AFM 21 Midterm Examination #2 Friday June 1, 2005 K. Vetzal Name: Answer Key Student Number: Section Number: Duration: 1 hour and 30 minutes Instructions: 1. Answer all questions in the space provided. 2. Show all of your calculations. 3. The examination has 9 pages (not including this cover page). Verify that your copy is complete. 4. Materials allowed: calculator. 5. Unless specifically instructed otherwise, provide final answers relating to percentage rates to four decimal places (e.g. 6.2% or.062) and provide final answers involving dollar amounts to two decimal places (e.g. $98.2). 6. To have your exam considered for re-grading, the exam must be written in ink.. Page 9 of the exam is a formula sheet. Do not write any part of your answers on this page. It will not be graded. If you find it easier to consult this page by detaching it from your exam, please do so. You are not expected to hand in the formula sheet. Mark Distribution 1. /20 2. /10 3. /15 4. /20 5. /10 Total: /5
Question 1: 20 marks. Each of parts (a)-(d) is worth 5 marks. (a) (5 marks) DMB Inc. is considering investing in a new project. The project will cost $250,000 today. It will generate annual after-tax net cash flows of $40,000 per year in perpetuity (the first of these will be received exactly one year from today). The opportunity cost of capital is %. (i) What is the payback period for this project? (ii) What is the discounted payback period for this project? (i) $250,000/$40,000 = 6.25 years. (1.5 marks) (ii) [ 1 1.0 T $250,000 = $40,000.0 0.435 = 1 1.0 T 1.0 T = 0.5625 T = ln(0.5625) ln(1.0) = 8.5 years. (3.5 marks) (b) (5 marks) Gerth Inc. can buy a new machine for $60,000. It has an economic life of 4 years and will be worthless after that time. The firm uses straight line depreciation. The new machine is expected to produce net income of $9,000 after one year. This amount will grow at a rate of 5% per year until the end of the 4th year. What is the average accounting return on this investment? The average net income can be calculated as or, more directly as $9,000 4 [ 1.05 4 1.05 = $9,69.8; $9,000 [ 1 + 1.05 + 1.05 2 + 1.05 3 = $9,69.8. (3 marks) 4 The average net investment is ($60,000 + $0)/2 = $30,000. (1 mark) The average accounting return is $9,69.8/$30,000 = 32.33%. (1 mark) Page 1 of 9
(c) (5 marks) MK Inc. has $500,000 available to fund new investments. It is considering investing in four potential projects (A, B, C, and D), with the following cash flows: Period 0 Period 1 Period 2 Period 3 A -$15,000 $0 $210,000 $0 B -$215,000 $0 $0 $310,000 C -$285,000 $345,000 $0 $0 D -$325,000 $390,000 $0 $0 The opportunity cost of capital is 8% for each project. Calculate the profitability index for each project. Which project(s) should the firm invest in? $210,000 1.08 2 PI A = = 1.03 (1 mark) $15,000 $310,000 1.08 3 PI B = = 1.14 (1 mark) $215,000 $345,000 1.08 PI C = = 1.12 (1 mark) $285,000 $390,000 1.08 PI D = = 1.11 (1 mark) $325,000 In this situation of capital rationing, the correct procedure is to take the projects with the highest PIs until the capital budget of $500,000 is spent. Here the firm should choose B and C, since they have the highest PIs and they use up the entire capital budget. (1 mark) (d) (5 marks) EM Inc. is considering purchasing some equipment to produce electric fans. The firm has estimated that the fans can be sold for a price of $50 each, and that variable costs will be $32 per fan. Fixed costs associated with the project are $14,000 per year. The equipment is expected to last for 5 years. It will be depreciated for tax purposes using the straight line method. The firm s corporate tax rate is 40%. The opportunity cost of capital is 10%. If the firm has estimated that the present value break-even point is 1,500 units, what is the initial cost of the equipment? 1,500 = I/A5.10 + 14,000(.6) (I/5)(.4) (50 32)(.6) 16,200 = I/3.908 + 8,400.08I,800 =.1839I I = $42,438.01 (2.5 marks) (2.5 marks) Page 2 of 9
Question 2: 10 marks. TC Co. is considering investing in one of two mutually exclusive investment projects, A and B. The opportunity cost of capital is 9% for each project. The projects cash flows are as follows: Period 0 Period 1 Period 2 A -$25,000 $32,000 $0 B -$40,000 $0 $55,000 (a) (5 marks) Calculate the NPV and IRR of each project. NPV A = $25,000 + $32,000 = $4,35.80 1.09 (1.5 marks) NPV B = $40,000 + $55,000 1.09 2 = $6,292.40 (1.5 marks) IRR A = $32,000 1 = 28.00% (1 mark) $25,000 ( ) $55,000 1/2 IRR B = 1 = 1.26% (1 mark) $40,000 (b) (5 marks) Based on the IRR criterion, which project should the firm choose? Since the projects are mutually exclusive, incremental cash flows must be considered (due to different scale and timing of cash flows): Period 0 Period 1 Period 2 B-A -$15,000 -$32,000 $55,000 (1 mark) Let x = (1 + r). Then the IRR is found by solving 15,000x 2 + 32,000x 55,000 = 0 x = 32,000 ± 32,000 2 4(15,000)( 55,000) 2(15,000) = {1.1252, 3.2586} (3 marks) The negative root is meaningless here, so the IRR is 12.52%. Since this exceeds the opportunity cost of capital of 9%, B should be chosen over A. (1 mark) Notes: (i) using A-B leads to the same IRR, but is a borrowing type of project, and so the conclusion is that B should be taken since the IRR is higher than the opportunity cost of capital; and (ii) simply picking A since it has a higher IRR from part (a) is worth 1 mark. Page 3 of 9
Question 3: 15 marks. Ubu Software Inc. is considering developing software for executing and recording trades on financial exchanges. An initial version of the software which is targeted at stock markets can be developed and released today at cost of $500,000. At this point, it is uncertain how successful the product will be. The firm believes there are two possibilities in the first year: high demand: the product is adopted by several stock markets, and cash flows received at the end of the first year are $450,000; low demand: the product is only purchased by a few stock markets, and cash flows received at the end of the first year are $160,000. Due to the risk involved, the discount rate for the first year of the project is 30%. If demand in the first year turns out to be high, the firm believes it will have to then choose from one of three options: A: Aggressive international expansion. This would involve further software development for futures and options exchanges and customization for various international markets. Costs are expected to be $2,000,000 at the end of year 1 and an additional $500,000 at the end of year 2. Cash flows are forecasted to be $50,000 at the end of year 3, and this amount is expected to grow at 5% per year forever. Due to the uncertainty involved, the discount rate for this alternative is 25%. B: Modest international expansion. Refinements to the software for stock exchange transactions are expected to cost $1,200,000 after year 1. Annual cash flows are expected to be $350,000 at the end of year 2, and to remain at this level forever. The discount rate for this option is 20%. C: Slow international expansion. A few additional features would have to be incorporated in the product, and these would cost $400,000 at the end of year 1. Annual cash flows are forecasted to be $15,000 in perpetuity, starting at the end of year 2. The discount rate for this alternative is 18%. If demand in the first year turns out to be low, the firm will be faced with one of two options: D: Domestic expansion. The firm believes it can more aggressively market the product domestically, at a cost at the end of year 1 of $200,000. Annual cash flows (starting at the end of year 2) are expected to be $45,000 in perpetuity. The discount rate for this option is 15%. E: No expansion. Additional maintenance costs of $50,000 are expected at the end of year 1. Annual cash flows are forecasted to be $30,000 at the end of year 2, and they are predicted to remain at this level for 10 years (i.e. at the end of years 2-11 the firm will receive $30,000). It is expected that the rights to the product could be sold off for a salvage value of $25,000 at the end of year 11. The discount rate for this option is 10%. Continued on next page... Page 4 of 9
Suppose that the probability that demand is high in the first year is 60%. Should the firm invest in this software development project today? Justify your answer. Analyzing options A-C: NPV of A t=1 = $2,000,000 $500,000 + 1.25 = $600,000 (3 marks) NPV of B t=1 = $1,200,000 + $350,000 0.20 = $550,000 (1 mark) NPV of C t=1 = $400,000 + $15,000 0.18 = $52,222.22 (1 mark) $50,000/(0.25 0.05) 1.25 Therefore, if demand is high in the first year, the firm should choose option A. (1 mark) Analyzing options D-E: NPV of D t=1 = $200,000 + $45,000 0.15 = $100,000 (1 mark) [ 1 1.10 10 NPV of E t=1 = $50,000 + $30,000 0.10 = $143,95.60 (3 marks) + $25,000 1.10 10 Therefore, if demand is low in the first year, the firm should choose option E. (1 mark) Overall project NPV:.6($450,000 + $600,000) +.4($160,000 + $143,95.60) NPV t=0 = $500,000 + 1.3 = $8,146.34 (3 marks) Since the project NPV is positive, the firm should make this investment. (1 mark) Page 5 of 9
Question 4: 20 marks. ST Company is considering investing in some new equipment. The cost of the equipment is $600,000 today. It is expected to be worth $50,000 after years, at which point it will be sold. The equipment is in CCA class 8 (25% depreciation rate). It is the only class 8 asset which the firm will ever have. The firm faces a corporate tax rate of 35%. The equipment will require the use of a factory site which has a current market value of $100,000. If the investment is made, pre-tax operating revenues are expected to be $235,000 (real) at the end of year 1. This amount will grow at an annual rate of 5% (real) until the end of year. Pre-tax operating expenses are expected to be $80,000 (real) at the end of year 1. This amount will grow at an annual rate of 4% (real) until the end of year. Moreover, the equipment will be used to manufacture a new product line, which is expected to reduce pre-tax sales of an existing product line by $20,000 (nominal) at the end of year 1. This amount will grow at an annual rate of 2% (real) until the end of year. The project will require an initial investment of $15,000 in working capital today. This amount will increase to $2,000 (nominal) at the end of year 1. It will remain at this level until the end of year, at which point the working capital investment will be fully recovered. The nominal opportunity cost of capital is 10%. The expected inflation rate is 3%. (a) ( marks) Calculate the present value of after tax operating revenues, the present value of after tax operating expenses, and the present value of side effects on revenues from other product lines. The real discount rate is 1.1/1.03 1 =.06961165. (1 mark) [ 1 (1.05/1.06961165) PV after tax operating revenues: =.65 $235,000.06961165.05 = $952,083. (2 marks) [ 1 (1.04/1.06961165) PV after tax operating expenses: =.65 $80,000.06961165.04 = $315,203.30 (2 marks) [ 1 (1.02/1.06961165) PV after tax side effects: =.65 ($20,000/1.03).06961165.02 = $2,39.42 (2 marks) Note that these calculations can also be done in nominal terms as follows: [ 1 (1.0815/1.10) PV after tax operating revenue: =.65 $235,000 1.03.10.0815 [ 1 (1.012/1.10) PV after tax operating expenses: =.65 $80,000 1.03.10.012 [ 1 (1.0506/1.10) PV after tax side effects: =.65 $20,000.10.0506 = $952,083. = $315,203.30 = $2,39.42 Page 6 of 9
(b) (8 marks) Calculate the present values of CCA tax shields. Include the present value of an initial perpetual tax shield, the present value of a lost tax shield when the asset is disposed of, and the present value of any recaptured depreciation or terminal loss. PV of perpetual CCA tax shield: = $600,000(.25)(.35) 1.05.10 +.25 1.10 = $143,181.82 (2 marks) UCC = $600,000(1.125)(1.25) 6 = $93,438.2 X = $93,438.2 $50,000 = $43,438.2 PV of lost tax shield: = $93,438.2(.25)(.35) 1.10.10 +.25 = $11,98.21 (2 marks) PV of terminal loss: = $43,438.2(.35)/1.10 = $,801.83 (1 mark) (2 marks) (1 mark) (c) (5 marks) Calculate the net present value of this investment project (be sure to include your present value calculations from parts (a) and (b) and the present values of any relevant items that were not calculated either in part (a) or in part (b)). PV of working capital requirements: = $15,000 $12,000/1.1 + $2,000/1.1 = $12,053.82 (1 mark) salvage: = $50,000/1.1 = $25,65.91 (1 mark) initial cost: = $600,000 (1 mark) opportunity cost: = $100,000 (1 mark) NPV: = $952,083. $315,203.30 $2,39.42 + $143,181.82 $11,98.21 + $,801.83 $12,053.82 + $25,65.91 $600,000 $100,000 = $1,101.58 (1 mark) Page of 9
Question 5: 10 marks. Assess whether each of the following statements is true, false, or uncertain. Justify your answer. All marks are based on the quality of your argument supporting your answer. (a) (5 marks) It does not matter whether a firm uses the profitability index rule or the net present value rule to evaluate corporate investments because these two rules always lead to the same conclusion. False. The profitability index is defined as the present value of future cash flows divided by the initial cost of the investment, and so it potentially suffers from scale problems when considering mutually exclusive investments (it can give a higher ranking to a smaller project which has a lower net present value). Also, in cases of capital rationing, the net present value rule can lead to incorrect conclusions since it does not take into account the amount earned back per dollar invested. In such cases, the profitability index works better because it finds the biggest bang for a buck invested. (5 marks) (b) (5 marks) A firm cannot have both a capital gain and a terminal loss at the same time in the same CCA asset class. Uncertain. If the firm only ever has one asset in the asset class, then the statement would be true. A terminal loss arises when the firm has not taken enough depreciation before the asset is sold, i.e. the CCA deductions have depreciated the asset down to some level, but it is sold for a lower price. Clearly, the selling price in this case must be lower than the initial cost (since it is lower than the initial cost less the accumulated CCA), and so it would not be possible for the firm to have a capital gain. However, if the firm has more than one asset in the asset class, then the statement could be false. Due to the pooling of all assets within the same asset class, it would be possible to have a situation where the entire pool is salvaged (so that there are no remaining assets in the class) with one (or more) asset(s) being sold for a higher amount than initial cost (thereby generating a capital gain), but for the overall undepreciated capital cost in the asset class to remain positive (i.e. the aggregate salvage value would be lower than the pool s collective undepreciated capital cost). In this case, there would be both a capital gain and a terminal loss. (5 marks) Page 8 of 9
Formula Sheet Present value of a single cash flow of C occurring n periods from now: PV = C (1 + r) n Present value of a perpetuity with first payment of C occurring one period from today (with an interest rate of r per period): PV = C r Present value of a perpetuity with first payment of C occurring one period from today and with payments growing at a rate of g per period (with an interest rate of r per period): PV = C r g (r > g) Present value of an ordinary annuity with first payment of C occurring one period from today and a total of n payments (with an interest rate of r per period): [ 1 (1 + r) n PV = C r Present value of a growing annuity with first payment of C occurring one period from today, payments growing at a rate of g per period, and a total of n payments (with an interest rate of r per period): ( ) n PV = C 1 1+g 1+r (r g) r g Roots of a quadratic equation: ax 2 + bx + c = 0 x = b ± b 2 4ac 2a Fisher relation: (1 + i) = (1 + r) (1 + π) Page 9 of 9