1. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury MANAGEMENT AND COST ACCOUNTING SIXTH EDITION COLIN DRURY

2. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury © 2000 Colin Drury Part Three: Information for decision-making Chapter Fourteen: Capital investment decisions 2

3. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.1a © 2000 Colin Drury Capital investments with unequal lives Machines A and B are two mutually exclusive machines A ’s life =3 years and B’s life =2 years Can we base the decision on the NPV or IRR ’s of each machine? (Only if the task for which they are required ceases at the end of the project lives). What if the task for which the machines are required is for many years (say >6 years)? We are faced with a replacement chain problem and as long as the common denominator for the project lives is less than the task life we can use either the lowest common multiple method or the equivalent annual cash flow method. Lowest common denominator method: Lowest common multiple =6 years (2 replacements of machine A and 3 of B)

4. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.1b © 2000 Colin Drury

5. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.2a © 2000 Colin Drury Equivalent annual cost (cash flow) method: 1.The costs are made comparable by converting the cash flows to an equivalent annual cost (EAC). 2. EAC = PV of costs /Annuity factor for n years at R% 3. EAC for A = £1 796.8/2.4869 (Based on years 0 –3) or £3 146.8/4.3553 (Based on years 0 –6) = £722.5 for both time periods 4 EAC for B =£705.7 (calculated as above) 5. The cash flow stream of A is equivalent in PV terms to an annual cash outflow of £722.5 (£705.7 for B). Therefore choose B

6. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.2b © 2000 Colin Drury Assume the task life < lowest common denominator Task life = 10 years Machine X life = 6 years Machine Y life = 8 years Lowest common multiple is 24 years Suggest use a 10 year horizon with each machine being replaced once and incorporate an estimate of machine realisable values at the end of year 10.

7. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.3a © 2000 Colin Drury Single period capital rationing 1. Refers to a situation where investment funds are restricted and it is not possible to accept all positive NPV projects. 2. Where capital rationing exists, ranking in terms of NPVs will normally result in an incorrect allocation of scarce capital. 3. The correct approach is to rank by profitability index (PI): PI = PV Investment outlay

8. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.3b © 2000 Colin Drury 4.Example Project NPV PI I 0 PV NPV PI ranking ranking £££ A 25 000 32 500 7 500 1.30 6 2 B 100 000 108 250 8 250 1.08 5 6 C 50 000 75 750 25 750 1.51 1 1 D 100 000 123 500 23 500 1.23 2 3 E 125 000 133 500 8 500 1.07 4 7 F 25 000 30 000 5 000 1.20 7 4 G 50 000 59 000 9 000 1.18 3 5 Funds available for investment are restricted to £200 000. 5. NPV ranking leads to acceptance of C,D and G (NPV = £58 250). PI ranking leads to acceptance of C,A,D and F (NPV = £61 750).

9. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.4a © 2000 Colin Drury Taxation and investment decisions 1.Taxation legislation specifies that net cash inflows of companies are subject to taxes,and capital allowances (writing down allowances) are available on capital expenditure. Example I 0 = £100 000, cash inflows = £50 000 for four years Estimated sale proceeds = Tax WDV at end of year 4 Capital allowances = 25% on a reducing balance basis Corporate tax rate = 35%

10. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.4b © 2000 Colin Drury 2.Calculation of capital allowances Annual Year WDAs WDV £ 0 0 100 000 1 25 000 (25% × 100 000) 75 000 2 18 750 (25% × 75 000) 56250 3 14 063 (25% × 56 250) 42187 4 10 547 (25% × 42 187) 31 640

11. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.4c © 2000 Colin Drury 3. Calculation of incremental taxes arising from the project: Year Year 1 2 3 4 £ £ £ £ Incremental profits 50 000 50 000 50 000 50 000 WDAs 25 000 18 750 14 063 10 547 Taxable profits 25 000 31 250 35 937 39 453 Taxes at 35% 8 750 10 937 12 578 13 809

12. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.5 © 2000 Colin Drury Taxation and investment decisions 4.If the estimated sale proceeds exceeded the WDV (say, £45 000) there would also be an additional balancing charge of £13 360 (£45 000 – £31 640) to deduct from the WDAs in year 4 (taxable profits would equal £52 813). 5.If the estimated sale proceeds were less than the WDV (say £25 000) there would be an additional balancing allowance of £6 640 (£31 640 –£25 000) to add to the WDAs in year 4.

13. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.6a © 2000 Colin Drury Dealing with inflation Inflation affects both future cash flows and interest rates (i.e.RRR /discount rate) Impact on Cash Flows Assume no inflation and estimated cash flows of £100 at time 1 and you can buy a basket of goods for £1 at time 0 Therefore your cash flow has the potential of buying 100 baskets at time 0 or time 1. Assume now estimated inflation is 10% Estimated cash flows at time 1 = £110 The cash flows have increased but your purchasing power is unchanged (You still have the potential to purchase 100 baskets i.e.£110 /£1.10)

14. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.6b © 2000 Colin Drury Cash flows can be expressed in monetary units at the time they are received (i.e.nominal cash flows = £110 at time 1) or they can be expressed in today ’s (time zero) purchasing power (i.e.real cash flows =£110 /£1.10 = £100) therefore £110 nominal cash flows is equivalent to £100 in real cash flows. Nominal CF ’s = Real CF ’s ×(1 + inflation rate) n = £100 (1.10) 1 =£110 Real CF ’s = Nominal CF ’s = £110 /1.10 1 =£100 (1 +inflation rate) n REAL CASH FLOWS ARE WHAT THE CASH FLOWS WOULD BE IN A WORLD OF NO INFLATION

15. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.7 © 2000 Colin Drury Impact of inflation on interest rates (also discount rates) Assume the interest rate is 2% in a world of no inflation therefore you require £102 for an investment of £100 (provides purchasing power to purchase 102 baskets) Now assume the anticipated rate of inflation is 10%. You require a NOMINAL return of 12.2% to maintain your purchasing power (£112.20 /£1.10 =102 baskets) REAL RATE OF INTEREST RATE = WHAT THE INTEREST RATE WOULD BE IN A WORLD OF NO INFLATION 1 +Nominal rate= (1 +Real rate)× (1 +Est.inflation rate) = (1 +0.02)× (1 +0.10) = 1.122 =12.2% 1 +Real rate = (1 +Nominal rate)/(1 +Est.inflation rate) = (1 +0.122)/(1 +0.10)=1.02 =2% Approximations may suffice 2%real rate +10% inflation rate =12%approximation Note that interest rates and RRR ’s on securities are derived from current financial market data (.they will already be expressed in nominal terms)

16. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.8a © 2000 Colin Drury Investment appraisal and inflation Two correct approaches: 1. Discount nominal cash flows at a nominal discount rate 2. Discount real cash flows at the real discount ate Example A company is appraising a project with an investment outlay of £200,000 with estimated annual cash inflows of £100,000 per annum for years 1, 2 and 3.The cost of capital is 9% and the expected rate of inflation is zero. NPV =100 /(1.09)+100 /(1.09) 2 +100 /(1.09) 3 – 200 = 53.1 NOW ASSUME ANTICIPATED RATE OF INFLATION =10%

17. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.8b © 2000 Colin Drury 1. Discount nominal cash flows at the nominal discount rate NPV = 100 (1.10) + 100 (1.10) 2 + 100 (1.10) 3 - 200 = 53.1 (1.09)(1.10) (1.09) 2 (1.10) 2 (1.09) 3 (1.10) 3

18. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.8c © 2000 Colin Drury 2. Discount real cash flows at the real discount rate NPV =100 /(1.09)+100 /(1.09) 2 +100 /(1.09) 3 –200 =53.1 We have assumed that current price cash flows are equivalent to real cash flows but this only applies if all company cash flows are subject to the general rate of inflation. WHAT IF THE CASH FLOWS ARE SUBJECT TO A SPECIFIC RATE OF INFLATION OF 8% AND THE GENERAL RATE FOR THE ECONOMY IS 10%? We must calculate real cash flows as follows: Year 1 =100 (1.08)/1.10; Year 2 =100 (1.08) 2 /(1.10) 2 In these circumstances it is easier to discount nominal cash flows at a nominal discount rate.

19. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.9a © 2000 Colin Drury Calculating risk adjusted discount rates 1. The returns which shareholders require from investing in risky securities = Risk free rate + Risk premium. 2. The greater the risk, the greater the return required by investors. 3. The market portfolio is used as a benchmark for determining risk/return relationships.The risk of an investment relative to the market portfolio is measured by beta: An investment with identical risk to the market portfolio will have a beta of 1. An investment half as risky as the market portfolio will have a beta of 0.5. An investment twice as risky as the market portfolio will have a beta of 2.

20. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.9b © 2000 Colin Drury 4. The return that shareholders require (i.e.the opportunity cost of an investment) is: Risk free rate + (Risk premium × Beta) = CAPM formula 5. The past average risk premium of 8% (defined as the return on the market portfolio less the risk free rate) is normally used. If the risk free rate is 4% then the following returns will be required: Security A (Beta of 1) = 4%+(8%×1) = 12% Security B (Beta of 0.5) = 4%+(8%×0.5) = 8% Security C (Beta of 2) = 4%+(8%×2) = 20% 6. Note the risk premium = (Return on the market – risk free rate)

21. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.10 © 2000 Colin Drury The capital asset pricing model Required return on a security = Rf +(Rm –Rf) × Beta

22. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.11 © 2000 Colin Drury Weighted average cost of capital (WACC) 1. The CAPM is used to calculate the cost of equity finance. 2. Most firms use a combination of debt and equity finance and both sources of finance should be taken into account when calculating the discount rate. 3. Where combinations of debt and equity are used, the WACC is used to discount project cash flows. Example Cost of equity capital = 18% Cost of debt capital = 10% Projects financed by 50% debt and 50% equity WACC = (0.5 × 18%)+(0.5 ×10%) = 14% 4.The WACC represents the firm ’s overall cost of capital based on the average risk of all the firm ’s projects. If the risk of a project differs from average firm risk the WACC of the firm will not reflect the correct risk-adjusted discount rate.

23. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.12 and 14.13 © 2000 Colin Drury Standard deviations and probability distributions Use overhead as transparency

24. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.14a © 2000 Colin Drury Sensitivity analysis 1.Shows how sensitive NPV is to a change in the assumptions relating to the variables used to compute it (e.g.pessimistic, most likely or optimistic estimates).Can also be used to indicate the extent to which variables may change before NPV becomes negative.

25. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.14b © 2000 Colin Drury Example Year Year Year 1 (£) 2 (£) 3 (£) Cash inflows (10 000 × £30)300 000 300 000 300 000 VC 200 000 200 000200 000 Net cash flows 100 000 100 000100 000 I 0 =£200 000, cost of capital =15%, NPV =£28 300 2. Sales volume NPV =0 when net cash flows are £87 600 (£200 000 / 2.283) Total net cash flows can decline by £12 400 p.a.before NPV becomes negative Total sales can fall by £37 200 p.a.(i.e.12.4%)or 1240 units Note net cash flows are one-third of sales.

26. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.14c © 2000 Colin Drury 3. Selling price Total sales revenue can fall to £287 600 (£300 000 – £12 400)before NPV becomes negative =£28.76 per unit (i.e.4.1% decline) 4. Variable costs Can increase by £12 400 p.a.(£1.24 per unit) = 6.2% decline. 5. Initial outlay Can increase by £28 300 (14.15%).

27. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.15 © 2000 Colin Drury Sensitivity analysis (cont.) 6. Cost of capital IRR =23%(cost of capital can increase by 53%). 7. Highlights those variables that are most sensitive so that their estimates can be thoroughly reviewed. 8. Limitations Considers variables in isolation. Ignores probabilities

28. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.16 © 2000 Colin Drury Classification of risk measurement techniques 1.CAPM approach Risk is compared relative to the variability with the market portfolio. Risk is divided into two categories: (i) Specific (diversifiable) risk (ii) Market (non-diversifiable) risk CAPM assumes specific risk can be avoided and it is not rewarded. CAPM assumes market rewards only non-diversifiable risk.

29. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.16 © 2000 Colin Drury 2. Stand-alone risk measurement approach Does not distinguish between specific and non-diversifiable risk. Does not provide a basis for determining the rates of return required for different levels of risk. 3. Corporate portfolio risk measurement approach Focuses on incremental total risk arising from a project. Recognizes that incremental risk may not be the same as the total risk of the project.

30. Management and Cost Accounting, 6 th edition, ISBN 1-84480-028-8 © 2004 Colin Drury 14.16 © 2000 Colin Drury Example SD of project X = £10 000 SD of existing projects = £60 000 SD of existing projects plus project X = £65 000 Incremental risk of project X = £5 000 (not £10 000) Does not distinguish between specific and non-diversifiable risk. Difficult practical problems in measuring risk of existing projects