo department is considering the following five investment projects with three years of initial investment expenditure, |
|followed by several years of positive cash inflows. The department’s initial investment expenditure limits are $9,000,000, $6,000,000 |
|and $5,000,000 for years one, two and three respectively. None of the projects can be deferred and all projects can be scaled down but|
|not scaled up. |
| |
| |
|Investment required at start of year |
| |
| |
|Project |
|Year one |
|Year two |
|Year three |
|Project NPV |
| |
| |
|(Immediately) |
| |
| |
| |
| |
| |
|$ |
|$ |
|$ |
|$ |
| |
|PDur01 |
|4,000,000 |
|1,100,000 |
|2,400,000 |
|464,000 |
| |
|PDur02 |
|800,000 |
|2,800,000 |
|3,200,000 |
|244,000 |
| |
|PDur03 |
|3,200,000 |
|3,562,000 |
|0 |
|352,000 |
| |
|PDur04 |
|3,900,000 |
|0 |
|200,000 |
|320,000 |
| |
|PDur05 |
|2,500,000 |
|1,200,000 |
|1,400,000 |
|Not provided |
| |
| |
|PDur05 project’s annual operating cash flows commence at the end of year four and last for a period of 15 years. The project generates|
|annual sales of 300,000 units at a selling price of $14 per unit and incurs total annual relevant costs of $3,230,000. Although the |
|costs and units sold of the project can be predicted with a fair degree of certainty, there is considerable uncertainty about the unit|
|selling price. The department uses a required rate of return of 11% for its projects, and inflation can be ignored. |
| |
|The Durvo department’s managing director is of the opinion that all projects which return a positive net present value should be |
|accepted and does not understand the reason(s) why Arbore Co imposes capital rationing on its departments. Furthermore, she is not |
|sure why maintaining a capital investment monitoring system would be beneficial to the company. |
| |
|Required: |
| |
|(a) Calculate the net present value of project PDur05. Calculate and comment on what percentage fall in the selling price would need |
|to occur before the net present value falls to zero. (6 marks) |
|(b) Formulate an appropriate capital rationing model, based on the above investment limits, that maximises the net present value for |
|department Durvo. Finding a solution for the model is not required. (3 marks) |
|(c) Assume the following output is produced when the capital rationing model in part (b) above is solved: |
| |
|Category 1: Total Final Value |
|$1,184,409 |
| |
|Category 2: Adjustable Final Values |
|Project PDur01: 0·958 |
|Project PDur02: 0·407 |
|Project PDur03: 0·732 |
|Project PDur04: 0·000 |
|Project PDur05: 1·000 |
| |
|Category 3: Adjustable Final Values |
|Constraints Utilised |
|Slack |
| |
|Year one: $9,000,000 |
|Year one: $0 |
| |
|Year two: $6,000,000 |
|Year two: $0 |
| |
|Year three: $5,000,000 |
|Year three: $0 |
| |
| |
|Required: |
| |
|Explain the figures produced in each of the three output categories. (5 marks) |
| |
|(d) Provide a brief response to the managing director’s opinions by: |
|(i) Explaining why Arbore Co may want to impose capital rationing on its departments; (2 marks) |
|(ii) Explaining the features of a capital investment monitoring system and discussing the benefits of maintaining such a system. (4 |
|marks) |
|(20 marks) |
|(ACCA P4 Advanced Financial Management December 2012 Q4) |
4. Monte Carlo Simulation
(Jun 10)
4.1 The main problem with sensitivity analysis is that it only allows us to assess the impact of one variable changing at a time. Simulation addresses this problem by considering how the NPV will be impacted by a number of variables changing at once.
4.2 Simulation employs random numbers to select specimen values for each variable in order to estimate a ‘trial value’ for the project NPV. This is repeated a large number of times until a distribution of NPVs emerge.
4.3 By analysing this distribution, the firm can decide whether to proceed with the project. For example, if 95% of the generated NPVs are positive, this might reassure the firm that the chances of suffering a negative NPV are small.
|Example 7 – Monte Carlo simulation |
|A business is choosing between two projects, project A and project B. It uses simulation to generate a distribution of profits for each|
|project. |
| |
|[pic] |
| |
|Required: |
| |
|Which project should the business invest in? |
| |
|Solution: |
| |
| |
|Project A has a lower average profit but is also less risky (less variability of possible profits). |
| |
|Project B has a higher average profit but is also more risky (more variability of possible profits). |
| |
|There is no correct answer. All simulation will do is to give the business the above results. It will not tell the business which is |
|the better project. |
| |
|If the business is willing to take on risk, they may prefer project B since it has the higher average return. |
| |
|However, if the business would prefer to minimize its exposure to risk it would take on project A. This has a lower risk but also a |
|lower average return. |
5. Value at Risk (VaR)
(Jun 12, Dec 14)
5.1 VaR can be defined as the maximum amount that it may lose at a given level of confidence.
5.2 For example, we may say that the VaR is $100,000 at 5% probability, or that it is $100,000 at 95% confidence level. The first definition implies that there is a 5% chance that the loss will exceed $100,000, or that we are 95% sure that it will not exceed $100,000.
5.3 VaR can be defined at any level of probability or confidence, but the most common probability levels are 1% and 5%.
|5.4 |Calculate of VaR |
| |When the random variable follows the normal distribution, the value at risk at specific probability levels is easily |
| |calculated as a multiple of the standard deviation. |
| | |
| |VaR for single period = K × σ |
| | |
| |Where: K is the confidence level |
| |For 10% confidence level, K = 1.282 |
| |For 5% confidence level, K = 1.645 |
| |For 1% confidence level, K = 2.33 |
| |σ is the standard deviation of a project |
| | |
| |VaR for multi-period = K × σ × [pic] |
| | |
| |Where: N is the periods over which we want to calculate the value at risk. |
|Example 8 – VaR |
|The annual cash flows from a project are expected to follow the normal distribution with a mean of $50,000 and standard deviation of |
|$10,000. The project has a 10 year life. What is the project value at risk? |
| |
|Solution: |
| |
|The project value at risk for a year is: |
|= 1.645 × $10,000 = $16,450 |
| |
|The project value at risk that takes into account the entire project life is: |
|= 1.645 × $10,000 × [pic] = $52,019 |
| |
|The figures mean that the company can be 95% confident that the cash flows will not fall by more than $16,450 in any one year and |
|$52,019 in total over 10 years from the average returns. |
6. Internal Rate of Return
(Jun 12, Dec 14)
6.1 IRR is defined as the discount rate at which the NPV equals zero. In other words, the IRR represents the breakeven discount rate for the investment.
6.2 Decision rule:
➢ IRR > cost of capital, project accepts
➢ The higher IRR is the better
6.3 Steps in calculating the IRR using linear interpolation:
1. Calculate two NPV at two different discount rates. One must be positive and another one must be negative.
2. Using the following formula to find the IRR
IRR = L + [pic]
where:
L = Lower rate of interest
H = Higher rate of interest
NL = NPV at lower rate of interest
NH = NPV at higher rate of interest
6.4 Advantages and disadvantages of IRR
|Advantages |Disadvantages |
|Considers the time value of money |It is not a measure of absolute increase in company value. |
|Is a percentage and therefore easily understood |Interpolation only provides an estimate and an accurate |
|Uses cash flows not profits |estimate requires the use of a spreadsheet program |
|Considers the whole life of the project |It is fairly complicated to calculate |
|Means a firm selecting projects where the IRR exceeds the |Non-conventional cash flows may give rise to multiple IRRs |
|cost of capital should increase shareholders’ wealth. |Can offer conflicting advice between IRR and NPV in the |
| |evaluation of mutually exclusive projects |
| |Assume cash inflows being reinvested at the IRR rate, this is|
| |unrealistic when IRR is high. |
6.5 IRR give a conflicting result when compared to NPV
(a) Non-conventional cash flows
(i) The project has conventional cash flows, i.e. an initial cash outflow followed by a series of inflows.
(ii) When flows vary from this they are termed non-conventional.
(b) Mutually exclusive projects:
(i) This is a situation when only one project can be chosen among two or more investment choices.
(ii) NPV and IRR may give a different ranking of projects, i.e. the project with the highest IRR may not be the one with the highest NPV.
|Example 9 – Non-conventional cash flows |
|The following project has non-conventional cash flows: |
| |
|Year |
|$000 |
| |
|0 |
|(1,900) |
| |
|1 |
|4,590 |
| |
|2 |
|(2,735) |
| |
| |
|Project X would have two IRRs as show in the following diagram. |
| |
|[pic] |
| |
| |
|The NPV rule suggests that the project is acceptable between costs of capital of 7% and 35%. |
| |
|Suppose that the required rate on project X is 10% and that the IRR of 7% is used in deciding whether to accept or reject the project. |
|The project would be rejected since it appears that it can only yield 7%. |
| |
|The diagram shows, however, that between rates of 7% and 35% the project should be accepted. Using the IRR of 35% would produce the |
|correct decision to accept the project. Lack of knowledge of multiple IRRs could therefore lead to serious errors in the decision of |
|whether to accept or reject a project. |
| |
|In general, if the sign of the net cash flow changes in successive periods, the calculations may produce as many IRRs as there are sign |
|changes. IRR should not normally be used when there are non-conventional cash flows. |
|Example 10 – Mutually exclusive projects |
|Consider two projects A and B. The discounted cash flow (DCF) from A is more sensitive to the discount rate and falls more sharply than |
|the DCF from B as the discount rate is increased. This is illustrated below. |
| |
|[pic] |
| |
|Hence, at low rates of discount NPV A > NPV B, and project A would be preferred to project B. However, IRR A < IRR B, which indicates |
|that project B would be preferred to project A. |
| |
|It can be seen that the decision depends not only on the IRR but also on the cost of capital being used. |
7. Modified Internal Rate of Return (MIRR)
(Jun 08, Jun 12, Dec 14)
7.1 The MIRR overcomes the problem of the reinvestment assumption and the fact that changes in the cost of capital over the life of the project cannot be incorporated in the IRR method.
|7.2 |MIRR formula |
| |MIRR = [pic] |
| | |
| |Where: |
| |PVR = the PV of the return phase (the phase of the project with cash inflows) |
| |PVI = the PV of the investment phase (the phase of the project with cash outflows) |
| |re = the cost of capital |
|Example 11 – MIRR |
|Consider a project requiring an initial investment of $24,500, with cash inflows of $15,000 in years 1 and 2 and cash inflows of $3,000 |
|in years 3 and 4. The cost of capital is 10%. |
| |
|Solution: |
| |
|[pic] |
|PVR = 30,327 |
|PVI = 24,500 |
|MIRR = [pic] = 16% |
| |
|The MIRR is calculated on the basis of investing the inflows at the cost of capital. |
| |
|Alternative method: |
| |
|An alternative way of calculating MIRR would be to calculate the terminal value of the return phase (assuming that the cash flows are |
|reinvested at the firm’s cost of capital). |
| |
|The MIRR formula to use in this case would be: |
| |
|MIRR = [pic] |
| |
|[pic] |
|Terminal value of return phase = 44,415 |
|PV of investment phase = 24,500 |
|MIRR = [pic] = 16% |
7.3 Advantages of MIRR
(a) It assumes that the reinvestment rate is the company’s cost of capital. However, IRR assumes that the reinvestment rate is the IRR itself, which is usually untrue.
(b) When there is conflict between the NPV and IRR methods, the MIRR will give the same indication as NPV. This helps when explaining the appraisal of a project to managers, who often find the concept of rate of return easier to understand than that of NPV.
7.4 Disadvantages of MIRR
(a) Like all rate of return methods, suffers from the problem that it may lead an investor to reject a project which has a lower rate of return but, because of its size, generates a larger increase in wealth.
(b) In the same way, a high-return project with a short life may be preferred over a lower-return project with a longer life.
|Question 5 |
|Tisa Co is considering an opportunity to produce an innovative component which, when fitted into motor vehicle engines, will enable |
|them to utilise fuel more efficiently. The component can be manufactured using either process Omega or process Zeta. Although this is |
|an entirely new line of business for Tisa Co, it is of the opinion that developing either process over a period of four years and then|
|selling the productions rights at the end of four years to another company may prove lucrative. |
| |
|The annual after-tax cash flows for each process are as follows: |
| |
|Process Omega |
|Year |
|0 |
|1 |
|2 |
|3 |
|4 |
| |
| |
|$000 |
|$000 |
|$000 |
|$000 |
|$000 |
| |
|After-tax cash flows |
|(3,800) |
|1,220 |
|1,153 |
|1,386 |
|3,829 |
| |
| |
|Process Zeta |
|Year |
|0 |
|1 |
|2 |
|3 |
|4 |
| |
| |
|$000 |
|$000 |
|$000 |
|$000 |
|$000 |
| |
|After-tax cash flows |
|(3,800) |
|643 |
|546 |
|1,055 |
|5,990 |
| |
| |
|Tisa Co has 10 million 50c shares trading at 180c each. Its loans have a current value of $3·6 million and an average after-tax cost |
|of debt of 4·50%. Tisa Co’s capital structure is unlikely to change significantly following the investment in either process. |
| |
|Elfu Co manufactures electronic parts for cars including the production of a component similar to the one being considered by Tisa Co.|
|Elfu Co’s equity beta is 1·40, and it is estimated that the equivalent equity beta for its other activities, excluding the component |
|production, is 1·25. Elfu Co has 400 million 25c shares in issue trading at 120c each. Its debt finance consists of variable rate |
|loans redeemable in seven years. The loans paying interest at base rate plus 120 basis points have a current value of $96 million. It |
|can be assumed that 80% of Elfu Co’s debt finance and 75% of Elfu Co’s equity finance can be attributed to other activities excluding |
|the component production. |
| |
|Both companies pay annual corporation tax at a rate of 25%. The current base rate is 3·5% and the market risk premium is estimated at |
|5·8%. |
| |
| |
|Required: |
| |
|(a) Provide a reasoned estimate of the cost of capital that Tisa Co should use to calculate the net present value of the two |
|processes. Include all relevant calculations. (8 marks) |
|(b) Calculate the internal rate of return (IRR) and the modified internal rate of return (MIRR) for Process Omega. Given that the IRR |
|and MIRR of Process Zeta are 26·6% and 23·3% respectively, recommend which process, if any, Tisa Co should proceed with and explain |
|your recommendation. 8 marks) |
| |
|(c) Elfu Co has estimated an annual standard deviation of $800,000 on one of its other projects, based on a normal distribution of |
|returns. The average annual return on this project is $2,200,000. |
| |
|Required: |
| |
|Estimate the project’s Value at Risk (VAR) at a 99% confidence level for one year and over the project’s life of five years. Explain |
|what is meant by the answers obtained. (4 marks) |
|(20 marks) |
|(ACCA P4 Advanced Financial Management June 2012 Q4) |
-----------------------
ACCA June 2016 Dec 2014
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