Solutions to Self-Test Questions

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1 CHAPTER ONE Qualitative Questions Question The financial market helps individuals lend or borrow. Lending transfers current wealth for consumption in future periods. Borrowing allows individuals to transfer future wealth for current consumption. Question 2 Individuals divide their wealth between current and future consumption. Assets allocated for future consumption are invested in productive assets. Investors seek to maximize the present value of their wealth. Investment projects with the highest net present values belong to the optimal investment strategy. Question 3 It is determined by ranking projects in order of their marginal rates of return. It is determined by choosing projects with returns above the opportunity cost of capital. Under perfect market conditions, the rate in the financial market is the opportunity cost of capital. Question 4 Differences in consumption preferences between investors should not affect the optimal investment strategy. Everyone should invest in the optimal investment strategy. Lending and borrowing activities enable individuals to invest in the optimal investment strategy and meet their consumption preferences simultaneously. The opportunity cost of capital is fully reflected in the investment decision. Question 5 Prices of securities fully reflect all publicly available information. Prices adjust quickly to new information. Prices of securities are always equal or very close to their intrinsic values. Question 6 Weak, semi-strong, and strong are the forms of market efficiency. The price of a security in one market should be close to the price in another market. Managers choose projects to maximize net present values. Shareholders will not reward managers for actions they can do themselves. Question 7 Shareholders of widely held corporations do not practically participate in decision making. Managers are hired by shareholders to act on behalf of shareholders. Managers should make their decisions with a view to maximizing shareholder wealth. Any managerial actions that deviate from the goal of maximizing shareholder wealth create agency costs. Question 8 The goals of managers may conflict with the goal of maximizing shareholder wealth. Many actions that will maximize shareholder wealth, at least in the short run, may not be ethical to take. Shareholders are not the only stakeholders in the firm.

2 Question 9 Estimate incremental after-tax cash flows. Determine the appropriate discount rate. Calculate the NPV for the projects. Use other capital budgeting acceptance criteria if desirable. Accept projects with positive NPV. In case of mutually exclusive projects, choose a project with the highest positive NPV. Question 0 Cash flows are identified and estimated rather than accounting profits. Incremental cash flows are determined on a project basis rather than cash flows on a stand-alone basis. After-tax cash flows are required. Economically dependent projects present complications in estimating cash flows. Question They are both discounted cash flow methods. A project may have multiple IRRs. The IRR technique may contradict the NPV technique when two projects are mutually exclusive. Question 2 The payback technique is simple to understand and communicate. The discounted payback technique is a discounted cash flow technique. The PI technique provides a measure of relative profitability. Qualitative Multiple Choice Questions Question v) a, b, and c: a) Terminal loss is written off as an expense only when a class of asset is liquidated. b) Allowable capital losses are written off against taxable capital gains. c) Flotation costs for new securities are amortized over five years. Question 2 iii) c only: Market value of the common shares of a firm Question 3 ii) Financial side-effects are included in the investment decision. Question 4 v) Deciding to delay the implementation of a project Question 5 i) Book value of spare machinery which has no alternative use but can be used in the project Question 6 i) Insiders can earn abnormal profits by trading on the basis of their privileged information. Question 7 i) Use of a nominal rate for cash flows expressed in current dollars Question 8 iv) Information is readily available to the public for evaluation. Question 9 iii) The profitability index will be greater than. 2

3 Question 0 iii) All information available, including information available only to insiders who possess privileged information Question ii) Stocks and stock options should be used to compensate members of the board of directors. Question 2 ii) NPV is the only approach that directly measures a project s contribution to shareholder wealth in dollars. Question 3 i) Historical information about price and volume cannot be used to earn higher trading profits than would be obtained with a naïve buy-and-hold strategy. Question 4 iv) Under the nominal method of capital budgeting, the discount rate will decrease. Question 5 iv) ABC should accept the project because it has a positive NPV. Question 6 ii) Prices reflect all publicly available information, past and present. Question 7 i) IRR assumes project cash flows are reinvested at a rate equal to the IRR, whereas NPV assumes they are reinvested at the cost of capital. Question 8 iii) Project B has a higher internal rate of return than Project A. Quantitative Multiple Choice Questions Question ii) $27,000 = 40,000( ) - 5,000 Question 2 ii) $ = 00, 0.2 Question 3 iv) $3,000 = 0,000 +, ,000 Question 4 v) $6.67 = $4, 0.2 Question 5 i) $835 Payback Period = 2.5 Q Initial Investment = CF + CF (CF 3) $0,000 = 4, ,000 + a 2 b (CF 3) CF 3 = $6,000 NPV = -0, ,000 (.5) + 3,000 (.5) 2 + 6,000 (.5) 3 + 2,000 (.5) 4 = $

4 Question 6 i) Project B, even though it has a longer discounted payback period. Choice is the only correct choice. As can be seen in the answer table below, the discounted payback for project B is longer than that of A, which in itself is not a good reason to select project B. However, the NPV of project B is much larger than that of A, and this is a good reason to select B over A. NPV, IRR, and PI computed with a financial calculator: Disc. payback A 2.5 years B 2.62 years IRR A 8.9% B 28.92% PI A.6 B.6 AAR A 93.33% B % NPV A $24,085 B $85,390 Choice 2 is incorrect as the projects do not have the same AARs. Choice 3 is incorrect as they do not have the same IRRs. Choice 4 is incorrect as the two projects are mutually exclusive and thus both cannot be selected. Choice 5 is incorrect because Project B s PI is greater than Project A s. Question 7 iv) 4% From a financial calculator, PV = -35,000 PMT = 5,000 N = 3 CPT i = 3.7% Question 8 ii) 2.79 years where $,990 is the amount of the initial investment not paid back after the 2nd year using the discounted year and 2 cash flows, and $42,356 is the present value of the year 3 cash flow. Question 9 ii) $8, [450, ,000 * PVIF (2%, year) - 200,000 * PVIF (2%, 2 years) ] [200,000 * PVIF (2%, 3 years) ] (450,000-78,57-59,439) , ,990 = , or approximately 2.79 years 42,356 4 PVTS = c (55,000)(0.5)(0.35) dc ( ) d (5,000) * c dc0.5 3 ( + 0.2) d = 5,347.22(.8929) - 0,676.70(0.944) = 0,2.76-2, = 8,046.2

5 Question 0 i) $2,700 PVTSL n = -c (70,000) (0.25)(0.45) dc 6 (.0) d =-39,53(0.324) = 2,700 Question ii) The project should be rejected because the weighted average cost of capital is 0.50% and the internal rate of return is less than 0.50%. The IRR of the project is 6.40% $200,000 = $48,000 PVIFA (IRR, 5) By financial calculator IRR = With capital structure weights of 0.5, the WACC is a simple average of the component costs, or 0.50%. The decision rule is to accept projects with an IRR that equals or exceeds the WACC, so this is clearly not an acceptable project. Question 2 a) ii).0886 PV benefits PI = PV costs [50,000 * PVIF (,5%) + 00,000 * PVIF (2,5%) + 50,000 * PVIF (3,5%)] = 00,000 [43, , ,627] = = ,000 b) iii) Project B has a higher IRR than project A. NPV for Project B is higher than NPV for Project A, even with a higher (6%) discount rate: NPV for B = -200, ,000 PVIF (, 6%) + 00,000 PVIF (2, 6%) + 50,000 PVIF (3, 6%) = -200, , , ,033 = $35,659 NPV for A =.0886(200,000) - 200,000 = $7,720 Also may compute NPV for A = -200, ,000 PVIF(, 5%) + 00,000 PVIF(2, 5%) + 50,000 PVIF(3, 5%) PI for B =.783 So Project B is the better project. As it has a positive NPV at a discount rate of 4%, it has an IRR above 4%, so it surely has a higher IRR than Project A. By financial calculator the IRR A = % and the IRR B = %. The payback approach should not be used for decision making as it is inferior to the NPV, PI, and IRR. Question 3 iii) 4.86 years Cash flows in $60,000 4 = $240,000 Remaining uncovered initial investment = $300,000 - $240,000 = $60,000 PB = 4 + $60,000 = 4.86 years $70,000 5

6 Quantitative Problems Problem First, determine the cash flows of Project Medium in order to calculate the crossover rate. It will represent the minimum IRR the independent Project Medium must have in order for us to consider it: Cash flows Cash flows Cash flows Time Project Tiny Project Huge Project Medium 0 $50 $425 $ So, the minimum IRR of Project Medium must be: Important graphing points: ( + IRR) = 95c - d IRR IRR = 4.394% Discount rate % (x axis) NPV $ (y axis) 0% $70 Tiny, $75 Huge. 2% $7.05 Tiny, $30.60 Huge, $3.55 Medium. This is the NPV since 2% is the cost of capital. 4.32% $9.2 the NPV of Tiny and Huge at the crossover point. Is the IRR of Medium. 5.37% $0, this is the IRR of Huge. 7.30% $0, this is the IRR of Tiny. $ $50.00 NPV $00.00 $50.00 Tiny Huge $ ($50.00) Discount rate 6

7 Since the cost of capital occurs to the left of (below) the crossover rate we would normally choose Huge since it has the higher NPV. However, there is an independent project (Medium) available. Although we have not been given any cash flow information on Medium we can conclude the following: Although independent to both, Medium can only be combined with Tiny due to rationing the maximum budget is $425 and is all used up by Huge. In order to consider Medium its minimum IRR% must equal at least 4.32%, the crossover rate and its scale (size) cannot be more than $275 initially (due to rationing). At this point we are indifferent between Huge or Tiny + Medium. Why? At a discount rate of 2%, the value of the firm increases by $30.60 with Huge compared to an increase of $ $3.55 = $30.60 with Tiny and Medium combined. Should the IRR of Medium exceed 4.32% (the crossover rate) and or its scale be less than $275, combining Tiny and Medium would result in more wealth than Huge alone. The final decision will probably centre around the differences in risk. Huge is riskier because its slope is steepest. Agency theory tells us managers may prefer less risky projects than shareholders, as it is harder for managers to diversify their stake in the corporation. Investing in two projects (Tiny + Medium) may appeal more to management as if one project fails the other may still succeed. Shareholders might prefer the riskier project Huge because they are better able to diversify risk, as their wealth is not limited to investment in one corporation. Problem 2 - NPV = (5.m - 5m)( )J + c (5.5m - 5m)( ) c (250,000)(0.40)(0.25) dc 2 + (0.2) 2( ) d - 250,000 NPV = 82, , , ,000 = $472,828 ( + 0.2) 4 K 0.2 dc ( + 0.2) 4 d Since NPV 0 Problem 3 : Go ahead and purchase the training program with equipment. - NPV = 6,000( )J + c (60,000)(0.20)(0.40) 2( ) dc ,000-8,000c ( + 0.2) 5 d - 60,000 = (3,600)( ) + 5, , , ,000-0, ,000 = -$20, ( + 0.2) K + 0,000c ( + 0.2) 5 d d - c (0,000) (0.20)(0.40) dc 5 (.2) d Notice in this problem the net working capital change is the reverse of the normal change. That is, in this problem the net working capital first decreases causing an immediate cash inflow. Reversing the initial change at the end of the project creates the year five net working capital cash outflow. 7

8 Cases Case : Sudbury Foundries Ltd. a) The net capital flows are shown in Solution Case Exhibit -. The initial cost flows are straightforward: cost of $20,000 for the new generator, $7,000 for working capital, and an inflow of $50,000 for the existing machine. In Year 5, it is assumed that working capital is 00% recoverable and that the salvage for the new machine is $5,000. However, these inflows are reduced by the salvage which would have been obtained from the existing machine. The net present value of capital outflows is -$69,045. Solution Case Exhibit - Sudbury Foundries Ltd. Investment Analysis Net Capital Flows: Year 0 Year Year 2 Year 3 Year 4 Year 5 New Generator $20,000 Salvage $5,000 Existing Generator $50,000 $6,000 Salvage Working Capital $7,000 $7,000 Recovery Net Capital Flows: $77,000 $6,000 Discount Rate = 5% Present Value (part a) $69,045.7 Cost Savings $35,000 $36,750 $38,588 $40,57 $42,543 Rental Lost $2,500 $2,500 $2,500 $2,500 $2,500 Incremental Savings $32,500 $34,250 $36,088 $38,07 $40,043 Incremental Taxes $9,750 $0,275 $0,826 $,405 $2,03 Incremental Cash Savings 22,750 23,975 25,262 26,62 28,030 Discount Rate = 5% PV (part b) $83,672 CCA Tax Shield Incremental UCC (part c) $70,000 Net Salvage (part d) $9,000 PV to Infinity (part c) $3,25 Tax Shield Lost on $,688 Salvage (part d) PV Total CCA $2,286 NPV (part e) $26,93 b) The present value of the annual after-tax savings without taking amortization into account is $83,672 as found in the Exhibit. c) The incremental UCC is $70,000 and the present value of the tax savings to infinity is $3,25, as found in the Exhibit. d) The net salvage value is $9,000 and the present value of the lost tax shield at year five is $,688, as found in the Exhibit. e) The net present value of the project is $26,93, as shown in the Exhibit. The acquisition should be made. Case 2: Digby Foods Ltd. The corrected calculations are shown in Solution Case Exhibit -2. You will find it useful to prepare this exhibit before attempting to answer the questions. 8

9 Solution Case Exhibit -2 Digby Foods Ltd. Investment Analysis Year 0 Year Year 2 Year 3 Year 4 Year 5 Capital Outlay: Equipment $500,000 Freight $20,000 Installation $0,000 Building repairs $50,000 TOTAL $580,000 Unit price $5 $5 $6 $6 $6 $6 Unit fixed and variable cost $3 $3 $3 $3 $4 $4 Unit sales $30,000 $7,000 $05,300 $94,770 $85,293 Sales $682,500 $644,963 $609,490 $575,968 $544,289 less cannibalism $5,000 $5,000 $5,000 $5,000 $5,000 Net sales $667,500 $629,963 $594,490 $560,968 $529,289 Cash Operating Expenses $405,600 $379,642 $355,345 $332,602 $3,36 Capital cost allowance: Equipment $66,250 $5,938 $86,953 $65,25 $48,9 46,733 UCC Building $2,500 $4,750 $4,275 $3,848 $3,463 3,65 UCC TOTAL operating expenses $474,350 $500,330 $446,573 $40,665 $363,690 Earnings before tax $93,50 $29,633 $47,97 $59,302 $65,599 Income tax $48,288 $32,408 $36,979 $39,826 $4,400 Net income $44,863 $97,225 $0,938 $9,477 $24,200 Add CCA back to net income $68,750 $20,688 $9,228 $69,063 $52,374 Operating Cash Flow $23,63 $27,93 $202,66 $88,540 $76,574 Working capital $25,000 $68,250 $64,496 $60,949 $57,597 $54,429 Investment in working capital (change) $25,000 $43,250 $3,754 $3,547 $3,352 $3,68 Recovery of working capital $54,429 Salvage values: Equipment $46,733 Building $3,65 TOTAL cash flows $605,000 $70,363 $22,666 $205,73 $9,892 $42,068 Discount rate = 5% PV one year hence $39,65 NPV $60,598 Decision: Accept the project 9

10 a) The procedures which are included in the consultant s report but which are summarized as follows: i) Freight and installation charges should be capitalized as part of equipment costs and depreciated. Revenue Canada will not allow the charges to be expensed. ii) Repairs to the building should be capitalized and depreciated. Revenue Canada will want this approach. iii) Interest expense should not be included since such financing effects are picked up in the cost of capital or discount rate. iv) The discount rate of 2% is incorrect. The cost of capital is 8% + 0.9(5.78% 8%) = 5.0%. This cost of capital reflects the business risk associated with the project. b) The procedures which are omitted are summarized as follows: i) Inflation effects are omitted. Sales should be increased by 5% per year and cash fixed and variable costs by 4% per year. ii) Lost sales of $5,000 per year should be treated as a cash outflow. These sales would not be lost if the project is rejected. It will also be correct if students choose to inflate the lost sales by 5% each year. iii) Initial working capital and annual reductions/increments should be treated as cash inflows/ outflows. At the end of the project, total working capital should be recovered. iv) Salvage value on equipment and buildings should be taken into account. Given case information, it should be assumed that these assets are liquidated at book values. c) The net present value is $39,65 and the project should be accepted. Case 3: Halifax Sea Service The corrected calculations are shown in Solution Case Exhibit -3. You will find it useful to prepare this exhibit before attempting to answer the questions. Solution Case Exhibit -3 Halifax Sea Service Ltd. Correct Project Evaluation Part A: Data Table Corrected Year 0 Year Year 2 Year 3 Year 4 Year 5 Cost of cranes $500,000 Salvage value $0 CCA rate = 30% (50,000/500,000) to infinity Discount rate = Cost of capital =5% Sales adjustement (less 00,000) $650,000 $700,000 $750,000 $800,000 $750,000 by inflation factor of 5% $682,500 $77,750 $868,29 $972,405 $957,2 Expenses: 70% of sales $477,750 $540,225 $607,753 $680,684 $670,048 Total current assets $00,000 $25,000 $30,000 $50,000 $35,000 $0,000 Change in NWC $00,000 $25,000 $5,000 $20,000 $5,000 $25,000 Recovery of NWC $0,000 Tax rate = 30% Part B: NPV Computations Capital spending Cost of cranes $500,000 Continued > 0

11 Operating Cash Flows: Sales $682,500 $77,750 $868,29 $972,405 $957,2 less expenses $477,750 $540,225 $607,753 $680,684 $670,048 Difference $204,750 $23,525 $260,466 $29,722 $287,63 After-tax ( 0.25) 53,563 73,644 95,349 28,79 25,373 5% $33,533 $3,300 $28,445 $25,095 $07,078 TOTAL PV $625,450 CCA tax shield to infinity $83,333 / 2 year rule $77,899 Change in NWC (equals use of cash) $00,000 $25,000 $5,000 $20,000 $5,000 $25,000 Recovery in NWC $0,000 5%(t to t5) $2,739 $3,78 $3,50 $8,576 $67,9 TOTAL PV $37,025 NPV (sum of column) $40,374 a) The errors or mistakes in the report are summarized as follows: i) Sales should be reduced by $00,000 per year (to remove optimism) and then inflated at an annual rate of 5%. Since cash operating expenses are a percentage of sales, this procedure captures some of the inflationary effects for operating expenses. ii) Interest should not be treated as an expense in the NPV analysis since the effect is captured through the use of the WACC as the discount factor. ii) Amortization (CCA) should be added to profit after taxes to calculate cash flow from operations. iv) The annual principal repayment on the loan should not be deducted from cash flows. The cost of the cranes in Year 0 is the relevant cash flow. v) The treatment of working capital (total current assets) is wrong. Only the initial and annual incremental working capital should be treated as investments. Also, working capital at the end of the life of the project should be recovered. vi) The use of the firm s before-tax borrowing rate as the discount rate is not correct. The WACC should be used in this NPV analysis since the new project has the same risk characteristics as the firm s existing projects. The WACC = (0.40)(0.0)( ) + (0.60)(0.20) = 0.5 vii) The tax shield to infinity on the UCC at the end of year 5 should be included in the analysis since it is a savings. b) The Exhibit contains the adjusted version of the report. Each error or mistake in part a) has been addressed and the necessary adjustments made. c) Based on the results in the Exhibit the NPV is positive $40,374 and this suggests the new project is profitable. CHAPTER TWO Qualitative Questions Question New projects can influence risk when combined with existing assets. The correlation coefficient of a project measures how the cash flows will diversify the risk of existing projects. When project cash flows are not highly correlated with existing cash flows, the new project reduces total risk. The correlation coefficient is required to determine the market risk of a project.