Chapter 7 Making Capital Investment Decisions: Further Issues

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1 Making Capital Investment Decisions: Further Issues Solutions to Even-Numbered Problems and Cases 7.2 James Bay Geological Engineering Company Discount rate, 8% Project Cash Flows thousands) Year Machine 1 Machine 2 Machine 3 0 (200) (400) (600) NPV Copyright 2009 Pearson Education Canada 1

2 (a) Common-period-of-time approach: Year Machine 1 Machine 2 Machine NPV $ $87.30 $52.76 Buy Machine 1, as it provides the highest net present value over the eight-year period. (b) Equivalent-annual-annuity approach using Table 5 in Appendix A: Machine 1: NPV = $ = Equivalent annuity payment of $25.82 Machine 2: NPV = $ ; Payment = $15.19 Machine 3: NPV = $ ; Payment = $9.18 Buy Machine 1, as it provides the highest equivalent annual annuity over the eight year period. (c) Yes, both methods selected Machine 1 as the best option. Copyright 2009 Pearson Education Canada 2

3 7.4 Wu and Chu Chocolates Emporium (a) For each year, sum the probability multiplied by cash flow for each growth scenario. For example, for Year 1, the expected cash inflow is 40% % % 100 = 155. The complete expected cash flow schedule for each year is as follows: Discount rate 14% Expected Cash Flows Year thousands) 0 (600.00) Expected NPV 6.17 (b) Based on the expected cash flows in part (a) and a 14% cost of capital, WCCE should buy the new machine because the net present value is positive. Copyright 2009 Pearson Education Canada 3

4 7.6 Lee Caterers Ltd Approach 1 Step 1: Calculate the NPV for each project: Cook/Chill Project Cash Flows Discount Rate Present Value 000) 10% 000) Initial outlay (200) 1.00 (200) 1 year s time years time years time years time NPV 62.1 Cook/Freeze Project Cash Flows Discount Rate Present Value 000) 10% 000) Initial outlay (390) 1.00 (390) 1 year s time years time years time years time years time years time years time years time NPV Step 2: Calculate the NPV for the eight-year period. Eight years is the minimum period over which the two projects can be compared. The cook/chill project will provide the following NPV over this period: NPV = $ $ = $104.5 This NPV of $104,500 is lower than the NPV for the cook/freeze project of $122,300 (see above). Hence, the cook/freeze project should be accepted. Copyright 2009 Pearson Education Canada 4

5 Approach 2 Using the equivalent-annual-annuity approach we derive the following: Cook/chill: $ = $19.59 Cook/freeze: $ = $22.92 This approach leads to the same conclusion as the earlier approach: the cook/freeze project should be accepted because it has a higher equivalent annual annuity. 7.8 Simonson Engineers Limited (a) Step 1: Determine the expected cash flow for each year. (a) (b) (a) (b) Estimated Cash Flows Probability Of Occurrence Expected Value Year Year Year Year Copyright 2009 Pearson Education Canada 5

6 Step 2: Calculate the expected net present value, ENPV. Year 1 Year 2 Year 3 Year 4 Year 5 Expected cash flows (9.0) Discount factor Expected present values (8.18) ENPV 2.35 The expected net present value is $2.35 million. (b) To find the NPV of the worst possible outcome and the probability of its occurrence, use the worst cash flow for each year. Year 1 Year 2 Year 3 Year 4 Year 5 Cash flows (worst) (9.0) Discount factor Present values (8.18) NPV (1.05) Probability of occurrence = (c) The ENPV of the project is positive, and so its acceptance will increase the wealth of shareholders. Copyright 2009 Pearson Education Canada 6

7 7.10 Devonia Laboratories Ltd. (a) Expected sales volume per year (11, ) + (14, ) + (16, ) = 13,300 units Expected annual sales revenue = 13,300 $20 = $266,000 Annual labour costs = 13,300 $8 = $106,400 Annual ingredient costs = 13,300 $6 = $79,800 Incremental cash flows Years $000 $000 $000 $000 $000 Sale of patent rights (125.0) Sale of equipment (85.0) 35.0 Sales Cost of ingredients (79.8) (79.8) (79.8) (79.8) Labour costs (106.4) (106.4) (106.4) (106.4) Termination Costs (10.0) Additional overhead (15.0) (15.0) (15.0) (15.0) (210.0) Discount factor (at 12%) (210.0) ENPV 2.7 (b) As the ENPV of the project is positive, the wealth of shareholders would be increased by accepting the project. However, the ENPV is low in relation to the size of the project and careful checking of the key estimates and assumptions would be advisable. A relatively small downward revision of sales or upward revision of costs could make the project ENPV negative. (c) Refer to the chapter material for a discussion of the strengths and weaknesses of the expected net present value method. Copyright 2009 Pearson Education Canada 7

8 7.12 Plato Pharmaceuticals Ltd. (a) The annual operating cash flows must first be calculated: Sales (150 $5) Variable costs (150 $3) Fixed costs $160 = $140 The net present value can now be calculated as follows: Discount rate 12% $000 Annual cash flows ( *) 505 Residual value of machinery (Yr 5) ( ) Less initial cost (Yr 0) (520) NPV 42 * This is the sum of the discount factors over the five-year period. This approach can be used as a short cut when cash flows are constant. (b) (i) If the discount rate was 20%, the NPV of the project would be: $000 Annual cash flows ( ) 419 Residual value of machinery and equipment ( ) Less Initial cost (520) NPV (61) An 8% change in the discount rate leads to a $103 change in the NPV of the project. Thus, for every 1% change in the discount rate there is a $13 103/8) change in the NPV. To achieve a NPV of zero, the discount rate must increase by 42/13 = 3.2%. Hence the IRR is 12% + 3.2% = 15.2%. This is an increase of nearly 27% [(15.2% 12%)/12%] on the cost of capital figure provided. (ii) The initial cost would have to increase by $42,000 for the project to become unprofitable. This represents an increase of 8.0% (42/520). Copyright 2009 Pearson Education Canada 8

9 (iii) The required reduction in the net cash flows from operations before the project became unprofitable is calculated as follows: Let F = the annual operating cash flows (F annuity factor for a five year period) NPV = 0 This can be rearranged: (F annuity factor for a five year period) = NPV F = $42,000 = $42,000/ = $11,651 This is a reduction of just over 8.0% /140) on the cash flow figures provided. (iv) The decrease necessary in the residual value is calculated as follows: Let V = the required residual value: (V discount factor at end of five years) NPV of project = 0 Which can be rearranged: (V discount factor at end of five years) = NPV of project V = $42,000 = $42,000/ = $74,022 This is a decrease of over 74.0% (74,022/100,000) on the figure provided. Copyright 2009 Pearson Education Canada 9

Chapter 6 Making Capital Investment Decisions

Chapter 6 Making Capital Investment Decisions 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