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1 Operating Cash Flows: Sales $682,500 $771,750 $868,219 $972,405 $957,211 less expenses $477,750 $540,225 $607,753 $680,684 $670,048 Difference $204,750 $231,525 $260,466 $291,722 $287,163 After-tax (1 0.25) 153, , , , ,373 15% $133,533 $131,300 $128,445 $125,095 $107,078 TOTAL PV $625,450 CCA tax shield to infinity $83,333 1 / 2 year rule $77,899 Change in NWC (equals use of cash) $100,000 $25,000 $5,000 $20,000 $15,000 $25,000 Recovery in NWC $110,000 15%(t1 to t5) $21,739 $3,781 $13,150 $8,576 $67,119 TOTAL PV $37,025 NPV (sum of column) $140,374 a) The errors or mistakes in the report are summarized as follows: i) Sales should be reduced by $100,000 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)(0.10)(1-0.25) + (0.60)(0.20) = 0.15 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 $140,374 and this suggests the new project is profitable. CHAPTER TWO Qualitative Questions Question 1 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. 11
2 Question 2 There is unique risk for individual securities. There is market risk for all securities. When security returns do not co-vary perfectly with each other, the variations of one will be countered by variations of another. Some combinations of securities are dominated by others in terms of their risk and return. There is an efficient set of portfolios that dominates all other combinations of portfolios. Question 3 When markets are perfect and efficient, an investor will lend or borrow at the same risk-free rate. The combinations between the market portfolio and the risk-free rate form the CML. The CML represents the linear relationship between expected return and portfolio risk. Portfolio risk is measured by standard deviation. A combination on the CML will have the highest return compared to any other combination of securities that has the same risk. Question 4 When markets are perfect and efficient and investors are well diversified, only systematic risk is important for pricing assets. The SML represents the linear relationship between expected return and a security s systematic risk as measured by beta. The risk-free asset has no systematic risk. The beta of the market portfolio is equal to 1. Question 5 Determine the risk-free rate. Determine the expected return on the market. Estimate the beta of the security. The cost of capital is equal to the risk-free rate plus a premium. This premium equals the product of beta times the market risk premium. Question 6 All investors are assumed to be diversified to the point that only systematic risk matters to them. Market imperfections make homemade diversification difficult to accomplish. Projects have long economic lives that require multi-period analysis. The rate is assumed to be constant over the project life. Estimation of betas for projects is difficult. Question 7 Project beta reflects how project returns are affected by conditions in the market. Project beta measures the covariance of a project s cash flows with the market return. Project beta is the security beta of an all-equity firm doing business similar to the project. Financial leverage magnifies beta of a security. Question 8 Calculate project beta and use the CAPM. Use the firm s beta and adjust the beta to various risk classes. Use the betas of similar firms as proxies for project betas. Use the divisional cost of capital for a division project. Question 9 The probability of defaulting on debt depends on the total risk of the firm. Excessive total risk might result in bankruptcy. 12
3 Shareholders may not be able to diversify their risk as suggested by the efficient markets hypothesis. Creditors and employees value stability in a firm. Question 10 Use sensitivity analysis to estimate pessimistic, most likely, and optimistic levels of cash flows. Some factors influence cash flows more than others. Assess the likely impact of influential factors. Use simulation to estimate the variability of the NPV. Question 11 Market imperfections limit the amount of funds for projects. Projects are ranked in terms of their relative profitability or contribution to NPV. The objective is to maximize the NPV that can be generated by the limited budget. The firm should be able to capture the positive net present value of projects regardless of budgetary limits in fully efficient markets. Question 12 Formalizes the process of idea generation to ensure due attention is paid to all potentially good projects. Develops a formal proposal preparation format to ensure that the cash flow estimates are reliable for evaluation purposes. Formalizes the process by which funds are released to maintain upper management s control over project costs. Allows for performance evaluation. Question 13 The project beta measures the covariance of a project s cash flows with the market return weighted by the variance of the market returns. That is, the project beta is the security beta of an all-equity firm doing business similar to the project. To calculate the required return on equity for investment in such a project, the following formula is used: Required return = risk-free rate + project beta (expected return on the market - risk-free rate) Required return is the discount rate to be used when calculating project NPV, discounting the expected future cash flows to determine their present value. If a project is not all equity financed, then an appropriate discount rate for project cash flows would be calculated by adjusting project beta, and hence required return, for the degree of financial leverage. Financial leverage magnifies the beta of a security. In the case of THEM Inc., the proposed project has no debt financing. Practical problems generally arise when trying to estimate the project beta. If there is a firm strictly in that line of business, then its security beta can be used (after adjusting for financial leverage effects if these differ from that of the proposed project). Such proxies are often difficult to find, however. Generally, other firms also have unrelated projects. Further, they may have assets that are not the same age, different patterns of expected cash flows over time, or different relative contributions of this line of business to total firm value, and these sorts of complications can make proxy betas unreliable as a tool to assess proposed projects. Qualitative Multiple Choice Questions Question 1 iii) Diversifiable risk 13
4 Question 2 ii) Question 3 ii) Question 4 A line with a slope equal to the security s beta The project that has the highest net present value i) The unique risk that can be eliminated by diversification Question 5 iii) M is a portfolio of all securities in the market held in proportion to their market values, relative to the value of the total market portfolio. Question 6 i) The line R f MDE is the security market line (SML). Question 7 ii) Question 8 All investors will prefer to invest in the portfolio of risky assets, M, in combination with borrowing or lending the risk-free asset, and this is how they achieve points on the line R f MDE. iii) Systematic risk is the contribution of a security to the overall risk of the market portfolio. Question 9 i) Beta is the slope of the characteristic line. Question 10 iv) The total risk Question 11 iv) Question 12 Increase the cost of capital used to evaluate the project to reflect the higher risk of the project iii) On line G 1, perfect negative correlation between security returns creates an opportunity for the investor to eliminate portfolio risk completely. Question 13 ii) The feasible choices on B 1 C include a risk-free alternative, B 1, which occurs because the correlation coefficient is -1. Quantitative Multiple Choice Questions Question 1 ii) 25% Alpha holdings = 100 ($20) = $2,000 Zeta holdings = 100 ($50) = $5,000 Total holdings = $7,000 Expected return = a 2,000 5,000 b(18%) + a b(28%) = 25.14% 7,000 7,000 Closest to 25% Question 2 iii) 35% Standard deviation is the square root of the variance: (0.2857) 2 (0.3) 2 + (0.7143) 2 (0.4) (0.2857) (0.7143) (0.65) (0.3) (0.4) = ( ) 1/2 14
5 Question 3 = (0.1208) 1/2 = 34.76% = 35.0% to closest 0.5% iii) Project C should be selected because it has the lowest coefficient of variation, which measures the risk per unit of return. CV A = = Question 4 iv) 1.28 Question 5 CV B = CV C = , so C is preferred CV D = Closest to 1.28 iii) 1.29 Portfolio beta can be calculated as follows: Investment in BXO = 1,000 $23 = $23,000 Investment in MBA = 500 $55 = $27,500 Total investment is $50,500 Question = 0.85(0.10)(0.15) (0.10) 2 = Weight in BXO = = Weight in XYZ = = Portfolio beta = = = ii) 1.21 Portfolio beta = ( ) + ( ) + ( ) + ( ) + ( ) = 1.21 Question 7 ii) E and F Compute PI and rank the projects according to it: PV annual Project Cost ($) cash flows ($) PI Ranking D 600, , REJECT E 400, , Second F 250, , First As project D has a PI of less than 1, it should be rejected. Accepting projects E and F, $400,000 + $250,000 = $650,000, which is within $800,
6 Question 8 iii) 14.21% Question 9 ii) 1.01 Question 10 iii) 1.26 Portfolio variance = (0.35) 2 (0.15) 2 + (0.65) 2 (0.22) 2 + 2(0.35)(0.65)(-0.2)(0.15)(0.22) = Standard deviation = (0.0202) 1/2 = = B u + (1-0.35)a 10,000,000 15,000,000 bb u 1.45 = B u B u B u = B L = (1-0.40)a b1.05 B L = 1.26 Quantitative Problems Problem = (MRP) MRP = % R(company X) = ( ) = % Let p stand for the percentage of your money invested in company W. 1 - p is the percentage of your money invested in company X. Beta (portfolio) = 1.2 = 1.7p + 0.8(1 - p) Therefore, p = %; and (1 - p) = % R(portfolio) = ( )(0.235) + ( )( ) = % Amount invested in stock W = ( )($20,000) = $8, Amount invested in stock X = ( )($20,000) = $11, Problem 2 E[R Marc ] = 0.20(0.08) (0.47) (0.23) = Using the CAPM equation: = b Marc (0.12) b Marc = s 2 Marc = 0.2( ) ( ) ( ) 2 = s Marc = [ ] 1/2 = E[R Unik ] = 0.2(-0.25) (0.16) (0.58) = Using the CAPM equation: = b Unik (0.12) 16
7 b Unik = s 2 Unik = 0.2( ) ( ) ( ) 2 = s Unik = [ ] 1/2 = Using a table helps us to compare: Stock E(R) Beta Std. dev. Marc 33.2% % Unik 18.3% % a) Unik has much less systematic risk, since its beta is much smaller than Marc s. Thus Marc has more systematic risk it has a bigger beta. b) Stock Unik has more total risk than stock Marc because its standard deviation is larger. c) This chapter does not provide a specific measure for unsystematic risk. However, in this problem we can logically deduce which stock has the most unsystematic risk using the following train of thought: The unsystematic risk part of total risk can be diversified away by simply holding a well-diversified portfolio. In Canada, it is diversified away by holding an average of 25 or more stocks in a portfolio. In the United States, it takes about 15 stocks to achieve the same diversification. By comparing Unik and Marc we see Unik s standard deviation is larger, but its beta is smaller. By placing Unik in a well-diversified portfolio, more of its risk will be diversified away. That is, the stand-alone risk as measured by its large standard deviation will ultimately be reduced to relevant risk as measured by its smaller beta, once Unik is placed in a well-diversified portfolio. Similarly, as Marc s beta is larger and its standard deviation is smaller, far less of its risk can be diversified away, since relative to Unik we attribute more of Marc s risk to its beta. Problem 3 Step 1. Find the beta of the original portfolio by taking a weighted average of the individual stock s betas. We calculate a beta of 1.3. b P = ca b(0.6) + a b(1.0) + a b(1.4) + a b(1.8) d = 1.3 1,600 1,600 1,600 1,600 Step 2. Find the market risk premium using the original portfolio. R portfolio = = (R m - R f ). Solving, we find a market risk premium (MRP) of Step 3. Calculate the new portfolio s beta. Now, Stock 1 has a 0 weight (we sold it) and Stock 4 has a weight of a $800 = 0.5. The portfolio s new beta is: $1,600 b b P = ca b(1.0) + a b(1.4) + a b(1.8) d = ,600 1,600 1,600 Step 4. Find the portfolio s expected return. R portfolio = (0.07)(1.525) = % 17
8 Problem 4 Old assets: $1.00 New assets: $0.50 New total assets: $1.50 Old required rate: 18% = 7% + 5%(old beta); thus, old beta = 2.2 New required rate: 16% = 7% + 5%(new beta); thus, new beta = 1.8 $1 $0.5 (2.2) + $1.5 $1.5 b = 1.8 b = 1.0 To achieve a required return of 16%, the new overall beta must be 1.8, so the beta on the new asset must equal 1. Problem 5 a) Portfolio expected return = 0.2(13%) + 0.4(14%) + 0.4(15%) = 0.142, or 14.2% Portfolio beta = 0.2(1.4) + 0.4(1.0) + 0.4(1.1) = 1.12 b) According to the security market line, required returns are calculated as follows: Required return = risk-free rate + beta(return on the market - risk-free rate) Required return Expected return For security A 5% + 1.4(14% 5%) = 17.6% 13% For security B 5% + 1.0(14% 5%) = 14% 14% For security C 5% + 1.1(14% 5%) = 14.9% 15% For the portfolio 5% (14% 5%) = 15.08% 14.2% overall Therefore, security A has expected returns less than required for its risk level. Security B offers exactly the expected return required for its risk level, which is also the same as the market since its beta equals 1. Security C has an expected return slightly in excess of its required return. Overall, the portfolio has an expected return lower than that required. The implication of these findings is that security C is a slightly better than average investment but Security A is a very poor investment. Security B is fair. Security A is dragging down the returns on the portfolio, even though its weight is smaller than the others. As a result, the portfolio is expected to perform poorly there will not be enough return to compensate investors for the risk. c) The beta of a security is a measure of its systematic risk. That is, it measures the volatility of a security s return in relation to market returns. It is the covariance between the return on the security and the market returns, divided by the variance of the market returns. If beta exceeds 1, then the security s returns are expected to be more volatile than the returns on the market portfolio. That is, it is riskier than the average security in the market. d) Some problems that might be experienced when trying to estimate the beta of an investment project in practice are as follows: incomplete or unreliable data difficulty in estimating periodic returns unpredictable outcomes and the possibility of large forecast errors historical data may not predict future risk e) The CAPM or SML is the relationship between systematic risk and return, for any security or portfolio. The CML is the relationship between risk and return for efficient (i.e., perfectly diversified) portfolios. 18
9 Cases Case 1: Phelps Corp. This question involves soft capital rationing by a firm that is growing rapidly. Various capital budgeting techniques from Chapter 1 are to be combined with additional techniques that are useful in a constrained capital situation from Chapter 2. There are both mutually exclusive and independent projects in the available set of investments. An additional complication is that the investments required in various projects result in it being optimal to undertake some projects with lower PIs than other projects that are not undertaken. Simply ranking on PIs will not maximize NPV, and NPV maximization is the objective because this results in maximum shareholder wealth. In this problem, the firm is constrained not by a lack of funds (hard rationing), but by a policy limiting the maximum number of new projects (soft rationing). a) Soft capital rationing refers to a decision by management to limit capital spending. Examples include the need to manage rapid growth, as in the Phelps Corp. situation, and spending limits that are imposed because there is a sense that managers overstate the benefits of capital projects in order to achieve growth in their divisions or areas of the firm. Hard capital rationing refers to a situation where the firm is not able to finance all its positive NPV projects due to a lack of funds. Hard capital rationing can arise due to information asymmetry regarding the value of potential projects, transaction costs in raising funds or hiring labour, and agency problems due to managers concern about total risk, rather than systematic risk. b) PI calculations for each project are as follows: Project PI PI ranking Per NPV A B C D E PI measures the relative profitability of each project; that is, how much NPV the project provides per dollar invested. NPV measures the absolute profitability of each project; that is, how much the project would contribute to shareholder wealth, in dollars. c) Sample Report Phelps Corp. Analysis of Project Proposals Project Assessment: Projects A and B are mutually exclusive and cannot both be undertaken. With $3 million to invest, the firm can undertake several projects. An additional constraint is that managers can effectively manage at most 3 new projects. The firm has been growing rapidly and managers are feeling the strain. According to the PI calculations, the best projects would be E, D, and C in that order. Total investment would be $1,760,000. This set of projects will not maximize shareholder wealth. Only NPV can be used to select among projects when some or all are mutually exclusive. In order to identify the combination of 3 projects that will maximize shareholder wealth, subject to the spending limit of $3 million, all feasible project combinations must be considered. 19
10 Feasible combination Total investment Total NPV A + C + D $1,960,000 $644,000 A + C + E 2,260, ,000 A + D + E 2,300, ,000 B + C + D 2,240, ,000 B + C + E 2,540, ,000 B + D + E 2,580, ,000 C + D + E 1,760, ,000 The best combination is B, D, and E, with $2,580,000 invested and total NPV maximized at $858,000. Case 2: Consolidated Company For one of the two projects, a full calculation of project beta is required, beginning with the distribution of expected returns. a) Expected return on the market and on the project: Expected return on the market = 0.3(6%) + 0.4(7%) + 0.3(8%) = 1.2% + 3.5% + 2.4% = 7.0% Expected return on Project B = 0.3(3%) + 0.4(9%) + 0.3(17%) = 0.6% + 4.5% + 5.1% = 9.6% b) Standard deviation of returns on Project B and on the market: Project Project (P i ) Market Market [R E(R)] [R E(R)] 2 [R E(R)] (P i ) [R E(R)] 2 6.6% % % % % % s B = = 5.44% s M = = % c) Beta of Project B: Covariance between return on Project B and market return: (P i )[R - E(R)][R - E(R)] (0.3)(-6.6%)(-1.0%) = (0.4)(-0.6%)(-0.10) = (0.3)( 7.4%)(1.0%) = b = Covariance Var(Returns on Market) = =
11 d) CV for Projects A and B: CV = s E(R) Project A CV = 12% 16% = 0.75 Project B CV = 5.44% 9.6% = 0.57 e) Report on Projects A and B A summary of project characteristics is as follows: Project A Project B Expected return 16% (given) 9.6% Standard deviation 12% (given) 5.44% Coefficient of variation Beta 1.7 (given) 7.0 Required return (CAPM) % Note: 5% + 1.7(7% 5%) = 8.4% 5% + 7.0(7% 5%) = 19.0% Analysis According to CAPM Project B is clearly unacceptable, with an expected return of only 9.6% and a required return of 19%. B is a highly risky project and does not offer high enough returns to compensate for the risk. In contrast, Project A is acceptable, with an expected return of 16% that is well in excess of its required return of 8.4%. It is interesting to note that when comparing B to A, most of B s risk can not be diversified away since its beta is large (beta = 7 for Project B whereas Project A s beta = 1.7), and its standard deviation relative to project A is small (only 5.44% for Project B compared to 12% for A). This was captured in the coefficient of variation measure: B has less total risk per unit of return than A. Since the projects are independent management may wish to further investigate the impact of each project on the firm. Case 3: GHI Corp. a) Possible investment opportunities with their initial outlays and after-tax cash flows are presented in Solution Case Exhibit 2-1. Solution Case Exhibit 2-1 After-Tax Cash Flows Opportunity Projects Initial outlay Year 1 Year $(100,000) $ 70,000 $ 70, (300,000) 200, , (200,000) 145, , (200,000) 130, , (300,000) 205, , (100,000) 75,000 60, (400,000) 275, ,000 21
12 b) Using the capital asset pricing model, the required return to GHI for these opportunities are based on the firm s beta, as they are of the same risk as the firm as a whole: Required return = 4% + 1(12% - 4%) = 12% The results of applying the NPV method to these investment opportunities are presented in Solution Case Exhibit 2-2. Solution Case Exhibit 2-2 Opportunity Projects NPV 1 1 $18, , , , , , ,807 Since the capital budget exceeded the $300,000 constraint, Project 1 (with the highest NPV) has to be eliminated. The opportunity with the second highest NPV, Project 2, is within the budget and should be selected. Case 4: Manitou Inc. a) Before a comparison can be made, first compute the profitability of each project using the IRR so that the answer format appears as a percent. We used a financial calculator to solve for the following: By financial calculator: PV = -400 PMT = 120 N = 5 COMP i = IRR A = 15.24% 400 = 120c1 - IRR A = 15.24% 575 = 180c1 - IRR B = 17.07% 370 = 120c1 - IRR C = 18.63% (1 + IRR)-5 d IRR (1 + IRR)-5 d IRR (1 + IRR)-5 d IRR The firm-wide discount rate is its WACC: 5% + 1.6(13% - 5%) = 17.8% If Manitou applies this discount rate to evaluate the three projects, only Project C will be accepted because it is the only project with an IRR exceeding 17.8%. 22
13 The consequence of failing to adjust the discount rate for the risk implicit in projects is that the firm will accept high-risk projects, which usually have higher IRR due to their high-risk nature, and reject low-risk or safe projects, which usually have a low IRR due to their low-risk nature. The firm will become increasingly risk-taking. If we apply a risk-adjusted discount rate to evaluate Manitou s projects, we will come to very different conclusions: Project C falls into the class of a new product. It should have a beta of 2.2; therefore, its required rate of return should be: 5% + 2.2(13% - 5%) = 22.6% > IRR So Manitou should reject this risky project because its return is not sufficient to compensate for taking such high risk. Project A falls into the class of capacity expansion and should have a beta of Its required rate of return should be: 5% (13% - 5%) = 17.32% > IRR Although it is close to break-even, the IRR of 17.07% is not enough reward to compensate investors for the required return of 17.32%. Therefore, Project A should also be rejected. Because it is so close, management may want to review the project beta estimate of 1.54 to ensure it is correct. Project B falls into the class of replacement and should have a beta of 1. Its required rate of return should be: 5% + 1(13% - 5%) = 13% < IRR Therefore, this project should also be accepted. Management s beta estimate may be faulty for Project B. Since it is a replacement project, one might argue the average asset beta should equal the firm s beta of 1.6. If the firm is replacing an average asset then the 1.6 beta is more appropriate and the IRR of the replacement project should be at least 17.8%, the firm s WACC or average return. b) Firms usually apply so-called comparative analysis. A firm may find for each of its divisions, units, or different kinds of projects a so-called pure-play firm; that is, a firm exclusively in the same line of business as the division, unit, or project. CHAPTER THREE Qualitative Questions Question 1 Term loans are often used to finance capital equipment or plant costs or to provide permanent working capital. Term loans are preferable when the cost of public offerings of bonds or shares is too high. Term loans are needed temporarily until cash flows from operations are sufficient to repay the loan. Term loans can be structured so that the cash flows from the asset coincide with the interest and repayment schedule of the loan. Term loan provisions can be worked out more quickly than the provisions for a new bond issue. Term loan provisions are more flexible than bond provisions. Question 2 An instalment loan is a type of term loan that specifies that the borrower will make periodic payments or instalments. These instalments include principal and interest. 23
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