1.9.Financial Management (1)

ACCA – FM FINANCIAL MANAGEMENT STUDY NOTES

Contents Sr. # TOPIC Page # 1. Investment Appraisal 01 2. Inflation 20 3. Risk & Uncertainty 32 4. Cost of Capital 39 5. Cost of Irredeemable Debt 46 6. Capital Structure and WACC 51 7. Business Valuation 57 8. Sources of Finance 64 9. Cost of Convertible Debt 70 10. Islamic Financing 77 11. Small and Medium Enterprises (SME) 80 12. Working Capital Management 94 13. Inventory Management 99

Study Notes Financial Management - FM Investment Appraisal Decision making Short term Long term (Single period effect) (Having multi period effects) Investment Appraisal:- A detailed evaluation of projects/investments to assess the viability, its effects on shareholders wealth is called investment appraisal, What is Appraisal:- Any expenditure in the expectation of future benefits. There are two types of investment: Capital expenditure: Capital expenditure is an expenditure which results in the acquisition of non-current assets or an improvement in their earning capacity. It is not charged as an expense in the income statement; this expenditure appears as a non- current asset in the balance sheet. Revenue expenditure: Charged to the income statement and is expenditure which is incurred. (i) For the purpose of the trade of the business this includes expenditure classified as selling and distribution, administration expenses and finance charges. (ii) To maintain the existing earning capacity of non-current asset. The capital budgeting process: The process of identifying, analyzing and selecting investments projects whose returns are expected to extend beyond one year. These steps are being followed in capital budgeting process. I. Creation of capital budgets This steps involves assessing the time required by projects, when they are anticipated to start, how they will be financed, how they would effect the current production budget, expected levels of production and long term development of organization. II. Investment Decision making process It involves the following steps Origination of Proposals Project screening Analysis Monitoring and Acceptance and Review 1

Study Notes Financial Management - FM i. Origination:- A good understanding of market demand, market conditions and customer perceptions are always needed in order to avail the opportunities. There should be a proper mechanism which identifies the potential opportunities available in the market for investment, and if technology is obsoleting, organization should know beforehand that new investment is required. ii. Project Screening:- Each proposal should be screened before doing financial analysis on it. This screening would involve the following questions:  What is the purpose of the project?  Does it align with organizations long term objectives? There should not be a single conflict between the organization objectives and projects objectives.  Are sufficient resources available?  Necessary management skills are present?  What kind of risk is involved in the project? iii. Analysis and acceptance:- It involves the following steps  Standard format of financial information as a formal investment proposal should be submitted.  Project should be classified e.g. what kind of financial appraisal is required, what % of return should be achieved.  Financial analysis should be done.  Outcome of financial analysis should be compared with predetermined criteria  Consider the project in the light of capital budget for the current and future operating periods  Make the decision (accept or reject).  Monitor the progress of the project. a) Financial Analysis:- This step would involve the application of organization’s preferred investment appraisal techniques e.g. IRR, NPV etc. Some projects e.g. marketing investment decisions have intangible returns in this case more weight may be given to the consideration and qualitative issues. b) Qualitative Issues:- Qualitative Issues are those issues which are difficult or impossible to quantify but decisions should be made after considering these issues e.g. (i) How the project will affect the company’s image (ii) Would the project help the organization in satisfying the customer needs c) Accept or Reject:- Acceptance depends on three factors (i) Type of investment 2

Study Notes Financial Management - FM (ii) Risk of the investment (iii) Amount of expenditure required iv. Monitoring the progress:- A project progress should be monitored regularly, to ensure that capital spending is not exceeding from the budget, implementation is not delayed and the anticipated benefits are eventually obtained. Financial Evaluation Methods Basic Methods Advanced Methods  Accounting Rate of Return (ARR)  Net Present Value NPV  Payback Period  Internal Rate of Return (IRR)  Discounted Payback Period In the above methods, ARR method is based on profits whereas all other methods are based on cash flows. The Advanced Methods Includes Time Value of money Basic Methods 1. Accounting Rate of Return (ARR) Definition:- The earnings of a project expressed as a percentage of the capital outlay or average investment Or Average return as a percentage of average investment. Formula:- ARR = Average Annual profit x 100 Initial investment Alternative Version of ARR is: ARR = Average Annual profit x 100 Average Investment Where “Average Investment” is = Initial Investment + Scrap value 2 Decision Rule:- Feasibility Decision: If ARR of the project > Target ARR, Accept the project If ARR of the project < Target ARR, Reject the project Comparison Decision: Project with higher ARR shall be preferred. Advantages of Accounting Rate of Return:-  It considers the readily available accounting information, that’s why eliminating the need of any other additional reporting.  ARR is simple to calculate and easy to understand, there is no technical knowledge required for its calculations. 3

Study Notes Financial Management - FM  It takes into account the whole life of the project, as it takes the average of all profits available in the project life.  It can be used as a relative measure in case of mutually exclusive projects.  The expected profitability of a project can be compared with the present profitability of business. Disadvantages of Accounting Rate of Return:-  ARR does not consider the time value of money. It ignores the timing, relevancy of cash inflows.  It includes:  Sunk costs (money already spent)  Net Book Values of Assets  Depreciation and amortization of intangibles  Allocated Fixed Overheads.  ARR calculations are based on accounting profits and they can be easily manipulated by applying different accounting policies.  It ignores the size of investment and length of the project.  It gives no absolute measure to reach at some conclusion, we need to do comparison that’s why it is a relative measure only.  Calculation of target ARR is a subjective approach.  ARR does not take into account the risk and uncertainty related to the profits of the project.  It is an average measure, so does not consider relative life of the project.  The average annual profit used to calculate ARR, is unlikely to be the profit earned in any year of the project life. Relevant Cash flows in Investment Appraisal:- Relevant cash flows are those cash flows which are: (i) Directly related with the project (ii) Incremental (iii) Future cash flows Any cash flows or cost incurred in the past, or any committed costs which will be incurred regardless of whether the investment is undertaken or not are non-relevant cash flows e.g. sunk lost, allocated overheads etc. The all other cash flows, which should be considered, are as follows: i. Opportunity Cost:- Cost incurred or revenues lost from diverting enlisting resources from their best use are called opportunity cost. As this will happen because of new project that’s why it is relevant. ii. Tax:- Relevant costs include the extra taxation that will be payable on extra profits, or the reductions in tax arising from capital allowances or operating losses in any year. iii. Residual value: The residual value or disposal value of equipment at the end of its life or its disposal date are relevant to the appraisal. iv. Infrastructure Costs v. Marketing Costs: 4

Study Notes Financial Management - FM May be substantial, particularly if the investment is in a new product or service, but if the market research has been done in the past and no further investment in marketing is required then this will be non-relevant cost. vi. Human resource costs: It includes training costs and the costs of reorganization arising from investment. vii. Finance Related Cash flows:- Finance related cash flows (e.g. Interest on Bank Loan) are normally excluded from project appraisal exercises because the discounting process takes account of the time value of money, that is opportunity cost of investing the money in the project. Finance Related cash flows are only relevant if the incur a different rate of interest from the rate which is being used as the discount rate. viii. Relevant Benefits of Investment:- Relevant benefits from investments, include not only increased cash flows but also savings and relationships with customer and employees. These might consist of benefits of several types; o Savings because assets used currently will no longer be used. The savings should include savings in staff costs, or savings in other operating costs, such as consumable materials. o Extra savings or benefits because of the improvements or enhancement that the investment might bring. These include more sales revenue, greater contribution, more efficient systems operation and savings in staff time. o Possibly some off revenue benefits from the sales of assets that are currently in use, but which will no longer be required. o Greater customer satisfaction, arising from a more prompt service (e.g. because of a computerized sales and delivery service). o Improved staff morale from working with high quality assets. o Better decision making may result from better information systems. Assumptions of Timing of Cash flows  If Cash flows arise during the period, then it is assumed as it arises at the end of that period.  If cash flow arises at the start of the period then it is assumed as if it arises at the end of the preceding period  Period ‘0’ is not a period, instead it represents start of period ‘1’. 2. PAYBACK PERIOD METHOD: Definition:- The time period in which initial investment gets recovered, known as payback period. The number of years for the cash out lay to be matched by cash inflows. Formula:- a. For constant(Even) cash flows: 5

Study Notes Financial Management - FM Payback period = Initial investment Annual inflows b. For Uneven cash flows: Draw a cumulative cash flow column, then calculate project payback period. Answer should be compared with the target payback period of the business. Decision rule:- i. Feasibility Decision: If payback period is less than target payback period then ACCEPT the project. If payback period is more than target payback period then REJECT the project. ii. Comparison Decision: Project with minimum payback period should be preferred. Advantages of payback period:-  It is simple to calculate and easy to understand, as it does not involve complex calculations.  Payback period method can also be used as a basic screening device at the first stage for short listed projects.  It considers cash flows rather than accounting profits, that’s why chances of manipulation are very low.  Payback period method indirectly avoids risk as it gives favor to those investments which have short payback periods. This method helps the company to grow, minimize risk and maximize liquidity.  In the situation of capital rationing, it can be used to identify the projects which generate additional cash for re- investment quickly. Disadvantages of payback period:-  It does not consider the time value of money.  It does not consider the whole life of project. It might be possible that it will favor the projects, giving high cash inflows in the starting years only and giving very low cash inflows in the remaining years.  There are no specific criteria or rule which can justify that company’s target payback period is measured accurately that’s why it is difficult to measure target payback period.  It may lead to excessive investment in short term projects.  It does not consider the risk and uncertainty in the projects. Uncertainty of cash inflows can deteriorate the results.  It does not focus on shareholders wealth maximization.  Life expectancy of a project is ignored.  Projects with same payback period may have different cash flows. Lecture Examples on Payback Period: Example.1 Initial investment in project A is $80,000. Life of the project is six years and project generating equal cash inflows of $20,000. If target payback period of the company is 5 year whether the project should be feasible or not. 6

Study Notes Financial Management - FM Required: Calculate payback period using non discounting payback period method and comment whether to accept or reject. Example.2 Initial investment in project Z is $5,000. Project life is five years. For the year cash flows from project Z are $2,000, $1,500, $1,000, $500 and $250 respectively. If target payback period of company is 7 year whether the project should be feasible or not. Required: Calculate how much time is required to regain its investment and comment of it acceptability. Example.3 Initial investment in project HMZ is $10,000. Project life is five years. For the year cash flows from the project HMZ are $5,000, $1,000, $1,500, $1,250 and $2000 respectively. If target payback period of the company is 4 year whether the project should be feasible or not. Required: Calculate time Compute payback period by using non discounting payback period method and comment of it acceptability. Solutions Ex #1 Payback period = Initial investment = = Constant cash inflow 80,000 20,000 4yrs < targeted 5y. So accept the project. Ex #2 Yr Cash flow Cumulative cash flow T0 (5,000) (5,000) T1 2,000 (3,000) T2 1,500 (1,500) T3 1,000 (500) T4 500 - T5 Payback period is 4 yrs. Ex #3 Yr Cash flow Cumulative cash flow Payback period T0 (10,000) (10,000) T1 (5,000) T2 5,000 (4,000) T3 1,000 (2,500) T4 1,500 (1,250) T5 1,250 750 2,000 = 4������������������ + ������������������ = 4������������������ & [1,250] ������12 ������������������ 2,000 4������������������ + 1,250 2,000 7

Study Notes Financial Management - FM = 4 + 0.625 4 years & 7.5 months = 4.625 yrs. Advanced Methods Time Value of Money Sum of money received today has more worth than same sum of money received in future because of these reasons. • Inflation • Opportunity to reinvest • Risk and uncertainty Simple interest 1. 1000 x 10% = $100 2. 1000 x 10% = $100 3. 1000 x 10% = $100 Cash flows are not reinvested each year Compound interest 1. 1000 x 10% = 100 + 1000 = 1100 2. 1100 x 10% = 110 + 1100 = 1210 3. 1210 x 10% = 121 + 1210 = 1331 Cash flows are reinvested each year resulting in higher principal that increases the interest amount. We can also calculate the future amounts using this formula FV = PV (1+r)n FV= future value= 1331 PV= Present Value= 1000 1331 = 1000 x (1+10%)3 Discounting Where r = cost of capital = WACC = required rate of return PV = FV (1+r)-n Assumption: All cash flows are reinvested in the same project or any other at a given rate of return (cost of capital). Year Cash flows Df@12% PV 1 1000 0.893 2 2000 0.797 892.9 3 3000 0.712 1594.39 2135 8

Study Notes Financial Management - FM Consistent Cashflows If Cashflows arises in a series of equal cashflows then it is called Consistent Cashflows. These are of two Types: Annuity: If Consistent cashflow for a certain Period. e.g Y1-5 or Y3-7 Perpetuity: If Consistent cashflow for infinite period e.g. Y1-∞ or Y3-∞ Present Values of Consistent Cashflows The Annuity Factor = ������−(1 + r)-n ������ The Perpetuity Factor = ������ ������ Annuity Perpetuity If Cash flows Start from Period 1. Annual Cash flow X Perpetuity Factor Annual Cash flow X Annuity Factor e.g. Y1-∞ $10,000 at Disc. Rate of 10% e.g. Y1-5 $10,000 at Disc. Rate of 10% $10,000 X (1/10%) = $100,000 $10,000 X 3.791(from annuity table) =$37,910 If Cashflows Start from Period 0. NET PRESENT VALUE (NPV): Definition:- The term NPV means absolute savings from a project today. Formula to calculate NPV:- NPV= P.V of cash inflows minus P.V of cash outflows. Decision Rule:- If NPV of the project, discounted at cost of capital, is positive, Accept the project If NPV of the project, discounted at cost of capital, is negative, Reject the project. Advantages of Net Present Value:  Net Present Value method takes into account the time value of money and this is giving a better picture of the projects viability.  It considers the timing of cash flows.  It considers the whole life of the project because all cash flows relating to the project life are incorporated in its calculations.  It gives an indication about the increase or decrease in the wealth of shareholders. Its decisions rule is consistent with the objective of maximization of shareholders wealth.  It focuses on cash flows rather than accounting profit, so it takes into account the relevancy and irrelevancy of cash flows.  Net Present Value is technically a strong method as compared to others as it is an absolute measure. Resultantly it can be used in isolation.  Change in cost of capital can be incorporated in it.  It can also be used for projects with non-conventional cash flows.  It gives a better ranking of mutually exclusive projects. 9

Study Notes Financial Management - FM  It assumes that cash flows are reinvested at the company’s cost of capital.  NPV is technically more superior method to IRR because of its less rigid assumptions. Disadvantages of Net Present Value:  It involves complex calculations as compared to other techniques. Resultantly, it is difficult to calculate and difficult to understand.  Managers feel it difficult to explain the calculations of Net Present Value method.  It does not take into account the risk and uncertainty of estimates and scarcity of resources.  Cost of capital used in NPV calculation is difficult to calculate and gets subjective when we incorporate risk and uncertainty within companies cost of capital.  Changing technology may render the product obsolete before the natural end of the project life.  It fails to relate the return of the project to the size of the cash outlay. Lecture Examples on Net Present Value: Example.5 Mr. Omar have $50,000 in his old age, he wants to invest into ASA. Project life is 5 years and Mr. Omar will get the cash benefit in following manner. Year Cash flow ($) 1 16,000 2 14,000 3 12,000 4 10,000 5 8,000 Rate of interest is 10% per annum. Required: Calculate net present value & comment on its acceptability. Example.6 Initial investment in a project is $80,000. Project life is 6 years. Yr Cash flow ($) 1 24,000 2 22,000 3 20,000 4 26,000 5 20,000 6 2000 Cost of capital 5% P(a). Required : i. Calculate NPV of the project ii. Decide whether the project should be accepted or not. 10

Study Notes Financial Management - FM Example.7 An Organization is considering a capital investment in new equipment the estimated cash flows are as follows. Yr Cash flow ($) 0 (240,000) 1 80,000 2 120,000 3 70,000 4 40,000 5 20,000 The company cost of capital is 9% Required : Calculate Net Present Value (NPV) of the project to access whether it should be undertaken or not. Example.8 Wheel Ltd. has the opportunity to invest in investment with the following initial cost & returns (cash profit). Year A B $$ 0 (90,000) (20,000) 1 40,000 10,000 2 30,000 8,000 3 20,000 6,000 4 20,000 4,000 5 20,000 4,000 Residual value in case of A $4,000 and in case of B $2,000. Cost of Capital in both situations are 10%. Required: Calculate NPV of A & B. Example.9 Initial investment in a project is $100,000. Net cash inflows from year 1 to 10 are $60,000, $30,000, $25,000, $20,000, $18,000, $15,000, $12,000 and $10,000. Cost of capital is 10% p.a Required: calculate NPV of the project. 11

Study Notes Financial Management - FM Ex #5 Solutions PV (50,000) Year Cash flow D.F. 14,545 T0 (50,000) 1 11,564 T1 16,000 T2 14,000 0.909 9,012 T3 12,000 0.826 6,830 T4 10,000 0.751 4,968 T5 0.683 NPV = - 3,082 8,000 0.621 Reject the Project Ex #6 PV (80,000) Yr Cash flow D.F. 22,848 T0 (80,000) 1 19,954 T1 24,000 17,280 T2 22,000 0.952 21,398 T3 20,000 0.907 15,680 T4 26,000 0.863 T5 20,000 0.823 1,492 T6 0.784 NPV = - 18,652 2,000 0.746 NPV of project = PV of cash inflow – PV of cash outflow D.F. = 98,652 – 80,000 1 = 18,652 It should be accepted 0.917 0.842 Ex #7 0.772 0.708 Yr Cash flow 0.650 PV T0 (240,000) (240,000) T1 D.F. T2 80,000 1 73,360 T3 120,000 101,040 T4 70,000 0.909 54,040 T5 40,000 0.826 28,320 20,000 0.751 0.683 1,304 Ex #8 29,760 Project A PV Yr Cash flow (90,000) T0 (90,000) 36,360 T1 40,000 24,780 T2 30,000 15,020 T3 20,000 13,660 T4 20,000 12

Study Notes Financial Management - FM T5 24,000 0.621 14,904 NPV = 14,724 Project B Yr Cash flow D.F. PV T0 (20,000) 1 (20,000) T1 40,000 T2 0.909 9,090 T3 8,000 0.826 6,608 T4 6,000 0.751 4,506 T5 4,000 0.683 2,732 6,000 0.621 3,725 NPV = +6,662 Ex #9 Yr Cash flow D.F. PV T0 (60,000) 1 (60,000) T1 22,500 21,218 T2 22,500 0.943 20,025 T3 22,500 0.890 18,900 T4 22,500 0.840 17,820 T5 22,500 0.792 16,808 0.747 NPV = +33,771 4. Internal Rate of Return (IRR): Definition:- IRR is the total rate of return offered by an investment over its life. Formula to calculate IRR:- and IRR =a% +[ ������ (b-a)]% ������−������ Where a = Lower discount rate b = Higher discount rate A = NPV at lower discount rate B = NPV at higher discount rate Decision Rule:- a) Feasibility Decision:  If IRR of the project > Cost of Capital, Accept the project because the project is adding value to the owner’s wealth resulting in positive NPV.  If IRR of the project < Cost of Capital, Reject the project because the project is destroying value in shape of negative NPV. b) Comparison Decision: Project with higher IRR shall be preferred. 13

Study Notes Financial Management - FM Advantages of IRR:  IRR takes into account the time value of money and thus giving a better picture of the projects viability.  It considers the timing and life of the project.  It can be calculated by assuming any discount rate in its calculation.  IRR is easier to understand as compared to NPV.  Risk can be incorporated into decision making by adjusting the company’s target discount rate. Disadvantages of IRR:  It ignores the size of investment and length of the project.  It gives no absolute measure to reach at some conclusion.  It is fairly complicated to calculate.  It can be confused with accounting ROCE.  Interpolation technique used in IRR calculation does not give exact answer. It only provides an estimate and if the margin between required rate of return and IRR is fairly small, this lack of accuracy could result in wrong decision being taken.  In case of non-conventional cash flows, there may be several IRRs which can mislead the decision makers.  IRR does not give indication about the increase or decrease in the wealth of shareholders.  It considers the long term viability of the project, losses may be made in the short term.  It requires assumption of reinvestment at IRR which may not be fulfilled in case of higher IRR. Lecture Example of IRR Example 1: Initial investment in a project is $100,000. Net cash flows in year1 are $32,000, year 2 $28,000 and from year 3 to year 6 $852,000 p.a. cost of capital is 10% p.a. Required: Calculate IRR of project. Example 2: Initial investment in a project is $50,000. Net cash inflows from year 1 to 8 are $30,000, $15,000, $15,000, $20,000, $18,000, $15,000, $12,000 and $10,000. Cost of capital is 10% p.a Required: calculate IRR of the project. Solutions Ex # 1 Yr Cash flow D.F. PV D.F. PV 0 (100) 1 (100) 1 (100) 1 32 29.088 26.656 2 28 0.909 23.128 0.833 23.128 3 852 0.826 639.852 0.694 492.456 0.751 0.578 14

Study Notes Financial Management - FM 4 852 0.683 581.916 0.482 410.664 5 852 0.621 529.092 0.402 342.504 6 852 0.576 490.752 0.334 284.568 NPV 2194 NPV 1480 IRR = 10% + 2194 (20 − 10) 2194−1480 IRR = 40% Ex # 2 Cash flow D.F. PV D.F PV Yr (50) 1 (50) 1 (50) T0 30 27.27 24.99 T1 15 0.909 12.39 0.833 10.41 T2 15 0.826 11.26 0.694 8.76 T3 20 0.751 13.66 0.578 9.64 T4 18 0.683 11.17 0.482 7.23 T5 15 0.621 8.64 0.402 5.01 T6 12 0.576 6.156 0.334 3.34 T7 10 0.513 4.66 0.279 2.32 T8 0.466 45.236 0.232 21.7 IRR = 10% + 45.236 (20 − 10) 45.236−21.7 IRR = 29% Discounted Payback period method: Definition: The time period in which initial investment is recovered in terms of present value, known as payback period or The number of years for the present value of the cash out lay to be matched by present value of cash inflows. It is similar to simple payback period. The only difference is that the discounted cash flows are used instead of simple cash flows for calculation. Decision Rule  Feasibility Decision: If discounted payback period is less than target discounted payback period then ACCEPT the project. If discounted payback period is more than target discounted payback period then REJECT the project.  Comparison Decision : Project with minimum discounted payback period should be preferred. Advantages of Discounted payback period:-  It takes into account the time value of money and timings of cash flows.  Payback period method can also be used as a basic screening device at the first stage for short listed projects. 15

Study Notes Financial Management - FM  It considers cash flows rather than accounting profits, that’s why chances of manipulation are very low.  Risk and uncertainty can be incorporated with the help of risk adjusted cost of capital.  In the situation of capital rationing, it can be used to identify the projects which generate additional cash for reinvestment quickly.  Short payback period result in increased liquidity and enable business to grow more quickly, so used in rapidly changing technologies and industries. Disadvantages of Discounted payback period:-  It does not consider the whole life of project.  Calculation of discounted target payback period is difficult to measure.  Disadvantages of Discounted payback period does not give indication about the increase or decrease in the wealth of shareholders.  It may lead to excessive investment in short term project.  It requires knowledge of cost of capital which is difficult to calculate.  Life expectancy of a project is ignored.  It takes into account the Risk of timing of cash flows but not the variability of those cash flows. Lecture Examples on Discounted Payback period Example.1 Initial investment in a project A is $60,000. Net cash inflows during project life of 7 years are $25,000, $20,000, $18,000, $16,000, $15,000, $13,000 & $10,000. Required: i) Calculate payback period ii) Calculate discounted payback period. (If cost of capital is 10% p.a.) Example.2 Initial investment in a project $500,000. Initial investment includes investment in working capital of 10%. Scrap value of initial investment is 10%. Project life is 5 years. Net cash flows from the project are $200,000, $180,000, $160,000, $(20,000) and $67,000. Working will be recovered evenly throughout the project life. Required: If cost of capital is 15% p.a. calculates the NPV. Example.3 Initial investment in a project $50,000.Project life 8 years .Net cash flows are as below: Years Cash flows ($) 1 24,000 2 20,000 3 16,000 4 12,000 5 10,000 16

Study Notes Financial Management - FM 6 68,000 Cumulative cash flow 7 6,000 (60,000) 8 4,000 (35,000) (15,000) Cost of capital is 15% p.a. 3,000 Required: Cum PV i. Calculate the simple payback period. (60,000) ii. Calculate discounted payback period. (37,275) (20,755) Solutions (7,237) Ex #1 (a) 3691 Yr Cash flow 17 T0 (60,000) T1 25,000 T2 20,000 T3 18,000 T4 T5 Pay period = 2 + 15,000 ������������ D.F. PV 1 (60,000) 18,000 22,725 0.909 16,520 = 2.83y 0.826 13,518 (b) 0.751 10,928 0.683 93,159 Yr Cash flow 0.621 T0 (60,000) T1 25,000 T2 20,000 T3 18,000 T4 16,000 T5 15,000 = 3yr + 7237 10928 = 3.66Yr Ex #2 Yr Cash flow Cum cash flow T0 50,000 (50,000) T1 24,000 (26,000) T2 20,000 (6,000) T3 16,000 (10,000) = 2.4 yr

Study Notes Cash flow D.F. PV Financial Management - FM 50,000 1 (50,000) Yr 24,000 20,856 Cum PV T0 20,000 0.867 15,120 (50,000) T1 16,000 0.756 10,512 (29,144) T2 12,000 0.650 (104,029) T3 0.572 6,864 (3,512) T4 (3,352) =3 +3,512 6,864 = 3.511 yrs. Yr D.F. PV Cum PV (550) (550) T0 (550) 1 181.8 (368.2) 148.68 219.52 T1 200 0.909 120.16 99.36 (13.660) T2 180 0.826 103.707 (113.02) (10.02) T3 160 0.751 T4 (20) 0.683 T5 167 0.621 The initial investment’s recovers so, reject the project Effect of Taxation in investment appraisal Taxation is a major practical consideration for business. It is vital to take it into account in making decisions. i. Basic Assumption Taxation has two effects in investment appraisal a) Negative effect:- Tax charged on net revenue cash flows. b) Positive effect:- Tax relief on assets purchased via writing down allowances (capital allowances) ii. Corporation tax on profits Calculate the taxable profits (before capital allowances) and calculate tax at the rate given. 1. Tax on Operating Cashflows: Operational Cashflows X Rate of Tax 2. Tax Savings on Capital Allowances: Calculate the capital Allowances/ Balancing Allowances and then multiply with Tax Rate.  The effect of taxation will not necessarily occur in the same year as the relevant cash flow that comes in. 18

Study Notes Financial Management - FM Follow the instructions given in exam question Example Initial Investment = 2000 Capital Allowances = 25% reducing balance Useful life = 4 years, Tax rate = 30% payable in arrears, Scrap Value = 500 Years Written Capital Tax Timing Down Value Allowances Savings @ 25% @ 30% 1 2000 500 150 2 2 1500 375 113 3 3 1125 281 84 4 4 844 344 103 5 Effect of Inflation in investment appraisal: 19

Study Notes Financial Management - FM Inflation Definition:- Inflation may be defined as a general increase in prices, leading to general decline in the real value of money. (Decrease in purchasing power) Inflation Real rate of General Money rate Return Inflation rate of return i. Real rate of return/cost of capital Real rate of interest reflects the rate of return that would be required in the absence of inflation. ii. Money rate of return/cost of capital Money or nominal rate of return is rate that will be required in presence of inflation. Relationship between real and nominal rates of interest (Fisher formula) (1 + i) = (1 + r) (1 + h) Where h= rate of inflation/RPI r = real rate of interest i = nominal (money rate of interest) Types of Cash Flows i. Money cash flows are those cash flows in which the effect of specific inflation has been adjusted. ii. Real cash flows are those cash flows which have not been adjusted for inflation. Nominal Cashflow = Real cashflows ( 1+ i)n Sometimes Examiners gives the value in year 1 terms instead of current prices terms then Nominal Cashflow = Real cashflows ( 1+ i)n-1 Why Inflation is a problem  It is hard to estimate, especially when rates are high  It has economic impacts which cause governments to take into account its impacts on business  Different inflation rates will occur, different costs and revenues will inflate at different rates  It alters the cost of capital  It makes historic costs irrelevant and therefore causes ROCE to be overstated  It creates uncertainty  It encourages business to be short term in looking  Inflation may not be constant  The longer a project, the more significant the impact of inflation 20

Study Notes Financial Management - FM Effect of inflation on the discount rate:- The discount rate used in investment appraisal reflects the finance providers required rate of return (e.g the rate of interest on a loan raised, or shareholders required return if financed by equity. In times of inflation, the fund providers will require a return made up of two elements. i. A return to compensate for inflation (to maintain purchasing power). ii. A real return on top of this for the use of their funds. The required return that incorporates both of these elements is known as a money return. Methods to be used in Investment Appraisal i. Money method  Adjust individual cash flows for specific inflation to convert to money cash flows  Discount using money rate ii. Real method  No need to adjust any individual cash flows for inflation to convert to money cash flows  Discount using Real rate  This is the simplest technique  Remove the effects of general inflation from money cash flows to generate real cash flows.  Achieves the same result as money method Note:  In case of general inflation, either of the two methods can be used.  In case of specific inflation, only applicable method is Money method Working Capital Change Every business requires working capital for its operations. Calculate working capital change in two steps: 1. Calculate working capital requirement one year in advance e.g. working capital is 10% of sales at the start of each year 2. Calculate incremental working capital by taking change of each year working capital 3. In last year, there will be an assumption that all working capital will be recovered (Only for project and not for ongoing business) ILUSTRATION 6 A company is considering to invest in a project with its life of 4 years. Total working capital required at the beginning of each year is as follows: Year Cashflows $’000 1 500 2 700 3 1000 4 600 21

Study Notes Financial Management - FM Required: Calculate the working capital cashflows of each year to be included in NPV calculation? Solution Total Working Capital Incremental Working capital $'000 $'000 Y0 500 (500) Y1 700 (200) Y2 1000 (300) Y3 600 400 Y4 0 600 The Finance Cost The Finance Cost will be a relevant cashflow however it will NOT become the part of cashflows. This is because it is part of cost of capital. Performa for Net Present Value 0 1 2 34 Years X X XX (X) (X) (X) (X) Sales Variable Cost Incremental Fixed Cost (X) (X) (X) (X) Operating Cashflows X X XX Tax Expense (X) (X) (X) (X) X X XX Tax Savings on Capital Allowances Change in Working Capital (X) (X) (X) (X) X Initial Investment (X) Scrap Value X Net Cash flows (X) X X X X X Discount Factor X X X XX Present Values (X) X X X X Net Present Value X Investment appraisal in Capital Rationing situation Capital rationing: Where the finance available for capital expenditure is limited to an amount which prevents acceptance of all new projects with a positive NPV, the company is said to experience “capital rationing”. 22

Study Notes Financial Management - FM There are two types of capital rationing. I. Hard capital rationing: This applies when a company is restricted from undertaking all worthwhile investment opportunities due to external factors over which it has no control. These factors may include government monetary restrictions and the general economic and financial climate (e.g., a depressed stock market, which precludes a rights issue of ordinary shares). II. Soft capital rationing: This applies when a company decides to limit the amount of capital expenditure which it is prepared to authorize. Segments of divisionalised companies often have their capital budgets imposed by the main board of directors. A company may purposely curtail its capital expenditure for a number of reasons e.g., it may consider that it has insufficient depth of management expertise to exploit all available opportunities without jeopardizing the success of both new and ongoing operations. Capital rationing may exist in a: Single period capital rationing : Available finance is only in short supply during the current period, but will become freely available in subsequent periods. Projects may be: i. Divisible – An entire project or any fraction of that project may be undertaken. In this event projects may be ranked by means of a profitability index, which can be calculated by dividing the present value (or NPV) of each project by the capital outlay required during the period of restriction. Projects displaying the highest profitability indices will be preferred. Use of the profitability index assumes that project returns increase in direct proportion to the amount invested in each project. ii. Indivisible – An entire project must be undertaken, since it is impossible to accept part of a project only. In this event the NPV of all available projects must be calculated. These projects must then be combined on a trial and error basis in order to select that combination which provides the highest total NPV within the constraints of the capital available. This approach will sometimes result in some funds being unused. Lecture example A company has four projects under consideration. Project A Initial investment $60,000 .project life 3 years. Net cash inflows per year are $30,000, $45,000 & $27,000 respectively. Project B Initial investment is $80,000. Project life is 4 yrs. Net cash inflows from the project in yr 1 $50,000, yr 2 $30,000, yr 3 $28,000 and yr 4 $25,000. Project C Initial investment $100,000.Project life 7 yrs Net cash inflows per Annum for whole life of project are $21,000. Project D Initial investment $120,000. Project life is 5 yrs. Net cash inflow from yr 1-5 is $60,000, $50,000, $30,000, $28,000 and $35,000 respectively. 23

Study Notes Financial Management - FM The company has only $335,000 currently available. Additional funds will be freely available in future years. If cost of capital is 10% p.a. Required: a) Calculate Net present value of each project. b) Assuming no capital rationing situation, decide which projects to be accepted and also calculate their total net present value. c) Assuming capital rationing situation, calculate profitability index for each project. d) If projects are divisible determine the optimal investment plan. e) Using the above investment plan calculate the associated NPV. f) Assuming that the projects are indivisible find out the optimal investment plan. g) Using the above investment plan, find out the relevant NPV. Solutions Ex # 1 Project A: NPV = PV of inflow – PV of outflow = 30,000 x 0.909 x 45,000 x 0.826 + 27,000 x 0.751 – 60,0000 x 1 = 84,717 – 60,000 = 24,717 Project B NPV = 50,000 x 0.909 + 30,000 x 0.826 + 28,000 x 0.751 + 25,000 x 0.683 – 80,000 x 1 = 45,450 + 24,780 + 21,028 + 17,075 – 80,000 = 28,333 Project C NPV = 21,000 x 4.865 – 100,000 = 102,288 – 100,000 = 2,228 Project D NPV = 60,000 x 0.909 + 50,000 x 0.826 + 30,000 x 0.751 + 28,000 x 0.680 + 35,000 x 0.621 – 120,000 x 1 NPV = 39,229 In case of divisibility: NPV P.I. (1) 24,717 1.4119 (2) A 28,333 1.354 (4) B 2,228 1.0222 (3) C 39,229 1.3269 D 24

Study Notes Financial Management - FM (C) $ NPV 24,717 A (100%) 335,000 28,333 B (100%) (60,000) 1,671 C (100%) 93,950 Total NPV 275,000 Indivisible 80,000 A+B+C A+ B + D 19,5000 B+C+D 120,000 A+C+D 75,000 Req. NPV 24,000 55,278 260,000 92,279 300,000 69,790 280,000 66,174 Asset replacement decisions Once the decision has been made to replace the asset, The decision how to replace an asset. The asset will be replaced but we aim to adopt the most cost effective replacement strategy. The key in all questions of this type is the lifecycle of the asset in years. Asset Replacement issues: 1. How frequently an asset be replaced? 2. Is it worth paying more for an asset that has a longer expected life?  In both of these scenarios, the ideal approach is to keep the costs per annum (in NPV terms) to a minimum. This is calculated as an equivalent annual cost (EAC).  EAC = NPV of costs annuity factor for the life of the project  The best decision is to choose the option with the lowest EAC. Key ideas/assumptions:  Cash inflows from trading (revenues) are not normally considered in this type of question. The assumption being that they will be similar regardless of the replacement decision.  The operating efficiency of machines will be similar with differing machines or with machines of differing ages.  The assets will be replaced in perpetuity. 25

Study Notes Financial Management - FM Lecture Examples on Asset Replacement Decision: Lecture example.1 A company operates a machine which has the following costs and resale values over its four year life. purchase cost: $25,000. Year1 Year2 Year3 Year4 $ $ $$ Running costs (cash expenses) 7,500 11,000 12,500 15,000 Resale value (end of year) 15,000 10,000 7,500 2,500 The organizations cost of capital is 10%. Required: You are required to assess how frequently the asset should be replaced. Lecture example.2 Naurfold regularly buys new delivery vans. Each van costs £30,000, has running costs of £3,000 and a scrap value of £10,000 in its 1st year. In its 2nd year the van has higher running costs (£4,000) & a lower scrap value (£7,000). Vehicles are not kept for > 2 years for reliability reasons. Required: Using Naurfold’s cost of capital of 15%, identify how often the van should be replaced. Ignore tax. Lecture example.3 A company operates a machine which has the following costs and resale values over its three year life .purchase cost: $30,000. Year1 Year2 Year3 Year4 $ $$$ Running costs (cash expenses) 7,000 12,500 13,000 17,500 Resale value (end of year) 12,000 9,250 8,200 1,000 The organization’s cost of capital is 25%.specific inflation in running cost and residual value is 6% & 7.5% respectively. Required : You are required to assess how frequently the asset should be replaced. Solutions Ex # 1 T0 T1 Everyone Yr $000) $(000) (25 Purchase cost (7.5) Running cost (25) 15 Residual value 1 7.5 Cash flow 0.909 D.F. 10% 26

Study Notes Financial Management - FM (25) 6.818 NPV = (18.181 Annual Equivalent Cost (AEC) = 18.181 0.909 = (2.001) Every two Yr T0 T1 T2 $(000) $(000) $(000) Purchase cost (25) Running cost (7.5) (11) Residual value (25) 10 1 (7.5) (1) D.F. 10% (25) 0.909 0.826 6.818 (0.826) NPT = - 32.644 EAC = −32.664 1.736 EAC = (18.804) Every three yr T0 T1 T2 T3 $(000) $(000) $(000) $(000) Purchase cost (25) Running cost (7.5) (11) (12.5) Residual value (25) 7.5 1 (7.5) (11) 0.909 0.826 (5) 0.751 NPV = (44.659) EAC = 44.659 2.486 EAC = (17,964) Every four yr Purchase cost T0 T1 T2 T3 T4 Running cost $(000) $(000) $(000) $(000) Residual value (25) (15) (7.5) (11) (12.5) 2.5 D.F. 10% (25) (12.5) 1 (7.5) (11) 12.5 0.683 0.909 0.826 0.751 (8.536) (25) (6.818) (9.086) (9.388) NPV= 58.830 EAC = 58.830 = (185.64) 3.169 27

Study Notes Financial Management - FM Every three yr is the best option 28 Ex #2 T0 T1 $(000) $(000) Purchase cost (30) Running cost (3) Residual value (30) 10 Cash flow 1 7 D.F. 10% (30) 0.869 6.083 NPV = (23.917) Annual Equivalent Cost (AEC) = (23.917) = (21.522) 0.869 Every two yr: T0 T1 T2 $(000) $(000) $(000) Purchase cost Running cost (30) (3) (4) Residual value 7 (30) (3) 3 D.F. 1 0.869 0.756 2.607 2.268 (30) NPV = - 30.339 EAC = (30.339) 1.625 = (18.670) Every two ye best. Ex #3 Purchase cost T0 T1 Running cost $(000) $(000) Residual value (30) (7.42) Cash flow (30) 12.9 D.F. 1 5.48 (30) 0.80 4.384 NPV = (25.62 EAC = 25.62 = (32.09) 0.80 Every 2 yr T0 T1 T2

Study Notes Financial Management - FM Purchase cost $(000) $(000) $(000) Running cost (30) Residual value (7.42) (14.045) (30) 10.68 D.F. 1 (7.42) (3.35) (30) 0.80 0.64 (5.936) (2.148) NPV = (38.084) EAC = (38.084) 1.44 = (26.44) Every three yr T0 T1 T2 T3 $(000) $(000) $(000) $(000) Purchase cost (30) Running cost (7.42) (14.045) (15.483) Residual value (30) 10.187 1 (7.42) (14.045) (5.296) (30) 0.80 0.64 0.512 (5.936) (2.71) (8.98) NPV = (47.637) EAC = 47.637 1.952 EAC = (24,404) Lease or Buy Decision: A specific decision that compares two specific financing options, the use of a finance lease or buying outright financing via a bank loan. Key information  Discount rate = post tax cost of borrowing. The rate is given by the rate on the bank loan in the question, if it is pre-tax then the rate must be adjusted for tax. If the loan rate was 10% pre-tax and corporation tax is 30% then the post -tax rate would be 7%. (10% x (1 – 0.3).  Cash flows : Bank loan Finance Lease 1. Cost of the investment 1.Lease rental - in advance 2. WDA tax relief on investment - annuity 3. Residual value 2.Tax relief on rental 29

Study Notes Financial Management - FM Other considerations:  Who receives the residual value in the lease agreement? It is possible that the residual value may be received wholly by the lesser or almost completely by the lessee.  There may be restrictions associated with the taking on of leased equipment. The agreements tend to be much more restrictive than bank loans.  Are there any additional benefits associated with lease agreement? Many lease agreements include within the payments, some measure of maintenance or other support service. The benefits of any type of lease to the lessee can be:  Availability; a firm that cannot get a bank loan to fund the purchase of an asset (capital rationing – see next section for further discussion); the same bank that refused the loan will often be happy to offer a lease.  Avoiding tax exhaustion; if a firm cannot use all of their capital allowances (the lesser can use the capital allowances and then set a lease that transfers some of the benefit to the lessee).  Avoiding covenants; restricting future borrowing capability. Benefits to the lesser:  Banks offer leases to exploit their ability to raise low cost capital.  Companies (e.g. IBM) offer leases to attract customers.  Profitable companies set up leasing subsidiaries to shelter their own profits from tax (eg M&S, Tesco).  Lecture examples on Lease or Buy Decision: Lecture example.4 Smicer plc is considering how to finance a new project that has been accepted by its investment appraisal process. For the four year life of the project the company can either arrange a bank loan at an interest rate of 15% before corporation tax relief. The loan is for $100,000 and would be taken out immediately prior to the year end. The residual value of the equipment is $10,000 at the end of the fourth year. An alternative would be to lease the asset over four years at a rental of $30,000 per annum payable in advance. Tax is payable at 33% one year in arrears. Capital allowances are available at 25% on the written down value of the asset. Required: Should the company lease or buy the equipment? Solutions Ex #4 100 Tax saving CA 8.25 W Capital allowance (25) 6.18 75 4.641 CAI (18.75) CAII 56.25 CAIII (14.063) 42.187 30

Study Notes (10) Financial Management - FM 10.622 R.V 32.187 CA IV (32.187) Lease or buy decision ∝ Initial T0 T1 T2 T3 T4 T5 Residual value $(000) $(000) $(000) $(000) $(000) $(000) Tax saving on CA (100) D.F. 10% - 8.25 6.18 10 10.622 NPV = - 71.942 (100) - 8.25 6.18 4.641 10.622 Lease 1 0.826 0.751 4.641 0.621 6.81 4.647 0.683 6.596 Tax saving on CA (100) D.F. 10% 10 NPV = 73.207 T0 T1 T2 T3 T4 $(000) $(000) $(000) $(000) $(000) (30) (30) (30) (30) (30) 9.90 9.90 9.90 9.90 (30) 1 (20.1) (20.1) (20.1) (20.1) 0.909 0.826 0.751 0.683 (30) (18.271) (16.603) (15.095) 6.762 31

Study Notes Financial Management - FM Risk & Uncertainty If the probability of projects out come are: Predictable Not predictable Risk Uncertain Before deciding to spend money on a project, managers will want to be able to make a judgment on the risk/uncertainty of its return. Risk:- A condition in which several possible outcomes exist, the probabilities of which can be quantified from historical data. Uncertainty:- The inability to predict possible outcomes due to a back of historical data being available for quantification. If project cashflows are: Risky (Techniques) Uncertain  Expected values (Techniques should be:)  Risk adjusted discount factor Adjusted payback period Sensitivity Analysis Certainty equivalents Simulation models Risk:- Expected values:- The quantitative result of weighting uncertain events by the probability of their occurrence. Or Using probabilities to create an assessment of the average expected net present value from an investment. The simple expected value decision rule is appropriate, if three conditions are met or nearly met.  There is a reasonable basis for making the forecast and estimating the probability of different outcomes.  The decision is relatively small in relation to the business. Risk is then small in magnitude.  The decision is for a category of decisions that are often made. A technique, which maximizes average pay off, is then valid.  Advantages of expected value method:-  Recognizes that there are several possible outcomes and is therefore, more sophisticated then single value forecasts.  Enable the probability of the different outcomes to be quantified. 32

Study Notes Financial Management - FM  Leads directly to a simple optimizing decision rule.  Calculations are relatively simple Disadvantages of expected value method:-  Forecasting procedure is complicated. In accurate evaluations already a major weakness in project evaluation. The probabilities used are also usually very subjective.  The expected value is merely a weighted average of the probability distribution, indicating the average pay off if the project is repeated many times.  The expected value gives no indication of the dispersion of possible outcomes.  About the expected value. The more widely spread out of the possible results are, the more risky the investment is usually see to be.; The expected value technique also ignores the investors attitude to risk. Some investors are more likely to take risks than others. Risk adjusted discount rate:- Risk adjusted discount rate technique shall be covered in cost of capital area because this technique involves the calculation of risk premium which requires the knowledge of Capital asset pricing model (CAPM). Lecture Examples on Expected value method: Example.1 Mr. Sajid wants to open a campus in Sargodha. Initial investment is $100,000. Project life is 4 years. Sales Revenue Probability Operating cost Probability ($) ($) 0.5 0.60 80,000 0.3 30,000 0.35 50,000 0.2 20,000 0.05 20,000 50,000 0.50 Residual value of project 10,000 0.50 5,000 Cost of capital of Mr. Sajid is 10% p.a. Required: Calculate the expected net present value of project. Example.2 Initial investment in a project is $300,000. Project life is 2 years. Net cash inflows from the project are : Year 1: Cash flows ($) Probability 100,000 0.25 200,000 0.50 300,000 0.25 33

Study Notes Financial Management - FM Year 2: Cash flows in year2 Probability is If cash inflow in year 1 ($): ($) i) 100,000 100,000 0.50 ii) 200,000 200,000 0.25 0.25 Nil 100,000 0.25 200,000 0.50 300,000 0.25 iii) 300,000 200,000 0.25 300,000 0.50 350,000 0.25 Cost of capital is 10% p.a. Required: Calculate the expected net present value of project. Uncertainty:- Uncertainty cannot be quantified, but can be described using different techniques e.g. payback period. Adjusted payback period, sensitivity analysis and simulation. Simple payback period and adjusted payback period:- We have covered in earlier studies (basic techniques of investment appraisal). The quicker the payback the less relevant a project is on the later, more uncertain cash flows. Sensitivity Analysis: Definitions:- Sensitivity analysis assess how responsive the projects’ NPV is to changes in the variables used to calculate that net present value. In general, risky projects are those whose future cash flows, and hence the project returns, are likely to be variable. The greater the variability is, the greater the risk. The problem of risk is more accurate with capital investment decisions than other decisions for the following reasons.  Estimates of capital expenditure might be for several years ahead, such as for major consumption projects. Actual costs may escalate well above budget as the work progresses.  Estimates for benefits will be for several years ahead, sometimes 10, 15 or 20 years ahead or even longer, and long-term estimates can be at best by approximations.  Practical factors may be those over which managers have no control. 34

Study Notes Financial Management - FM Formula to calculate sensitivity of a particular cashflow: - ������������������������������������������������������������������ (%) = ������������ ������������ ������������������ ������ 100% ������������������������ ������������ ������������������������������������������������������������ Formula to calculate sensitivity of cost of capital:- ������������������������������������������������������������������ (%) = ������������������ − ������������������������ ������������ ������������������������������������������ ������ 100% ������������������������ ������������ ������������������������������������������ The best approach of sensitivity analysis is to calculate the projects net present value under alternative assumptions to determine how sensitive it is to changing conditions. This indicates which variables may impact most upon the net present value (critical variables) and the extent to which those variables may change before the investment results in a negative NPV. Advantages of sensitivity analysis:-  This is not a complicated theory to understand  Information will be presented to management in a form, which facilitates subjective judgment to decide the likelihood of the various possible outcomes considered  Identifies areas, which are crucial to the saucers of the project, if it is proceed with, those areas can be carefully monitored  Indicates just how critical are some of the forecast which are considered to be uncertain Disadvantages of sensitivity analysis:-  It assumes that changes to variables can be made independently e.g. in isolation, material prices will change independently of others variables. This is unlikely. If material prices went up, the firm would probably increase selling price at the same time and there would be little effect on net present value  It only identifies how far a variable needs to change; it does not look at the probability of such a change. In the above analysis, sales volume appears to be the most crucial variable, but if the firm were facing volatile raw material markets a 65% change in raw material prices would be far more likely than a 29% change in sales volume.  It is not an optimizing technique. It provides information on the basis of which decision can be made. It does not point to the correct decision directly. Lecture example: $/unit Initial investment in a project is $1,000,000. 100 Project life is 4 years. 50 Sales limits per year are 20,000. 20 5.0 Selling price Material cost Labour cost Variable overheads Increment fixed cost is $100,000 per annum cost of capital is 10% p.a. 35

Study Notes Financial Management - FM Required: a) Calculate net present value of the project. b) Calculate sensitivity of each variable of the project. Solutions Sensitivity Analysis Initial inv. Cash flow D.F. PV Yr Sales (1000) 1 (1000) T0 Mat 2000 6338 Lab (1000) 3.169 (3169) T1 – T4 v.FOH (400) 3.169 (267) T1 – T4 Inc. F.C (100) 3.169 (316.9) T1 – T4 RV (150) 3.169 (475.35) T1 – T4 50 3.169 34.150 T1 – T4 0.683 + 143.37 T4 % age sensitivity = ������������������ ������������ ������������ ������������������������������������������������ Initial NPV = 143.3 × 100 1000 = 14.33% Sales = 143.3 × 100 => 2.26% Mat 6338 Lab V.FOH = 143.3 × 100 => 4.526% In. FC 3169 R.V = 143.3 × 100 => 11.3% 1267.6 = 143.3 × 100 => 45.22% 3169 = 143.3 × 100 => 30.14% 475.35 = 143.3 × 100 => 419.61% 34.150 Certainty equivalents: Definition:- One particular approach to sensitivity analysis, the certainty equivalent approach, involves the conversion of the expected cash flows of the project to risk less equivalent amounts. The greater the risk of an expected cash flow, the smaller the certainty equivalent value (for receipts) or the larger the certainty equivalent value (for payments). The disadvantage of the certainty equivalent approach is that the amount of the adjustment to each cash flow is decided subjectively by management. As the cash flow are reduced to supposedly certain amounts they should then be discounted at a risk free rate. 36

Study Notes Financial Management - FM Lecture example: Initial investment in a project is $20,000. Sales Revenue $/Annum Material cost 40,000 Labour cost 15,000 Cost of capital 5,000 10% Project life is 4 years. Following are the ratio of certainty equivalent for cash inflows and cash outflow. Year Cash inflow Cash outflow 1 0.95 1.06 2 0.90 1.10 3 0.85 1.15 4 0.80 1.18 Required: Calculate the NPV of project using certainty equivalent approach. Solutions Ex #1 T0 T1 T2 T3 T4 $(000) $(000) $(000) $(000) $(000) Sales Less MC (20) 38 36 34 32 Less VC (200 (15.9) (16.5) (17.25) (17.7) Initial (5.3) (5.5) (5.75) (5.9) 1 D.F (20) 16.8 14 11 8.4 0.909 0.826 0.751 0.683 NPV = +20.833 15..271 11.564 8.261 5.737 Simulation: use of simulation:- Simulation is a technique, which allows more than one variable to change at the same time. One example of simulation is a mathematical model, which could be approached using the “Monte Carlo” method. 37

Study Notes Financial Management - FM Stages in simulation:-  Specify the major variables  Specify the relationship between the variables  Attach probability distribution to each variable and assign random members to reflect the distribution.  Stimulate the environment by generating random numbers.  Reward the outcomes of each simulation.  Repeat simulation many times to obtain a probability distribution of likely outcomes. Advantages of simulation:  It gives more information about the possible outcomes and their relative probability.  It is useful for problems, which cannot be solved analytically. Limitations in simulation:  It is not a technique for making a decision only for obtaining more information about the possible outcomes.  It can be very time-consuming without a computer.  It could prove expensive in designing and running the simulation on a computer.  Simulations are only as good as the probabilities assumptions and estimates made. Variables:- The net present value could depend on a number of certain independent variables.  Selling price  Sales volume  Cost of capital  Initial cost  Operating costs  Benefit 38

Study Notes Financial Management - FM Cost of Capital A fundamental calculation for all companies is to establish its financing costs, both individually for each component of finance and in total terms. These will be of use both in terms of assessing the financing of the business and as a cost of capital for use in investment appraisal. Risk and Return The relationship between risk and return is easy to see, the higher the risk, the higher the required to cover that risk. Overall Return A combination of two elements determine the return required by an investor for a given financial instrument. 1. Risk-free return – The level of return expected of an investment with zero risk to the investor. 2. Risk premium – the amount of return required above and beyond the risk-free rate for an investor to be willing to invest in the company Degree of Risk Risk Free High Risk Investment Government Secured Un-Secured Preference Ordinary Debt Loans Loans Shares Shares WACC Capital structure theories Ke=Cost of Kd= Cost of debt Kp=Cost of Project specific equity preference Discount rate share 39

Study Notes Financial Management - FM Different types of Cost of Capital Cost of equity: the rate of return that is required by the equity holders of the company. The symbol used to represent cost of equity is Ke. Cost of debt: this the after-tax return required by the debt holders of the company. The symbol used to represent after-tax cost of debt is Kd (1 – t). Cost of preference shares: the return required by the the preference shareholders of the company. The symbol used to represent cost of preference shares is Kp. Methods of calculating the cost of Equity It can be calculated using two of the following methods: Dividend Valuation Model: used for companies that pay: Constant dividend Constant growth in dividends Capital Asset Pricing Model (CAPM): The Dividend Valuation Method Constant Dividend per Year M.v = ������������������������������������������ ������������������������������������������������ ������������ Ke = ������������������������������������������ ������������������������������������������������ ������ 100% ������0 Where, ������0= Current market value of equity share ������������= cost of equity Dividends With Constant Growth Per Year M.v = ������������������������������������������ ������������������������������������������������ (1+������) ������������−������ Where, ������0= Current Ex-market value of equity share g = sustainable growth rate 40

Study Notes Financial Management - FM Difference between cum dividend and ex dividend price Ex-dividend price (P0) is the market price excluding dividend and cum-dividend price is the market price including dividend. Cum-Dividend Price Less: Dividend Ex-Dividend Price Calculating the sustainable growth rate for dividends There are 2 main methods of determining growth: 1 THE AVERAGING METHOD ������ = ���√��� d������ − 1 d������ where do = current dividend Example dn = dividend n years ago Munero Ltd paid a dividend of 6p per share 8 years ago, and the current dividend is 11p. The current share price is $2.58 ex div Required: Calculate the cost of equity Solution ������ = 8√11 − 1 = 7.9% 6 Ke = 0.11(1+7.9%) + 7.9% = 12.47% 2.58 2. GORDON’S GROWTH MODEL g = rb where r = return on reinvested funds b = proportion of funds retained Example The ordinary shares of Titan Ltd are quoted at $5.00 ex div. A dividend of 40p is just about to be paid. The company has an annual accounting rate of return of 12% and each year pays out 30% of its profits after tax as dividends. Required: Estimate the cost of equity 41

Study Notes Financial Management - FM SOLUTION g = 12% X (1-30%) = 8.4% Ke = 0.4(1+8.4%) + 8.4% = 17.07% 5 Capital asset pricing Model (CAPM) There are two types of risk 1. Market or systematic risk is risk that cannot be diversified away. 2. Non- systematic or unsystematic risk applies to specific individual company or industry, and can be reduced or eliminated by diversification. Systematic risk is how market factors effect that investment. Market factors are:-  Macroeconomic variables  Political factors CAPM assumes that the investor has eliminated the unsystematic risk. Diversification By holding a portfolio, the unsystematic risk is diversified away but the systematic risk is not and will be present in all portfolios. If we were to enlarge our portfolio to include approximately 25 shares we would expect the unsystematic risk to be reduced to close to zero, the implication being that we may eliminate the Unsystematic portion of overall risk by spreading investment over a sufficiently diversified portfolio. Capital Asset Pricing Model(.CAPM) Unsystematic Risk Systematic Risk Related to general economy  Specific to company  includes Macro-economic factors and affects the whole economy  individual industries  Cannot be reduced through diversification. E.g. political risk, interest rate, inflation rate  A method for reducing this risk is through Beta:It is a relative systematic risk of company's earnings with the market systematic risk. diversification.  As market risk =1  E.g. employees on strike,key employee  Beta can be > 1 More risky compare to market  Diversification: it is process whereby we Beta can be < 1 Less risky compare to market spread our investment by holding a portfolio of unrelated stocks which results in the reduction of un  CAPM assumes that all investors are rational and will hold well diversified portfolio (means there is no unsystematic risk.) 42

Study Notes Financial Management - FM CAPM Formula = Rf + β (Risk Premium) Cost of Equity Cost of Equity = Rf + β (Rm-Rf) Where, Rf = Risk free rate β = measure of relative systematic risk Risk Premium = ERM Rf RM = Expected Return on Market (Rm-Rf)=Market risk premium or equity risk premium It is assumed that investors are rational & will hold a well diversified portfolio (unsystematic risk will be reduced to minimum level).  Transaction cost is low or nil.  Investors have homogeneous expectations about the market.  Market is perfect and all investors have same level of information & no individual can dominate the market.  Debt beta is zero.  There is no cost of acquiring information. No individual can dominate the market. Advantages of CAPM  It considers only systematic risk, reflecting a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated.  It generates a theoretically – derived relationship between required return and systematic risk which has been subject to frequent empirical research and testing.  It is generally seen as a much better method of calculating the cost of equity than the dividend growth model (DGM) in that it explicitly takes into account a company’s level of systematic risk relative to the stock market as a whole.  It is clearly superior to the WACC in providing discount rates for use in investment appraisal. Limitations of CAPM  It might be difficult to locate information needed for calculating CAPM. Government securities are assumed to be risk- free, but the return on these securities varies according to their term to maturity. Market rate of return is hard to estimate different economic environments and the probabilities of the various environments. An appropriate Beta equity might not be located, as it might not be feasible to find a proxy company with business operations similar to the proposed investment project. Moreover, most companies have a range of business operations they undertake and so their equity betas do not reflect only the desired level and type of business risk.  It assumes that a perfect capital market exists, when in reality capital markets are only semi- strong form efficient at best.  It assumes that investors hold diversified portfolio’s, i.e. the investors will only require a return for the systematic risk of their portfolios, since unsystematic risk has been removed and can be ignored. This is not necessarily the case, meaning that some unsystematic risk may remain.  The CAPM is really just a single Period model. Few investment projects last for one year only and to extend the use of the return estimated from the model to more than one time period would require both project performance relative to the market and the economic environment to be reasonably stable. 43

Study Notes Financial Management - FM  CAPM assumes no transaction costs associated with trading securities.  Additionally, the idea that all unsystematic risk is diversified away will not hold true if stocks change in term of volatility. As stock change over time it is very likely that the portfolio becomes less than optimal.  CAPM assumes investors can borrow and lend at the risk- free rate of return.  CAPM assumes that debt beta is zero which may not be appropriate in many cases Dividend Growth Model vs CAPM The dividend growth model allows the cost of equity to be calculated using empirical values readily available for listed companies. Measure the dividends, estimate their growth (usually based on historical growth), and measure the market value of the share (though some care is needed as share values are often very volatile). Put these amounts into the formula and you have an estimate of the cost of equity. However, the model gives no explanation as to why different shares have different costs of equity. Why might one share have a cost of equity of 15% and another of 20%? The reason that different shares have different rates of return is that they have different risks, but this is not made explicit by the dividend growth model. That model simply measures what’s there without offering an explanation. Note particularly that a business cannot alter its cost of equity by changing its dividends. Dividend valuation model might suggest that the rate of return would be lowered if the company reduced its dividends or the growth rate. That is not so. All that would happen is that a cut in dividends or dividend growth rate would cause the market value of the company to fall to a level where investors obtain the return they require. The CAPM explains why different companies give different returns. It states that the required return is based on other returns available in the economy (the risk free and the market returns) and the systematic risk of the investment – its beta value. Not only does CAPM offer this explanation, it also offers ways of measuring the data needed. The risk free rate and market returns can be estimated from economic data. So too can the beta values of listed companies. It is, in fact, possible to buy books giving beta values and many investment websites quote investment betas. When an investment and the market is in equilibrium, prices should have been adjusted and should have settled down so that the return predicted by CAPM is the same as the return that is measured by the dividend growth model. Implications of systematic risk & unsystematic risk  If an investor wants to avoid risk altogether, he must invest entirely in risk-free securities.  If an investor holds shares in just a few companies, there will be some unsystematic risk as well as systematic risk in his portfolio, because he will not have spread his risk enough to diversify away the unsystematic risk. To eliminate unsystematic risk, he must build up a well diversified portfolio on investments.  If an investor holds a balanced portfolio of all the stocks and shares on the stock market, he will incur systematic risk which is exactly equal to the average systematic risk in the stock market as a whole. Factors determining the beta of a company’s equity shares  Sensitivity of the company’s cash flow to economic factors, as stated above. for example sales of new car are more sensitive than sale of basic food and necessities.  The company’s operating gearing. A high level of fixed cost in the company’s cost structure will cause high operating profit compared with variations in sales. 44

Study Notes Financial Management - FM  The company’s financial gearing. High borrowing and interest cost will cause high variation in equity earning compared with variation in operating profit, increasing the equity beta as equity returns become more variable in relation to market as whole. This effect will countered by the low beta of debt when computing the weighted average beta of the whole company. Cost of Debt Capital Each item of debt finance for a company has a different cost. This is because debt capital has differing risk, according to whether the debt is secured, whether it is senior or subordinated debt, and the amount of time remaining to maturity. Cost of debt is adjusted for taxation because of the tax savings available on annual interest. The different types of debt are:  Irredeemable debt  Redeemable debt (redeemable fixed rate bonds)  Variable rate debt (floating rate debt)  Non-tradable debt  Convertible debt  Corporate debt 45

Study Notes Financial Management - FM COST OF IRREDEEMABLE DEBT ������������(������������������) = ������(1−������) ������100% ������������ where i = interest paid t = marginal rate of tax P0 = ex interest (similar to ex div) market price of the loan stock. Example The 10% irredeemable loan notes of Rifa plc are quoted at $120 ex-interest. Corporation tax is payable at 30% Required: What is the cost of debt net? SOLUTION ������������(������������������) = 10(1−30%) ������100% = 5.83% 120 Cost of Redeemable Debt The cost of redeemable bonds is their redemption yield. This is calculated as the rate of return that equates the present value of the future cash flows payable on the bond (to maturity) with the current market value of the bond. In other words, it is the IRR of the cash flows on the bond to maturity, assuming that the current market price is a cash outflow. In order to calculate Kd calculate after tax value of interest. Year Cash Flow D.F @ 5% P.Values D.F @other rate P.Values 0 (M.v) 1.000 (××) 1.000 (××) 1–5 Interest(1-t) A.f ×× A.f ×× 5 Redemption Value D.f ×× D.f ×× ×× ×× 46

Study Notes Financial Management - FM Example of Cost of Redeemable Debt The current market value of a company’s 7% loan stock is 96.25. Annual interest has just been paid. The bonds will be redeemed at per after four years. The rate of taxation on company profits is 30%. Required: Calculate the after-tax cost of the bonds for the company. Year Cash Flow D.F @ 5% P.Values D.F @ 10% P.Values 0 (96.25) 1.000 (96.25) 1.000 (96.25) 1–4 4.90 3.546 17.38 3.170 15.53 4 100 0.823 82.30 0.683 68.30 3.43 (12.42) Kd (1 – t) =5% + [ 3.43 ������(10 − 5)] % = ������. ������������% 3.43+12.42 Convertible Debt Here bond holders have choice to either redeem the debt or convert the debt into predetermined number of shares. The method of calculating cost of debt for convertible is same as calculating the cost of debt of redeemable debt. The problem here is that we do not know whether the bond holder would exercise the conversion option or not. Therefore we take higher value of redemption value or conversion value. Conversion Value is calculated as: Conversion Value = M.V per share at time of conversion x No. of Shares M.V at the time of conversion = Current M.v × (1+g)^n Where, g = Share price growth n = no. of years in conversion Example of Cost of Convertible Debt The current market value of a company’s 7% loan stock is 96.25. Annual interest has just been paid. The bonds will be redeemed at per after four years or convertible into 20 ordinary shares. Current share price is $4.44 and it is expected that it will grow with a growth of 5% per year. The rate of taxation on company profits is 30%. 47

Study Notes Financial Management - FM Required: Calculate the after-tax cost of the bonds for the company. Answer: Conversion Value = 20× 4.44 × 1.05^4=$108 Redemption Value=$100 Investor are rational and will chose the higher Value Year Cash Flow D.F @ 10% P.Values D.F @ 5% P.Values 1.000 (96.25) 0 (96.25) 1.000 (96.25) 17.38 3.546 88.88 1–4 4.90 3.170 15.53 10 0.823 4 108 0.683 73.76 (7) Kd (1 – t) =5% + [ 10 ������(10 − 5)] % = ������. ������������% 10+7 Cost of Variable Rate Debt & Non-Tradable Debt Variable or Floating Rate Debt Company will pay what you demand. Interest rate and required rate if same then market value will be same as redemption. Because Kd=Interest % x (1-t) book value = market value Non-tradable Debt An example of non-tradable debt is bank loan. Kd=Interest % x (1-t) 48