Capital investment decisions: 1

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1 Capital investment decisions: 1 Solutions to Chapter 13 questions Question (i) Net present values: Year 0% 10% 20% NPV Discount NPV Discount NPV ( ) Factor ( ) Factor ( ) 0 ( ) ( ) ( ) NPV (14 922) (ii) Project NPV Profile NPV Approx. IRR = 14% Discount Rate % 10 Figure Q x 104 CAPITAL INVESTMENT DECISIONS: 1

2 (a) The answer should include the following points: 1 Computations of the payback period and accounting rate of return (see below for the calculations), a description of the methods and their benefits and limitations (see text for a discussion of the payback and accounting rate of return methods). 2 A computation of the net present value (see below) and an explanation as to why this method is preferred to the other methods (see text for an explanation). 3 A recommendation that since the project has a positive net present value it should be accepted. 4 A discussion of the difficulties associated with NPV. These include the greater potential for a lack of understanding by non-accountants, difficulties in estimating cash flows over the whole life of the asset and the difficulty in deriving the discount rate. Question Computation of the payback period The cumulative cash flows for years 4 and 5 are and Therefore, the payback period occurs between years 4 and 5. Assuming that cash flows accrue evenly throughout the year, a cash flow of is required in year 5 to reach the payback period. This represents 7 months ( / months). Therefore, the payback period is 4 years and 7 months. This is above the target payback period of 4 years, so the project would be rejected using this method. Computation of accounting rate of return Total cash flows = ( 400 3) + ( 500 2) + ( 450 3) + ( 400 2) = Less depreciation/initial outlay = Total profits over the period = Average annual profit = Average investment (Initial cost/2) = Accounting rate of return = 23.5% This is below the target return so the project would be rejected. (b) Computation of NPV Year Cash flows ( 000 s) Discount factor (15%) a Present value ( 000 s) Less initial outlay NPV Note a The discount factors are derived by summing the factors for years 1 3, 4 5, 6 8 and 9 10 in the discount tables. The project has a positive NPV and should be accepted. 1 For the answer to this question see Controlling the capital expenditure during the installation stage and Post-completion audits in Chapter 13. CAPITAL INVESTMENT DECISIONS: 1 105

3 Question (a) Estimated incremental net cash flows and NPV from project VZ Inflows: 20X1 20X2 20X3 20X4 20X5 ( 000) ( 000) ( 000) ( 000) ( 000) Sales a Savings in salaries of employees made redundant b Residual value of new machine 242 Material XNT, savings on cost of disposal Outflows: Purchases c Loss of sale proceeds from old machine 12 Employee promoted d Redundancy pay 62 Material XPZ, lost residual value 3 Sub-contractors Lost contribution from existing product Overheads and advertising e Taxation Total Incremental net cash flow Discount factors at 10% Present value ( 000) Less net investment outlay ( ) NPV ( 000s) 56.3 Notes a The cash inflows from sales are calculated as follows: 20X1 20X2 20X3 20X4 20X5 ( 000) ( 000) ( 000) ( 000) ( 000) Opening debtors Add sales Less closing debtors Cash from sales b Four employees at per year inflated at 5% per annum c The cash outflows for purchases is calculated as follows: 106 CAPITAL INVESTMENT DECISIONS: 1

4 Opening creditors Add purchases Less closing creditors Cash paid for purchases d incremental costs inflated at 5% per annum e Difference in costs between new and old product line (b) (i) The report should explain that the figures incorporate only the incremental cash flows arising from undertaking the project. In addition the following information should be included in the report: (i) The feasibility study is a sunk cost. (ii) Depreciation is a non-cash item and the net investment cost is incorporated as a deduction from the total present value of the net cash flows. Including depreciation will result in double counting. (iii) The paid to the three employees is not a relevant cash flow because it will be paid whether or not the project goes ahead. (iv) The original purchase price for both types of materials is a sunk cost and is not relevant to the decision. (v) The relevant figures for a NPV calculations are cash flows and therefore no adjustment is required for prepayments. (b) (ii) The report should indicate that on the basis of the financial appraisal the project should be undertaken because it has a positive NPV. However, it should be pointed out that the cash flows have been discounted at the company s average cost of capital of 10%. If the risk of the project is higher than the average for the firm as a whole then a higher cost of capital should be used. Other factors that should be incorporated in the report include the effect on staff morale of the redundancies, the reliability of the estimates, the likely response from the competitors and the alternative use of the capacity. (a) Alternative 1 NPV: Question Year Cash flow Discount factor PV ( 000) ( 000) NPV IRR: The cash flow sign changes after year 1, which implies that the project will have two IRRs. Using the interpolation method, the NPV will be zero at a cost of capital of 5% and 50%. Therefore the IRRs are 5% and 50%. Alternative 2 NPV: Year Cash flow Discount factor PV ( 000) ( 000) NPV 3.34 CAPITAL INVESTMENT DECISIONS: 1 107

5 IRR: At a 25% discount rate the project has an NPV of Using the interpolation formula: 3340 IRR ( 1616) (25 20) 23.4% Summary NPV IRR Alternative % or 50% Alternative % (b) The projects are mutually exclusive and capital rationing does not apply. In these circumstances the NPV decision rule should be applied and alternative 2 should be selected. Because of the reasons described in Chapter 13, the IRR method should not be used for evaluating mutually exclusive projects. Also, note that alternative 1 has two IRRs. Therefore, the IRR method cannot be used to rank the alternatives. Before a final decision is made, the risk attached to each alternative should be examined. For example, novelty products are generally high-risk investments with short lives. Therefore alternative 1 with a shorter life might be less risky. Other considerations include the possibility of whether the promotion of this novelty product will adversely affect the sales of the other products sold by the company. Also, will the large expenditure on advertising for alternative 1 have a beneficial effect on the sales of the company s other products? (c) The answer should include a discussion of the payback method, particularly the limitations discussed in Chapter 13. It should be stressed that payback can be a useful method of investment appraisal when liquidity is a problem and the speed of a project s return is particularly important. It is also claimed that payback allows for uncertainty in that it leads to the acceptance of projects with fast paybacks. This approach can be appropriate for companies whose products are subject to uncertain short lives. Therefore there might be an argument for using payback in Khan Ltd. The second comment by Mr Court concerns the relationship between reported profits and the NPV calculations. Projects ranked by the NPV method can give different rankings to projects that are ranked by their impact on the reported profits of the company. The NPV method results in the maximization of the present value of future cash flows and is the correct decision rule. If investors give priority to reported profits in valuing shares (even if reported profits do not give an indication of the true economic performance of the company) then Mr Court s comments on the importance of a project s impact on reported profits might lead to the acceptance of alternative 1. However, if investors are aware of the deficiencies of published reported profits and are aware of the company s future plans and cash flows then share values will be based on PV of future cash flows. This is consistent with the NPV rule. Question (a) Attending 6 training courses per year Year Travel and accommodation Course costs Total cash flows Discount Present etc. ( 000 s) a ( 000 s) a ( 000 s) factor value ( 000 s) CAPITAL INVESTMENT DECISIONS: 1

6 Note: a Travel etc. = delegates 6 courses = Courses = courses = Travel etc. Year 2 = 522 (1.05), Year 3 = 522 (1.05) 2 and so on. Course costs Year 2 = 70.5 (1.025), Year 3 = 70.5 (1.025) 2 and so on. Proposed e-learning solution Year ( 000 s) ( 000 s) ( 000 s) ( 000 s) ( 000 s) ( 000 s) Hardware a 1500 (50) Software Technical manager and trainers ( ) b Camera and sound Broadband connection Discount factor Present value Total present value = The e-learning solution should be recommended since this has the lowest present value. Notes: a Depreciation is not a relevant cost and should not be included in the analysis. b The technical manager will have to be replaced resulting in an incremental cash flow of per annum. (b) (i) Note that equivalent annual costs/cash flows are explained in Chapter 14. To answer this question it is necessary to separate those costs that are variable with the number of delegates and those that are fixed and thus do not change with the number of candidates. It is assumed that 6 courses will be provided per year. For the course attendance alternative, the course costs are fixed and travel, etc. is variable with the number of delegates. Separate present values must be calculated for course costs and travel, etc. If you discount the second and third columns for the course attendance alternative you will find that the present values are (variable cost) and (fixed cost). Dividing both of these items by an annuity factor for 5 years at 14% (3.433) gives annual equivalent costs of (variable costs) and (fixed cost). For the e-learning costs alternative, the broadband connection is variable with the number of delegates and the remaining costs are fixed. The respective present values are (variable) and (fixed) giving equivalent annual costs of (variable) and (fixed). Therefore, the additional annual equivalent fixed costs for the e-learning alternative are The savings in annual equivalent variable costs from this alternative are ( ) per 100 delegates or 5419 per delegate. Therefore the minimum number of delegates required to achieve the fixed cost savings is ( / 5419). (b) (ii) The required number of delegates to break even is 87%. This is a very high required take-up rate and so the company must ensure that virtually all of the delegates will favour this method of delivery. CAPITAL INVESTMENT DECISIONS: 1 109

7 Question (a) Three alternatives can be identified from the question: 1 Produce product A and replace it with AA at the UK factory. 2 Produce product A, then sell the UK factory in year 2 and make AA in Eastern Europe for 8 years. 3 Produce product A for a limited period, replace with product X and sell the UK factory in year 4 and make Product AA in Eastern Europe for 8 years. Alternative 1 Years Cash flows ( m) Discount factor NPV ( m) 1 Normal sales of product A Normal sales of product A Equipment and training costs for product AA Net cash inflows from AA ( ) Sale of factory a Note: a 5.5m m redundancy costs (2m) = 3.85m Alternative 2 Years Cash flows ( m) Discount factor NPV ( m) 1 Normal sales of product A Normal sales of product A Sale of factory Equipment and training costs for product AA Net cash flows from AA with additional transport costs ( ) Alternative 3 Years Cash flows ( m) Discount factor NPV ( m) 1 Purchase of equipment for X Normal sales of product A Sales of stock of A ( m) Inflows from product X ( ) Inflows from product X ( ) Inflows from product X ( ) Sale of factory Equipment and training costs for product AA Sales of AA with additional transport costs ( ) The first alternative yields the highest NPV. (b) (i) Both alternatives 2 and 3 involve the same transport cost but alternative 3 yields a significantly higher NPV. Therefore it is appropriate to test the sensitivity of transport costs by comparing alternative 3 against alternative 1, which does not involve transport costs. The NPV of alternative 1 exceeds the NPV of alternative 3 by 4.443m ( m ). The present value of 110 CAPITAL INVESTMENT DECISIONS: 1

8 the transport costs is m ( a discount factor of for years 3 10). Therefore, the present value of transport costs would have to fall below 7.283m ( m 4.443m) for alternative 3 to be preferred to alternative 1. This represents annual cash flows of ( 7.283m/5.863 discount factor). Estimated annual cash flows for transport costs are 2m so cash flows would have to decline by which represents a 37.9% decline. (b) (ii) Based on the discussion in (b) (i), it is again appropriate to compare alternatives 1 and 3 where the NPV for alternative 1 exceeds that of alternative 3 by Let SV = net difference in sales value for NPV to be the same for both alternatives so that: SV year 4 discount factor (0.823) SV year 10 discount factor (0.614) = SV = SV = Given that the existing sales value is 5.5m, the sales value can increase to m ( m + 5.5m), representing an increase of approximately 400%. (c) The answer should include a discussion of the following points: 1 the availability of skilled labour; 2 closeness to the market in terms of being able to respond quickly to demand; 3 taxation implications; 4 management problems arising from differences in national cultures; 5 the difficulties that may be encountered in operating a business that is located a considerable distance from central headquarters. (a) The expected number of passengers is derived from the demand at each exchange rate: Expected demand at 1.52 H/ = 0.33 ( ) = 460 Expected demand at 1.54 H/ = 0.33 ( ) = Expected demand at 1.65 H/ = 0.33 ( ) = 560 Expected demand = 0.2(460) + 0.5(506.67) + 0.3(560) = per train (or per day). (b) Cash flows: in-house option Year Sales a Variable costs b ( ) ( ) ( ) ( ) ( ) Contribution Labour costs c (74 844) (78 586) (82 516) (86 641) (90 973) Purchase and insurance d (37 422) (37 422) (37 422) (37 422) (37 422) Asset sale/purchase ( ) Net cash flow ( ) Discount factor at 12% Present value ( ) Net present value = Cash flows: contract out option Year Contract fee f (90 000) (90 000) (90 000) (90 000) (90 000) Asset purchase/sale Purchase and insurance e (16 422) (16 422) (16 422) (16 422) (16 422) Question CAPITAL INVESTMENT DECISIONS: 1 111

9 Net cash flow ( ) ( ) ( ) ( ) ( ) Discount factor Present value (95 035) (84 818) (75 772) (67 684) (60 341) Net present value = The contract out option is preferred because it has the higher NPV of Notes: a Sales revenues = = b Direct materials = = Variable overhead = = Variable costs = c Labour costs = = for year 1, Year 2 = (1.05), Year 3 = (1.05) 2 d Purchase and insurance = = (for in-house provision) e Purchase and insurance = = (for contracting out) f Provision of catering service by outside supplier = days = g Gross catering receipts are 2079 per day ( /360) do not exceed 2200 so the 5% commission does not apply. h Depreciation is not a cash flow and is therefore not a relevant cost. (c) A 10% increase in sales would increase the annual contribution by giving an increase in present value of ( discount factor at 12%). The present value of the additional costs is ( ) resulting in an increase in NPV of This exceeds the NPV of from changing to the contracting out alternative. However, the revised annual sales per day would be 2287 ( ), thus enabling the company to receive 5% of gross sales receipts once sales exceed 2200 per day. The company would therefore receive per annum (5% sales 1.10). This would result in the contracting out alternative having the higher NPV. The choice is highly dependent on future sales being in excess of 2200 per day. (d) The answer should draw attention to the difficulties in deriving probabilities and using past data to estimate probabilities based on the view that the past is indicative of the future. The outcome using probabilities represents an average outcome, which may be unlikely to occur. Also expected values ignore risk. For a more detailed discussion of these points you should refer to the sections on probabilities, probability distributions and expected value and measuring the amount of uncertainty in Chapter 12. (e) The following non-financial factors need to be taken into account: 1 The loss of ability to control the quality and reliability of the service if the service is contracted out. These factors may influence the number of passengers choosing to travel with Amber plc. 2 Impact on staff morale as a result of the reduction in labour costs. Existing staff may be concerned that their jobs are under threat and may leave the company. 3 The difficulty and high costs of changing back to in-service provision once the company has contracted out the service. 4 Willingness of the supplier to respond to changes in market demand. 112 CAPITAL INVESTMENT DECISIONS: 1

Describe the importance of capital investments and the capital budgeting process

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