Making Capital Investment Decisions Solutions to Even-Numbered Problems and Cases 6.2 Manitoba Railroad Limited (MRL) (a) Discount Rate 7% Cash Cash Net Cash Cumulative Year Outflows Inflows Flows Cash Inflows 0 (522) (522) 1 75 75 75 2 75 75 150 3 75 75 225 4 75 75 300 5 75 75 375 6 50 50 425 7 50 50 475 8 50 50 525 9 50 50 10 50 50 11 40 40 12 40 40 13 40 40 14 40 40 15 50 40 90 Average 55 (i) Average annual profit ARR ARR = Average investment to earn that profit 55 = (522 + 50)/2 = 19.23% (ii) PP 8 years See the cumulative cash flow column to see when the initial investment of $522 million is paid back. (iii) NPV $33.18 Calculated by discounting all the net cash flows at 7%. Copyright 2009 Pearson Education Canada 1
(iv) IRR 8.11% The internal rate of return is approximately 8%, found by trial and error. (b) MRL should go ahead with the train cars purchase because the project has a positive $33.18 million NPV. Data: 6.4 Moncton Semiconductors Corporation (MSC) Year 0 Year 1 Year 2 Year 3 Year 4 Sale price per chip ($) P 10 15 25 20 Estimated unit sales (number of chips) Q 100,000 125,000 140,000 110,000 Variable costs per chip ($) V 2.00 3.00 3.00 2.50 Fixed costs ($) 200,000 200,000 200,000 200,000 (a) Cash flows related to the expansion Additional sales revenue (P Q) $1,000,000 $1,875,000 $3,500,000 $2,200,000 Less: Lost contribution 35,000 35,000 35,000 35,000 Variable costs (V Q) 200,000 375,000 420,000 275,000 Fixed costs (increased overhead) 20,000 20,000 20,000 20,000 Total additional costs 255,000 430,000 475,000 330,000 Operating cash flows 745,000 1,445,000 3,025,000 1,870,000 Working capital increase (40,000) Capital cost of the expansion (4,000,000) Net relevant cash flows $(4,040,000) $745,000 $1,445,000 $3,025,000 $1,870,000 Notes 1. Only incremental fixed costs are relevant. Amortization is not a cash flow. 2. The $500,000 already spent is a sunk cost and is not relevant to the decision at hand. Copyright 2009 Pearson Education Canada 2
(b) Payback period Year 0 Year 1 Year 2 Year 3 Year 4 Net relevant cash flows $(4,040,000) $745,000 $1,445,000 $3,025,000 $1,870,000 Net cumulative cash flows $(4,040,000) $(3,295,000) $(1,850,000) $1,175,000 So the payback period is 2 years + 1,850,000/3,025,000 years = 2.6 years. (c) Net present value Year 0 Year 1 Year 2 Year 3 Year 4 Net relevant cash flows $(4,040,000) $745,000 $1,445,000 $3,025,000 $1,870,000 NPV = $2,131,744 The net present value is $2,131,744 was found by discounting the relevant cash flows at 5%. So the project should proceed. 6.6 Mylo Ltd. (a) The annual amortization of the two projects is: Project 1: ($ 100,000 $7,000) 3 = $31,000 Project 2: ($ 60,000 $6,000) = $18,000 3 Copyright 2009 Pearson Education Canada 3
Project 1 (i) Year 0 Year 1 Year 2 Year 3 ($000) ($000) ($000) ($000) Net profit (loss) 29 (1) 2 Amortization 31 31 31 Capital cost (100) Residual value 7 Net cash flows (100) 60 30 40 10% discount factor* 1.000 0.909 0.826 0.751 Present value (100.00) 54.54 24.78 30.04 NPV 9.36 * Rounded to three decimal places (ii) Clearly the IRR lies above 10%; try 16%: 16% discount factor* 1.000 0.862 0.743 0.641 Present value (100.00) 51.72 22.29 25.64 NPV 0.35 * Rounded to three decimal places Thus the IRR is around 16%. (iii) To find the payback period, the cumulative cash flows are calculated: Year 0 Year 1 Year 2 Year 3 ($000) ($000) ($000) ($000) Cumulative cash flows (100) (40) (10) 30 Thus the payback will occur after about two years and three months (assuming that the cash flows accrue equally over the year), or three years if we assume year-end cash flows. Copyright 2009 Pearson Education Canada 4
Project 2 (i) Year 0 Year 1 Year 2 Year 3 ($000) ($000) ($000) ($000) Net profit (loss) 18 (2) 4 Amortization 18 18 18 Capital cost (60) Residual value 6 Net cash flows (60) 36 16 28 10% discount factor 1.000 0.909 0.826 0.751 Present value (60.00) 32.72 13.22 21.03 NPV 6.97 (ii) Clearly the IRR lies above 10%; try 16%: Year 0 Year 1 Year 2 Year 3 ($000) ($000) ($000) ($000) 16% discount factor 1.000 0.862 0.743 0.641 Present value (60.00) 31.032 11.888 17.948 NPV 0.868 Thus the IRR lies a little above 16%; perhaps around 17%. (iii) The cumulative cash flows are: Year 0 Year 1 Year 2 Year 3 ($000) ($000) ($000) ($000) Cumulative cash flows (60) (24) (8) 20 Thus, the payback will occur after about two years and three months (assuming that the cash flows accrue equally over the year), or three years (assuming year-end cash flows). Copyright 2009 Pearson Education Canada 5
(b) (c) Presuming that Mylo Ltd. is pursuing a wealth-maximization objective, Project 1 is preferable since it has the higher NPV. The difference between the two NPVs is not significant, however. NPV is the preferred method of assessing investment opportunities because it fully addresses each of the following: The timing of the cash flows. Discounting the various cash flows associated with each project, according to when they are expected to arise, takes account of the fact that cash flows do not all occur simultaneously. Associated with this is the fact that, by discounting using the opportunity cost of capital (namely the return that the next-best alternative opportunity would generate), the net benefit, after financing costs have been met, is identified (as the NPV). The whole of the relevant cash flows. NPV includes all of the relevant cash flows when they are expected to occur. It treats them differently according to their date of occurrence, but they are all taken into account in the calculation of the NPV and they all have, or can have, an influence on the decision. The objectives of the business. NPV is the only method of appraisal in which the output of the analysis has a direct bearing on the wealth of the business. (Positive net present values enhance wealth; negative net present values reduce it.) Since most private sector businesses seek to increase their value and wealth, NPV clearly is the best approach to use. Copyright 2009 Pearson Education Canada 6
6.8 The Accountant (a) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 $000 $000 $000 $000 $000 $000 Sales revenue 450 470 470 470 470 Working capital recovered 180 450 470 470 470 650 Materials 126 132 132 132 132 Labour 90 94 94 94 94 Overheads 30 30 30 30 30 Working capital 180 New equipment 500 680 246 256 256 256 256 Incremental cash flows (680) 204 214 214 214 394 Notes: Working capital invested in this project at the start will be recovered at the end of the project s life. The relevant overheads figure is $30,000 a year additional cost that the project is expected to cause. Amortization is not a cash flow. Interest on the working capital investment, and indeed on other aspects of this investment, is dealt with by discounting. The development cost is not a relevant cost, since it has been incurred already and is not affected by the decision to be made. The cost of the equipment to start this project is the $500,000 that must be spent. The book value of the old machine is not relevant since this does not represent an outlay or an opportunity cash flow. (b) (i) Payback period Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 $000 $000 $000 $000 $000 $000 Incremental cash flows (680) 204 214 214 214 394 Cumulative incremental cash flows (680) (476) (262) (48) 166 560 Thus the payback point occurs in Year 4, that is, after just over 3 years (assuming cash flows accrue evenly over the year). Copyright 2009 Pearson Education Canada 7
(ii) NPV Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 $000 $000 $000 $000 $000 $000 Incremental cash flows (680) 204 214 214 214 394 Discount factor (rounded to 1.000 0.893 0.797 0.712 0.636 0.567 3 decimals) Present values (680) 182.2 170.6 152.4 136.1 223.4 NPV 184.7 (c) A memo to the board might include the following points: The fact that the project has a significant positive NPV, which would increase shareholder wealth. The fact that the project has a relatively short payback period. The figures in the analysis ignore taxes, which should be considered before a final decision is made. The question of risk should be considered before a final decision is made. 6.10 Newton Electronics Ltd. (a) Option 1 ($ millions) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Plant and equipment (9.0) 1.0 Sales 24.0 30.8 39.6 26.4 10.0 Variable costs (11.2) (19.6) (25.2) (16.8) (7.0) Fixed costs (excl. amort.) (0.8) (0.8) (0.8) (0.8) (0.8) Working capital (3.0) 3.0 Marketing costs (2.0) (2.0) (2.0) (2.0) (2.0) Opportunity costs (0.1) (0.1) (0.1) (0.1) (0.1) (12.0) 9.9 8.3 11.5 6.7 4.1 Discount factor 10% (to 3 decimals) 1.000 0.909 0.826 0.751 0.683 0.621 Present value (12.0) 9.0 6.9 8.6 4.6 2.5 NPV 19.6 Option 2 ($ millions) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Royalties 4.4 7.7 9.9 6.6 2.8 Discount factor 10% (to 3 decimals) 1.000 0.909 0.826 0.751 0.683 0.621 Present value 4.0 6.4 7.4 4.5 1.7 NPV 24.0 Copyright 2009 Pearson Education Canada 8
Option 3 Year 0 Year 2 Installments 12.0 12.0 Discount factor 10% (to 3 decimals) 1.000 0.826 Present value 12.0 10.0 NPV 22.0 (b) Before making a final decision, the board should consider the following factors: The long-term competitiveness of the business may be affected by the sale of the patents. At present, the business is not involved in manufacturing and marketing products. Would a change in direction be desirable? The business will probably have to invest in the skills necessary to produce the product itself. This will involve costs, and problems will be incurred. Has this been taken into account? How accurate are the forecasts that were made, and how valid are the assumptions on which they are based? (c) Option 2 has the highest NPV and is therefore the most attractive to shareholders. However, the accuracy of the forecasts should be checked before a final decision is made. 6.12 Haverhill Engineers Ltd. (a) The first step is to calculate the cash savings from the new machine: Per unit cash flow Old line New line $ $ Selling price 1.50 1.50 Less Materials 0.40 0.36 Labour 0.22 0.10 Variable overheads 0.14 0.14 Cash contribution 0.74 0.90 The cash savings per unit is ($0.90 0.74) = $0.16, thus the cash savings for 1,000,000 units per year is 1,000,000 $0.16 = $160,000. Copyright 2009 Pearson Education Canada 9
The incremental cash flows arising from the project are: Year 0 1 2 3 4 5 $000 $000 $000 $000 $000 $000 Cash savings 160 160 160 160 160 New machine (700) 100 Old machine residual value 50 Working capital 160 (160) Net cash flows (490) 160 160 160 160 100 (b) NPV method: Discount factor 10% (to 3 1.000 0.909 0.826 0.751 0.683 0.621 decimals) Present value (490.0) 145.4 132.2 120.2 109.3 62.1 Net present value 79.2 Thus, the project s NPV is $79,200. (c) IRR method: Discount factor (20%) (to 3 1.000 0.833 0.694 0.579 0.482 0.402 decimals) Present value (490.0) 133.3 111.0 92.6 77.1 40.2 NPV (35.8) Increasing the discount rate from 10% to 20%, decreases the NPV from + 79.2 to 35.8, a decrease of 115.0. This is an average decrease of 11.5 per 1% increase in the discount rate. The rate at which the project would have a zero NPV (the IRR) is therefore about 10% + (79.2/11.5) = 16.9%, that is, about 17.0%. Copyright 2009 Pearson Education Canada 10
(d) NPV is the difference between the future cash inflows and outflows relating to a project after taking account of the time value of money. The time value of money is taken into account by discounting the future cash flows using the cost of finance as the appropriate discount rate. The decision rule for NPV is that projects with a positive NPV should be accepted, as this will lead to an increase in shareholder wealth. The internal rate of return is the discount rate that, when applied to the future cash flows of the projects, produces a zero NPV. The IRR is compared to a hurdle rate determined by management to see whether the project should be undertaken. The IRR approach is currently as popular as the NPV method among practising managers. Managers appear to like to use percentage figures as a basis for evaluating projects rather than absolute figures. However, the IRR method has a number of disadvantages compared to the NPV method, which were discussed in the chapter. Normally, the two methods will always give the same solution concerning acceptance or rejection of a project, and will usually give the same solution concerning the ranking of projects. However, where a difference occurs, the NPV method provides the more reliable answer. As a result, the NPV approach is considered to be the more appropriate method to adopt. Total PV Amount $50.00 $1000.00 n, number of 6-month periods (2 x 8) 16 16 PV factor at 6% 10.1059 0.3936 Present value $505.30 $393.60 $898.90 As the interest amounts are paid every six months, using a discount rate of 6% per six-month period represents a current interest rate of 6% 2 = 12%. Copyright 2009 Pearson Education Canada 11
Or as an internal rate of return question: 6-Month Periods Cost Interest Principal Total 900.00 900.00 1 50.00 50.00 2 50.00 50.00 3 50.00 50.00 4 50.00 50.00 5 50.00 50.00 6 50.00 50.00 7 50.00 50.00 8 50.00 50.00 9 50.00 50.00 10 50.00 50.00 11 50.00 50.00 12 50.00 50.00 13 50.00 50.00 14 50.00 50.00 15 50.00 50.00 16 50.00 1000.00 1050.00 IRR 5.99% or 6% So the annual interest rate is 2 6% = 12%. Copyright 2009 Pearson Education Canada 12