Solution manual financial management 10e by keown chapter 11

CHAPTER 11 Capital Budgeting and Risk Analysis CHAPTER ORIENTATION The focus of this chapter will be on how to adjust for the riskiness of a given project or combination of projects CHAPTER OUTLINE I II Risk and the investment decision A Up to this point we have treated the expected cash flows resulting from an investment proposal as being known with perfect certainty We will now introduce risk B The riskiness of an investment project is defined as the variability of its cash flows from the expected cash flow What measure of risk is relevant in capital budgeting? A In capital budgeting, a project can be looked at on three levels First, there is the project standing alone risk, which is a project’s risk ignoring the fact that much of this risk will be diversified away as the project is combined with the firm’s other projects and assets Second, we have the project’s contribution-to-firm risk, which is the amount of risk that the project contributes to the firm as a whole; this measure considers the fact that some of the project’s risk will be diversified away as the project is combined with the firm’s other projects and assets, but ignores the effects of diversification of the firm’s shareholders Finally, there is systematic risk, which is the risk of the project from the viewpoint of a well-diversified shareholder; this measure considers the fact that some of a project’s risk will be diversified away as the project is combined with the firm’s other projects, and, in addition, some of the remaining risk will be diversified away by shareholders as they combine this stock with other stocks in their portfolio 34 B III Because of bankruptcy costs and the practical difficulties involved in measuring a project’s level of systematic risk, we will give consideration to the project’s contribution-to-firm risk and the project’s systematic risk Methods for incorporating risk into capital budgeting A The certainty equivalent approach involves a direct attempt to allow the decision maker to incorporate his or her utility function into the analysis In effect, a riskless set of cash flows is substituted for the original set of risky cash flows, between which the financial manager is indifferent To simplify calculations, certainty equivalent coefficients ( t's) are defined as the ratio of the certain outcome to the risky outcome between which the financial manager is indifferent Mathematically, certainty equivalent coefficients can be defined as follows: αt certain cash flow t risky cash flow t = The appropriate certainty equivalent coefficient is multiplied by the original cash flow (which is the risky cash flow) with this product being equal to the equivalent certain cash flow Once risk is taken out of the cash flows, those cash flows are discounted back to present at the risk-free rate of interest and the project's net present value or profitability index is determined If the internal rate of return is calculated, it is then compared with the risk-free rate of interest rather than the firm's required rate of return Mathematically, the certainty summarized as follows: n NPV = ∑ t =1 equivalent approach can be α t FCFt - IO (1 + k rf ) t where αt = the certainty equivalent coefficient for time period t FCFt = the annual expected free cash flow in time period t IO = the initial cash outlay n = the project's expected life krf = the risk-free interest rate 35 B The use of the risk-adjusted discount rate is based on the concept that investors demand higher returns for more risky projects If the risk associated with the investment is greater than the risk involved in a typical endeavor, then the discount rate is adjusted upward to compensate for this risk The expected cash flows are then discounted back to present at the risk-adjusted discount rate Then the normal capital budgeting criteria are applied, except in the case of the internal rate of return, in which case the hurdle rate to which the project's internal rate of return is compared now becomes the risk-adjusted discount rate Expressed mathematically, the net present value using the riskadjusted discount rate becomes n NPV = ∑ t =1 where FCFt IV FCFt - IO (1 + k*) t = the annual expected free cash flow in time period t IO = the initial outlay k* = the risk-adjusted discount rate n = the project's expected life Methods for measuring a project's systematic risk A Theoretically, we know that systematic risk is the "priced" risk, and thus, the risk that affects the stock's market price and thus the appropriate risk with which to be concerned However, if there are bankruptcy costs (which are assumed away by the CAPM), if there are undiversified shareholders who are concerned with more than just systematic risk, if there are factors that affect a security's price beyond what the CAPM suggests, or if we are unable to confidently measure the project's systematic risk, then the project's individual risk carries relevance Moreover, in general, a project's individual risk is highly correlated with the project's systematic risk, making it a reasonable proxy to use B In spite of problems in confidently measuring an individual firm's level of systematic risk, if the project appears to be a typical one for the firm, then using the CAPM to determine the appropriate risk return tradeoffs and then judging the project against them may be a warranted approach C If the project is not a typical project, we are without historical data and must either estimate the beta using accounting data or use the pure-play method for estimating beta Using historical accounting data to substitute for historical price data in estimating systematic risk: To estimate a project's beta using accounting data we need only run a time series regression of the 36 division's return on assets on the market index The regression coefficient from this equation would be the project's accounting beta and serves as an approximation for the project's true beta V Additional approaches for dealing with risk in capital budgeting A B VI The pure play method for estimating a project's beta: The pure play method attempts to find a publicly traded firm in the same industry as the capital-budgeting project Once the proxy or pure-play firm is identified, its systematic risk is determined and then used as a proxy for the project's systematic risk A simulation imitates the performance of the project being evaluated by randomly selecting observations from each of the distributions that affect the outcome of the project, combining those observations to determine the final output of the project, and continuing with this process until a representative record of the project's probable outcome is assembled The firm's management then examines the resultant probability distribution, and if management considers enough of the distribution lies above the normal cutoff criterion, it will accept the project The use of a simulation approach to analyze investment proposals offers two major advantages: a The financial managers are able to examine and base their decisions on the whole range of possible outcomes rather than just point estimates b They can undertake subsequent sensitivity analysis of the project A probability tree is a graphical exposition of the sequence of possible outcomes; it presents the decision maker with a schematic representation of the problem in which all possible outcomes are graphically displayed Other sources and measures of risk A Many times, especially with the introduction of a new product, the cash flows experienced in early years affect the size of the cash flows experienced in later years This is called time dependence of cash flows, and it has the effect of increasing the riskiness of the project over time ANSWERS TO END-OF-CHAPTER QUESTIONS 11-1 The payback period method is frequently used as a rough risk screening device to eliminate projects whose returns not materialize until later years In this way, the earliest returns are emphasized, which in all likelihood have less uncertainty surrounding them 37 11-2 The use of the risk-adjusted discount rate assumes that risk increases over time When using the risk-adjusted discount rate method, we are adjusting downward the value of future cash flows that occur later in the future more severely than earlier ones This assumption can be justified because flows that are expected further out in the future are more difficult to forecast and less certain than are flows that are expected in the near future 11-3 The primary difference between the certainty equivalent approach and the riskadjusted discount rate approach is where the adjustment for risk is incorporated into the calculations The certainty equivalent approach penalizes or adjusts downwards the value of the expected annual free cash flows, while the riskadjusted discount rate leaves the cash flows at their expected value and adjusts the required rate of return, k, upwards to compensate for added risk In either case the net present value of the project is being adjusted downwards to compensate for additional risk An additional difference between these methods is that the riskadjusted discount rate assumes that risk increases over time and that cash flows occurring later in the future should be more severely penalized The certainty equivalent method, on the other hand, allows each cash flow to be treated individually 11-4 A probability tree is a graphical exposition of the sequence of possible outcomes, presenting the decision maker with a schematic representation of the problem in which all possible outcomes are graphically displayed Moreover, the computations and results of the computations are shown directly on the tree, so that the information can be easily understood Thus the probability tree allows the manager to quickly visualize the possible future events, their probabilities, and outcomes In addition, the calculation of the expected internal rate of return and enumeration of the distribution should aid the financial manager in his decision-making process 11-5 The idea behind simulation is to imitate the performance of the project being evaluated This is done by randomly selecting observations from each of the distributions that affect the outcome of the project, combining each of those observations and determining the final outcome of the project, and continuing with this process until a representative record of the project's probable outcome is assembled In effect, the output from a simulation is a probability distribution of net present values or internal rates of return for the project The decision maker then bases his decision on the full range of possible outcomes 11-6 The time dependence of cash flows refers to the fact that, many times, cash flows in later periods are dependent upon the cash flows experienced in earlier periods For example, if a new product is introduced and the initial public reaction is poor, resulting in low initial cash flows, then cash flows in future periods are likely to be low also Examples include the introduction of any new products, for example, the Edsel on the negative side, and hopefully this book on the positive side 38 SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A n 11-1A (a) = ∑ i =1 A Xi P(Xi) = $4,000 (0.15) + $5,000 (0.70) + $6,000 (0.15) = $600 + $3,500 + $900 = $5,000 B = $2,000 (0.15) + $6,000 (0.70) + $10,000 (0.15) = $300 + $4,200 + $1,500 = $6,000 n (b) NPV = ∑ t =1 NPVA FCFt - I0 (1 + k*) t = $5,000 (3.605) - $10,000 = $18,025 - $10,000 = $8,025 NPVB = $6,000 (3.352) - $10,000 = $20,112 - $10,000 = $10,112 (c) One might also consider the potential diversification effect associated with these projects If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced 39 n 11-2A (a) = ∑ i =1 Xi P(Xi) = $35,000 (0.10) + $40,000 (0.40) + $45,000 (0.40) A + $50,000 (0.10) = $3,500 + $16,000 + $18,000 + $5,000 = $42,500 = $10,000 (0.10) + $30,000 (0.20) + $45,000 (0.40) B + $60,000 (0.20) + $80,000 (0.10) = $1,000 + $6,000 + $18,000 + $12,000 + $8,000 = $45,000 n (b) NPV = ∑ t =1 NPVA FCFt - IO (1 + k*) t = $42,500 (3.605) - $100,000 = $153,212.50 - $100,000 = $53,212.50 NPVB = $45,000 (3.517) - $100,000 = $158,265 - $100,000 (c) = $58,265 One might also consider the potential diversification effect associated with these projects If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced 11-3A Project A: (A) Year Expected Cash Flow -$1,000,000 500,000 700,000 600,000 500,000 (B) αt 1.00 95 90 80 70 (A x B) Present Value (Expected Factor at Present Cash Flow ) × (αt) 5% Value -$1,000,000 1.000 -$1,000,000 475,000 952 452,200 630,000 907 571,410 480,000 864 414,720 350,000 823 288,050 NPVA = $ 726,380 40 Project B: (A) (B) (A x B) Present Value Year Expected Cash Flow -$1,000,000 500,000 600,000 700,000 800,000 αt 1.00 90 70 60 50 (Expected Cash Flow ) × (αt) -$1,000,000 450,000 420,000 420,000 400,000 Factor at Present 5% Value 1.000 -$1,000,000 952 428,400 907 380,940 864 362,880 823 329,200 NPVB = $ 501,420 Thus, project A should be selected, as it has a higher NPV 11-4A (A) (B) (A x B) Present Value Year Expected Cash Flow -$90,000 25,000 30,000 30,000 25,000 20,000 αt 1.00 0.95 0.90 0.83 0.75 0.65 (Expected Cash Flow ) × (αt) -$90,000 23,750 27,000 24,900 18,750 13,000 Factor at Present 7% Value 1.000 -$90,000 935 22,206 873 23,571 816 20,318 763 14,306 713 9,269 NPV = $ -330 Thus, this project should not be accepted because it has a negative NPV 11-5A NPVA = n ∑ t =1 FCFt - I0 (1 + k*) t = $30,000 (.893) + $40,000(.797) + $50,000(.712) + $90,000(.636) + $130,000(.567) - $250,000 = $26,790 + $31,880 + $35,600 + $57,240 + $73,710 - $250,000 = - $24,780 NPVB = n ∑ t =1 FCF - I0 (1 + k*) t = $135,000(3.127) - $400,000 = $422,145 - $400,000 41 = $22,145 42 11-6A Project A: (A) Year Expected Cash Flow -$ 50,000 15,000 15,000 15,000 45,000 (B) αt 1.00 95 85 80 70 (A x B) (Expected Cash Flow ) × (αt) -$ 50,000 14,250 12,750 12,000 31,500 Present Value Factor at Present 6% Value 1.000 -$ 50,000.00 943 13,437.75 890 11,347.50 840 10,080.00 792 24,948.00 NPVA = $ 9,813.25 Project B: (A) Year Expected Cash Flow -$ 50,000 20,000 25,000 25,000 30,000 (B) αt 1.00 90 85 80 75 (A x B) (Expected Cash Flow ) × (αt) -$ 50,000 18,000 21,250 20,000 22,500 Present Value Factor at Present 6% Value 1.000 -$ 50,000.00 943 16,974.00 890 18,912.50 840 16,800.00 792 17,820.00 NPVB = $ 20,506.50 Thus project B should be selected, as it has a higher NPV 43 Year p = 0.3 p = 0.6 $700,000 Years Joint each Branch Probability (A)(B) $300,000 -12.95% 0.18 -2.33% $700,000 10.92% 0.36 3.93% $1,100,000 29.25% 0.06 1.76% $400,000 3.15% 0.06 0.19% $700,000 19.60% 0.15 2.94% $1,000,000 33.33% 0.06 2.00% $1,300,000 45.36% 0.03 1.36% $600,000 23.74% 0.01 0.24% $900,000 37.77% 0.05 1.89% $1,100,000 46.08% 0.04 1.84% P = 0.1 p = 0.6 p = 0.2 p = 0.5 299 p = 0.3 - $1,200,000 p = 0.2 $850,000 p = 0.1 p = 0.1 p = 0.1 p = 0.5 $1,000,000 p = 0.4 1.00 Expected internal rate of return d The range of possible IRR’s from –12.95% to 46.08% = 13.82% 11-7A (a –c) Internal Rate of Return for Year Years Years p = 0.5 Internal Rate Joint each Branch Probability (A)(B) $230,000 130.25% 0.09 11.72% $180,000 124.68% 0.09 11.22% $205,000 121.09% 0.15 18.16% $155,000 114.96% 0.15 17.24% $180,000 111.30% 0.06 6.68% $130,000 104.46% 0.06 6.27%] $10,000 -42.44% 0.24 -10.19% $0 -90.00% 0.16 -14.40% p = 0.5 $200,000 p = 0.3 p = 0.5 p = 0.5 p = 0.5 300 $175,000 p = 0.6 $100,000 p = 0.2 p = 0.5 $-100,000 p = 0.5 $150,000 p = 0.4 p = 1.0 p = 0.6 $10,000 $10,000 p = 1.0 p = 0.4 $0 d The range of possible IRR’s from –90.00% to 130.25% 1.00 Expected internal rate of return = 46.70% 11-8A (a –c) of Return for Year Year SOLUTIONS TO INTEGRATIVE PROBLEM First there is the project standing alone risk, which is a project's risk ignoring the fact that much of this risk will be diversified away as the project is combined with the firm's other projects and assets Second, we have the project's contribution-tofirm risk, which is the amount of risk that the project contributes to the firm as a whole; this measure considers the fact that some of the project's risk will be diversified away as the project is combined with the firm's other projects and assets, but ignores the effects of diversification of the firm's shareholders Finally, there is systematic risk, which is the risk of the project from the viewpoint of a well diversified shareholder; this measure considers the fact that some of a project's risk will be diversified away as the project is combined with the firm's other projects, and, in addition, some of the remaining risk will be diversified away by the shareholders as they combine this stock with other stocks in their portfolio According to the CAPM, systematic risk is the only relevant risk for capital budgeting purposes; however, reality complicates this somewhat In many instances a firm will have undiversified shareholders; for them the relevant measure of risk is the project's contribution to firm risk The possibility of bankruptcy also affects our view of what measure of risk is relevant Because the project's contribution to firm risk can affect the possibility of bankruptcy, this may be an appropriate measure of risk since there are costs associated with bankruptcy The primary difference between the certainty equivalent approach and the riskadjusted discount rate approach is where the adjustment for risk is incorporated into the calculations The certainty equivalent approach penalizes or adjusts downwards the value of the expected annual free cash flows, while the riskadjusted discount rate leaves the cash flows at their expected value and adjusts the required rate of return, k, upwards to compensate for added risk In either case the net present value of the project is being adjusted downwards to compensate for additional risk An additional difference between these methods is that the riskadjusted discount rate assumes that risk increases over time and that cash flows occurring later in the future should be more severely penalized The certainty equivalent method, on the other hand, allows each cash flow to be treated individually A probability tree is a graphical exposition of the sequence of possible outcomes, presenting the decision maker with a schematic representation of the problem in which all possible outcomes are graphically displayed Moreover, the computations and results of the computations are shown directly on the tree, so that the information can be easily understood Thus the probability tree allows the manager to quickly visualize the possible future events, their probabilities, and outcomes In addition, the calculation of the expected internal rate of return and enumeration of the distribution should aid the financial manager in his decision-making process The idea behind simulation is to imitate the performance of the project being evaluated This is done by randomly selecting observations from each of the distributions that affect the outcome of the project, combining each of those 40 observations and determining the final outcome of the project, and continuing with this process until a representative record of the project's probable outcome is assembled In effect, the output from a simulation is a probability distribution of net present values or internal rates of return for the project The decision maker then bases his decision on the full range of possible outcomes Sensitivity analysis involves determining how the distribution of possible net present values or internal rates of return for a particular project is affected by a change in one particular input variable This is done by changing the value of one input variable while holding all other input variables constant The time dependence of cash flows refers to the fact that, many times, cash flows in later periods are dependent upon the cash flows experienced in earlier periods For example, if a new product is introduced and the initial public reaction is poor, resulting in low initial cash flows, then cash flows in future periods are likely to be low also Examples include the introduction of any new products, for example, the Edsel on the negative side, and hopefully this book on the positive side Project A: (A) (B) (A x B) Present Value Expected Cash Flow Year -$150,000 40,000 40,000 40,000 100,000 αt (Expected Cash Flow ) × (αt) Factor at 7% 1.00 90 85 80 70 -$150,000 36,000 34,000 32,000 70,000 1.000 935 873 816 763 (B) (A x B) Present Value -$150,000 33,660 29,682 26,112 53,410 NPVA = - $ 7,136 Project B: (A) Expected YearCash Flow -$200,000 50,000 60,000 60,000 50,000 αt 1.00 95 85 80 75 (Expected Cash Flow ) × (αt) -$200,000 47,500 51,000 48,000 37,500 Present Value Factor at Present 7% Value 1.000 -$200,000 935 44,413 873 44,523 816 39,168 763 28,613 NPVB = - $ 43,283 Thus, neither project should be selected, as they both have negative NPVs 41 Year Joint each Branch Years p = 0.3 Probability (A)(B) $200,000 -12.08% 0.12 -1.45% $300,000 0.00% 0.28 0.00% $250,000 0.00% 0.08 0.00% $450,000 20.55% 0.20 4.11% $650,000 37.26% 0.12 4.47% $300,000 17.54% 0.04 0.70% $500,000 36.19% 0.10 3.62% $700,000 51.84% 0.04 2.07% $1,000,000 71.94% 0.02 1.44% p = 0.7 $300,000 p = 0.4 p = 0.2 p = 0.5 298 p = 0.4 -$600,000 p = 0.3 $350,000 p = 0.2 p = 0.2 p =0.5 p = 0.2 $450,000 p = 0.1 1.00 Expected internal rate of return The range of possible IRR’s from -12.08% to 71.94% = 14.96% Part Internal Rate of Return for Year Solutions to Problem Set B n 11-1B (a) ∑ X = XA = $5,000 (0.20) + $6,000 (0.60) + $7,000 (0.20) = $1,000 + $3,600 + $1,400 = $6,000 = $3,000 (0.20) + $7,000 (0.60) + $11,000 (0.20) = $600 + $4,200 + $2,200 = $7,000 XB i =1 n (b) NPV = ∑ t =1 NPVA = FCFt - I0 (1 + k*) t $6,000 (3.517) - $10,000 = $21,102 - $10,000 = $11,102 NPVB = (c) Xi P(Xi) $7,000 (3.127) - $10,000 = $21,889 - $10,000 = $11,889 One might also consider the potential diversification effect associated with these projects If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced 43 n 11-2B (a) X = XA = ∑ i =1 Xi P(Xi) $40,000 (0.10) + $45,000 (0.40) + $50,000 (0.40) + $55,000 (0.10) XB = $4,000 + $18,000 + $20,000 + $5,500 = $47,500 = $20,000 (0.10) + $40,000 (0.20) + $55,000 (0.40) + $70,000 (0.20) + $90,000 (0.10) = $2,000 + $8,000 + $22,000 + $14,000 + $9,000 = $55,000 n (b) NPV = ∑ t =1 NPVA = $47,500 (3.696) - $125,000 = $175,560 - $125,000 = $50,560 NPVB = (c) FCFt - I0 (1 + k*) t $55,000 (3.517) - $125,000 = $193,435 - $125,000 = $68,435 One might also consider the potential diversification effect associated with these projects If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced 44 11-3B Project A: (A) (B) (A x B) Present Value Year Expected Cash Flow -$100,000 600,000 750,000 600,000 550,000 αt 1.00 90 90 75 65 (Expected Cash Flow ) × (αt) -$100,000 540,000 675,000 450,000 357,500 Factor at Present 5% Value 1.000 -$100,000 952 514,080 907 612,225 864 388,800 823 294,222.50 NPVA = $ 1,709,327.50 Project B: (A) Year Expected Cash Flow -$100,000 600,000 650,000 700,000 750,000 (B) (A x B) αt 1.00 95 75 60 60 (Expected Cash Flow ) × (αt) -$100,000 570,000 487,500 420,000 450,000 Present Value Factor at Present 5% Value 1.000 -$100,000 952 542,640 907 442,162.50 864 362,880 823 370,350 NPVB = $1,618,032.50 Thus, project A should be selected, as it has a higher NPV 11-4B (A) (B) Year Expected Cash Flow -$100,000 30,000 25,000 30,000 20,000 25,000 (A x B) αt 1.00 0.95 0.90 0.83 0.75 0.65 Present Value (Expected Factor at Present Cash Flow ) ×.( αt) 8% Value -$100,000 1.000 -$100,000 28,500 926 26,391 22,500 857 19,283 24,900 794 19,771 15,000 735 11,025 16,250 681 11,066 NPV = -$ 12,464 Thus, this project should not be accepted because it has a negative NPV 45 11-5B NPVA FCFt - IO (1 + k*) t n ∑ = t =1 = $30,000 (.885) + $40,000(.783) + $50,000(.693) + $80,000(.613) + $120,000(.543) - $300,000 = $26,550 + $31,320 + $34,650 + $49,040 + $65,160 - $300,000 = NPVB - $93,280 n ∑ = t =1 FCF - IO (1 + k*) t = $130,000(3.127) - $450,000 = $406,510 - $450,000 = -$43,490 11-6B Project A: (A) Year Expected Cash Flow -$ 75,000 20,000 20,000 15,000 50,000 (B) αt 1.00 95 85 80 70 (A x B) (Expected Cash Flow ) x (αt) -$ 75,000 19,000 17,000 12,000 35,000 Present Value Factor at Present 7% Value 1.000 -$ 75,000.00 935 17,765.00 873 14,841.00 816 9,792.00 763 26,705.00 NPVA = ($ 5,897.00) Project B: (A) Year Expected Cash Flow -$ 75,000 25,000 30,000 30,000 25,000 (B) αt (A x B) (Expected Cash Flow ) x (αt) 1.00 95 85 80 75 -$ 75,000 23,750 25,500 24,000 18,750 Thus project B should be selected, as it has a higher NPV 46 Factor at 7% Present Value Present Value 1.000 -$ 75,000.00 935 22,206.25 873 22,261.50 816 19,584.00 763 14,306.25 NPVB = $ 3,358.00 Year Years Probability (A)(B) $300,000 -15.12% 0.06 -0.9072% $700,000 7.69% 0.30 2.3070% $1,100,000 25.25% 0.24 6.0600% $400,000 0.00% 0.06 0.0000% $700,000 15.75% 0.15 2.3625% $900,000 24.73% 0.06 1.4838%] $1,300,000 40.44% 0.03 1.2132% $600,000 46.82% 0.03 1.4046% $900,000 58.94% 0.06 3.5364% $1,100,000 66.27% 0.01 1.00 Expected internal rate of return 0.6627% p = 0.1 p = 0.5 $750,000 p = 0.4 p = 0.6 p = 0.2 303 -$1,300,000 p = 0.5 p = 0.3 p = 0.2 $900,000 p = 0.1 p = 0.1 p = 0.3 p = 0.6 $1,500,000 (d) p = 0.1 The range of possible IRR’s from -15.12% to 66.27 = 18.1230% 11-7B (a –c) of Return for Year Internal Rate Joint each Branch Years Years p = 0.5 Probability (A)(B) $255,000 115.83% 105 12.16227% $205,000 110.76% 105 11.6298% $210,000 101.15% 175 17.7013% $160,000 95.18% 175 16.6565% $170,000 86.57% 070 6.0599% $120,000 79.42% 070 5.5594% $10,000 -46.70% 180 -8.4060% $0 -91.67% 120 -11.0004% p = 0.5 $225,000 p = 0.3 p = 0.5 p = 0.5 p = 0.5 $180,000 p = 0.2 p = 0.7 304 $100,000 p = 0.5 -$120,000 p = 0.5 $140,000 p = 0.3 p = 1.0 p = 0.6 $10,000 $10,000 p = 1.0 p = 0.4 $0 1.00 Expected internal rate of return (d) The range of possible IRR’s from –91.67% to 115.83% = 50.3627% 11-8B (a –c) of Return for Year Year Internal Rate Joint each Branch MADE IN THE U S A., DUMPED IN BRAZIL, AFRICA, (Ethics in Capital Budgeting) OBJECTIVE: To force the student to recognize the role ethical behavior plays in all areas of Finance DEGREE OF DIFFICULTY: Easy Case Solution: With ethics cases there are no right or wrong answers - just opinions Try to bring out as many opinions as possible without being judgmental In this case the question centers around what to when a product is no longer salable 49 ... negative side, and hopefully this book on the positive side 38 SOLUTIONS TO END-OF -CHAPTER PROBLEMS Solutions to Problem Set A n 11- 1A (a) = ∑ i =1 A Xi P(Xi) = $4,000 (0.15) + $5,000 (0.70) +... to 66.27 = 18.1230% 11- 7B (a –c) of Return for Year Internal Rate Joint each Branch Years Years p = 0.5 Probability (A)(B) $255,000 115 .83% 105 12.16227% $205,000 110 .76% 105 11. 6298% $210,000... 46.08% = 13.82% 11- 7A (a –c) Internal Rate of Return for Year Years Years p = 0.5 Internal Rate Joint each Branch Probability (A)(B) $230,000 130.25% 0.09 11. 72% $180,000 124.68% 0.09 11. 22% $205,000