Part Three: Information for decision-making Chapter Fourteen: Capital investment decisions: the impact of capital rationing, taxation, inflation and risk Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.1a 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

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.1b 4.Example Project NPV PI I 0 PV NPV PI ranking ranking £££ A B C D E F G Funds available for investment are restricted to £ 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).

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.2a 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 = £ , cash inflows = £ 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%

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.2b 2. Calculation of capital allowances Annual Year WDAs WDV £ (25% × ) (25% × ) (25% × ) (25% × )

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.2c 3. Calculation of incremental taxes arising from the project: Year Year £ £ £ £ Incremental profits WDAs Taxable profits Taxes at 35%

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.3 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 £ (£ – £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 (£ –£25 000) to add to the WDAs in year 4.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.4a 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)

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.4b 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 CFs = Real CFs ×(1 + inflation rate) n = £100 (1.10) 1 =£110 Real CF ’s = Nominal CFs = £110 / =£100 (1 +inflation rate) n REAL CASH FLOWS ARE WHAT THE CASH FLOWS WOULD BE IN A WORLD OF NO INFLATION

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.5 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 (£ /£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) = ( )× ( ) = =12.2% 1 +Real rate = (1 +Nominal rate)/(1 +Est.inflation rate) = ( )/( )=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)

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.6a 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) /(1.09) 3 – 200 = 53.1 NOW ASSUME ANTICIPATED RATE OF INFLATION =10%

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.6b 1. Discount nominal cash flows at the nominal discount rate NPV = 100 (1.10) (1.10) (1.10) = 53.1 (1.09)(1.10) (1.09) 2 (1.10) 2 (1.09) 3 (1.10) 3

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.6c 2. Discount real cash flows at the real discount rate NPV =100 /(1.09)+100 /(1.09) /(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.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.7a 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.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.7b 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)

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.8 The capital asset pricing model Required return on a security = Rf +(Rm –Rf) × Beta

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.9 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.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.10a 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.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.10b Example Year Year Year 1 (£) 2 (£) 3 (£) Cash inflows ( × £30) VC Net cash flows I 0 =£ , cost of capital =15%, NPV =£ Sales volume NPV =0 when net cash flows are £ (£ / 2.283) Total net cash flows can decline by £ p.a.before NPV becomes negative Total sales can fall by £ p.a.(i.e.12.4%)or 1240 units Note net cash flows are one-third of sales.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.10c 3. Selling price Total sales revenue can fall to £ (£ – £12 400)before NPV becomes negative =£28.76 per unit (i.e.4.1% decline) 4. Variable costs Can increase by £ p.a.(£1.24 per unit) = 6.2% decline. 5. Initial outlay Can increase by £ (14.15%).

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 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

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.12a Stages in the capital investment process 1.Search for investment opportunities  Without a creative search for new investment opportunities appraisal techniques are worthless 2.Initial screening  Preliminary assessment to ascertain if projects satisfy strategic and risk criteria 3.Project authorizations  Approval by top management committee or lower levels (below specified ceilings) based on financial appraisal and strategic considerations.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.12b Stages in the capital investment process (cont.) Control during the installation stage  Periodic reports required on over/under spending relative to stage of completion, estimated costs to complete and estimation completion date compared with original estimates Post-completion audit  Involves a comparison of the actual results with those included in the investment proposal.  Difficult to undertake because it is not easy to isolate the actual cash flows that stem from individual projects.  Recriminatory post-mortems should be avoided.

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.13a Capital investments with unequal lives (see Learning Note 14.1) ● 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 IRRs 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)

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.13b

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.14a Equivalent annual cost (cash flow) method: 1.The costs are made comparable by converting the cash flows to an equivalent annual cost/cash flow (EAC). 2. EAC = PV of costs /Annuity factor for n years at R% 3. EAC for A = £ / (Based on years 0–3) or £ / (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

Use with Management and Cost Accounting 8e by Colin Drury ISBN © 2012 Colin Drury 14.14b 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.