CH-13 Risk and Capital Budgeting – Foundations of Financial Management : Book Guide

Chapter 13 Risk and Capital Budgeting Discussion Questions 13-1. If corporate managers are risk-averse, does this mean they will not take risks? Explain. Risk-averse corporate managers are not unwilling to take risks, but will require a higher return from risky investments. There must be a premium or additional compensation for risk taking. 13-2. Discuss the concept of risk and how it might be measured. Risk may be defined in terms of the variability of outcomes from a given investment. The greater the variability, the greater the risk. Risk may be measured in terms of the coefficient of variation, in which we divide the standard deviation (or measure of dispersion) by the mean. We also may measure risk in terms of beta, in which we determine the volatility of returns on an individual stock relative to a stock market index. 13-3. When is the coefficient of variation a better measure of risk than the standard deviation? The standard deviation is an absolute measure of dispersion, while the coefficient of variation is a relative measure and allows us to relate the standard deviation to the mean. The coefficient of variation is a better measure of dispersion when we wish to consider the relative size of the standard deviation or compare two or more investments of different size. 13-4. Explain how the concept of risk can be incorporated into the capital budgeting process. Risk may be introduced into the capital budgeting process by requiring higher returns for risky investments. One method of achieving this is to use higher discount rates for riskier investments. This risk-adjusted discount rate approach specifies different discount rates for different risk categories as measured by the coefficient of variation or some other factor. Other methods, such as the certainty equivalent approach, also may be used. 13-5. If risk is to be analyzed in a qualitative way, place the following investment decisions in order from the lowest risk to the highest risk: a. New equipment b. New market c. Repair of old machinery d. New product in a foreign market e. New product in a related market f. Addition to a normal product line Referring to Table 13-3, the following order would be correct: Repair of old machinery (c) New equipment (a) Addition to a normal product line (f) New product in a related market (e) New market (b) New product in a foreign market (d) 13-6. Assume a company, correlated with the economy, is evaluating six projects, of which two are positively correlated with the economy, two are negatively correlated, and two are not correlated with it at all. Which two projects would you select to minimize the company’s overall risk? In order to minimize risk, the firm that is positively correlated with the economy should select the two projects that are negatively correlated with the economy. 13-7. Assume a firm has several hundred possible investments and that it wants to analyze the risk-return trade-off for portfolios of 20 projects. How should it proceed with the evaluation? The firm should attempt to construct a chart showing the risk-return characteristics for every possible set of 20. By using a procedure similar to that indicated in Figure 13-11, the best risk-return trade-offs or efficient frontier can be determined. We then can decide where we wish to be along this line. 13-8. Explain the effect of the risk-return trade-off on the market value of common stock. High profits alone will not necessarily lead to a high market value for common stock. To the extent large or unnecessary risks are taken, a higher discount rate and lower valuation may be assigned to our stock. Only by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market. 13-9. What is the purpose of using simulation analysis? Simulation is one way of dealing with the uncertainty involved in forecasting the outcomes of capital budgeting projects or other types of decisions. A Monte Carlo simulation model uses random variables for inputs. By programming the computer to randomly select inputs from probability distributions, the outcomes generated by a simulation are distributed about a mean, and instead of generating one return or net present value, a range of outcomes with standard deviations are provided. Chapter 13 Problems 1. Risk-averse (LO13-2) Assume you are risk-averse and have the following three choices. Which project will you select? Compute the coefficient of variation for each. Expected Value Standard Deviation A $2,200 $1,400 B 2,730 1,960 C 2,250 1,490 13-1. Solution: A. $1,440/$2,200 = .65 B. 1,960/2,730 = .72 C. $1,490/$2,250 = .66 Based on the coefficient of variation, you should select Project A because it is the least risky. 2. Expected value and standard deviation (LO13-1) Myers Business Systems is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given next: Possible Market Reaction Sales in Units Probabilities Low response 20 .10 Moderate response 40 .30 High response 55 .40 Very high response 70 .20 a. What is the expected value of unit sales for the new product? b. What is the standard deviation of unit sales? 13-2. Solution: Myers Business Systems a. D P DP 20 .10 2 40 .30 12 55 .40 22 70 .20 14 60 = b. D P P 20 50 –30 900 .10 90 40 50 –10 100 .30 30 55 50 +5 25 .40 10 70 50 +20 400 .20 80 210 3. Expected value and standard deviation (LO13-1) Sampson Corp. is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given. Possible Market Reaction Sales in Units Probabilities Low response 30 .10 Moderate response 50 .20 High response 75 .40 Very high response 90 .30 a. What is the expected value of unit sales for the new product? b. What is the standard deviation of unit sales? 13-3. Solution: Sampson Corp a. D P DP 30 .10 3 50 .20 10 75 .40 30 90 .30 27 70 = b. D P P 30 70 –40 1600 .10 160 50 70 –20 400 .20 80 75 70 +5 25 .40 10 90 70 +20 400 .30 120 370 4. Coefficient of variation (LO13-1) Shack Homebuilders Limited is evaluating a new promotional campaign that could increase home sales. Possible outcomes and probabilities of the outcomes are shown next. Compute the coefficient of variation. Possible Outcomes Additional Sales in Units Probabilities Ineffective campaign 40 .30 Normal response 100 .30 Extremely effective 120 .40 13-4. Solution: Shack Homebuilders Limited Coefficient of Variation (V) = Standard Deviation / Expected Value D P DP 40 .30 12 100 .30 30 120 .40 48 90= D P P 40 90 –50 2,500 .30 750 100 90 +10 100 .30 30 120 90 +30 900 .40 360 1,140 5. Coefficient of variation (LO13-1) Al Bundy is evaluating a new advertising program that could increase shoe sales. Possible outcomes and probabilities of the outcomes are shown next. Compute the coefficient of variation. Possible Outcomes Additional Sales in Units Probabilities Ineffective campaign 40 .20 Normal response 60 .50 Extremely effective 140 .30 13-5. Solution: Al Bundy Coefficient of Variation (V) = Standard Deviation / Expected Value D P DP 40 .20 8 60 .50 30 140 .30 42 80 = D P P 40 80 –40 1,600 .20 320 60 80 –20 400 .50 200 140 80 +60 3,600 .30 1,080 1,600 6. Coefficient of variation (LO13-1) Possible outcomes for three investment alternatives and their probabilities of occurrence are given next. Alternative 1 Outcomes Probability Alternative 2 Outcomes Probability Alternative 3 Outcomes Probability Failure 50 .2 90 .3 95 .2 Acceptable 90 .4 190 .3 215 .6 Successful 135 .4 225 .4 380 .2 Rank the three alternatives in terms of risk from lowest to highest (compute the coefficient of variation). 13-6. Solution: Alternative 1 Alternative 2 Alternative 3 D × P = DP D × P = P D × P = DP $50 0.2 $10 $90 0.3 $27 $95 0.2 $19 90 0.4 36 190 0.3 57 215 0.6 129 135 0.4 54 225 0.4 90 380 0.2 76 = $100 = $174 = $224 Standard Deviation Alternative 1 D P P $ 50 $100 $–50 $2,500 .2 $500 90 100 –10 100 .4 40 135 100 +35 1,225 .4 490 $1,030 13-6. (Continued) Alternative 2 $ 90 $174 $–84 $7,056 .3 $ 2,116.80 190 174 +16 256 .3 76.80 225 174 +51 2,601 .4 1040.40 $3,234.00 Alternative 3 $ 95 $224 $–129 $ 16,641 .2 $3,328.20 215 224 –9 81 .6 48.60 380 224 +156 24,336 .2 4,867.20 $8,244.00 Rank by Coefficient of Variation Coefficient of Variation (V) = Standard Deviation / Expected Value V Alternative 1 Alternative 1 Alternative 3 7. Coefficient of variation (LO1) Five investment alternatives have the following returns and standard deviations of returns. Alternative Returns— Expected Value Standard Deviation A $ 5,000 $1,200 B 4,000 600 C 4,000 800 D 8,000 3,200 E 10,000 900 Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk. 13-7. Solution: Coefficient of variation (V) = Standard deviation/Mean return Ranking from lowest to highest A $1,200/$5,000 = .24 E (.09) B $600/$4,000 = .15 B (.15) C $800/$4,000 = .20 C (.20) D $3,200/$8,000 = .40 A (.24) E $900/$10,000 = .09 D (.40) 8. Coefficient of variation (LO13-1) Five investment alternatives have the following returns and standard deviations of returns. Alternative Returns: Expected Value Standard Deviation A $ 1,980 $ 970 B 820 1,190 C 12,700 3,100 D 1,140 630 E 62,700 14,100 Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk. 13-8. Solution: Coefficient of Variation (V) = Standard deviation/Expected value Ranking from Lowest to Highest A $970/$1,980 = .49 E (.22) B $1,190/$820 = 1.45 C (.24) C $3,100/$12,700 = .24 A (.49) D $630/$1,140 = .55 D (.55) E $14,100/$62,700 = .22 B (1.45) 9. Coefficient of variation and time (LO13-1) Digital Technology wishes to determine its coefficient of variation as a company over time. The firm projects the following data (in millions of dollars): Year Profits: Expected Value Standard Deviation 1 $180 $62 3 240 104 6 300 166 9 400 292 a. Compute the coefficient of variation (V) for each time period. b. Does the risk (V) appear to be increasing over a period of time? If so, why might this be the case? 13-9. Solution: Digital Technology a. Year Profits: Expected Value Standard Deviation Coefficient of Variation 1 180 62 .34 3 240 104 .43 6 300 166 .55 9 400 292 .73 b. Yes, the risk appears to be increasing over time. This may be related to the inability to make forecasts far into the future. There is more uncertainty. 10. Risk-averse (LO13-2) Tim Trepid is highly risk-averse, while Mike Macho actually enjoys taking a risk. a. Which one of the four investments should Tim choose? Compute coefficients of variation to help you in your choice. Investments Returns: Expected Value Standard Deviation Buy stocks $ 9,140 $ 6,140 Buy bonds 7,680 2,560 Buy commodity futures 19,100 26,700 Buy options 17,700 18,200 b. Which one of the four investments should Mike choose? 13-10. Solution: Coefficient of Variation (V) = Standard Deviation / Expected Value Buy Stocks $6,140/9,140 = .672 Buy Bonds $2,560/7,680 = .333 Buy Commodity Futures $26,700/19,100 = 1.398 Buy Options $18,200/17,700 = 1.028 a. Tim should buy the bonds because bonds have the lowest coefficient of variation. b. Mike should buy the commodity futures because they have the highest coefficient of variation. 11. Risk-averse (LO13-2) Mountain Ski Corp. was set up to take large risks and is willing to take the greatest risk possible. Lakeway Train Co. is more typical of the average corporation and is risk-averse. a. Which of the following four projects should Mountain Ski Corp. choose? Compute the coefficients of variation to help you make your decision. b. Which one of the four projects should Lakeway Train Co. choose based on the same criteria of using the coefficient of variation? Year Returns: Expected Value Standard Deviation A 527,000 834,000 B 682,000 306,000 C 74,000 135,000 D 140,000 89,000 13-11. Solution: Mountain Ski Corp. and Lakeway Train Co. Coefficient of Variation (V) = Standard Deviation / Expected Value Project A $834,000/527,000 = 1.58 Project B 306,000/682,000 = .449 Project C 135,000/74,000 = 1.82 Project D 89,000/140,000 = .636 a. Mountain Ski Corp should choose Project C because it has the largest coefficient of variation. b. Lakeway Train Co. should choose Project B because it has the smallest coefficient of variation. 12. Coefficient of variation and investment decision (LO13-1) Kyle’s Shoe Stores Inc. is considering opening an additional suburban outlet. An aftertax expected cash flow of $130 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values. Which store site would you select based on the distribution of these cash flows? Use the coefficient of variation as your measure of risk. Site A Site B Probability Cash Flows Probability Cash Flows .3 80 .2 50 .3 130 .2 80 .1 160 .3 130 .3 170 .1 180 .2 235 13-12. Solution: Kyle’s Shoe Stores Inc. Standard Deviations of Sites A and B Site A D P P $ 80 $130 $–50 $2,500 .3 $750 130 130 –0– –0– .3 –0– 160 130 +30 900 .1 90 170 130 +40 1,600 .3 480 $1,320 Site B D P P $ 50 $130 $–80 $6,400 .2 $ 1,280 80 130 –50 2,500 .2 500 130 130 –0– –0– .3 –0– 180 130 +50 2,500 .1 250 235 130 +105 11,025 .2 2205 $4,235 VA = $36.33/$130 = .2795 VB = $65.08/$130 = .5006 Site A is the preferred site since it has the smallest coefficient of variation. Because both alternatives have the same expected value, the standard deviation alone would have been enough for a decision. A will be just as profitable as B but with less risk. 13. Risk-adjusted discount rate (LO13-3) Waste Industries is evaluating a $70,000 project with the following cash flows. Year Cash Flows 1 $11,000 2 16,000 3 21,000 4 24,000 5 30,000 The coefficient of variation for the project is .847. Based on the following table of risk-adjusted discount rates, should the project be undertaken? Select the appropriate discount rate and then compute the net present value. Coefficient of Variation Discount Rate 0 – .25 6% .26 – .50 8 .51 – .75 10 .76 – 1.00 14 1.01 – 1.25 20 13-13. Solution: Waste Industries Year Inflows PVIF @ 14% PV 1 $11,000 .877 $ 9,647 2 16,000 .769 12,304 3 21,000 .675 14,175 4 24,000 .592 14,208 5 30,000 .519 15,570 PV of Inflows $65,904 Investment 70,000 NPV $(4,096) Based on the negative net present value, the project should not be undertaken. Calculator solution: Find the PV of cash inflow using a financial calculator at 14 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 70,000 and press +|–, press the Enter key. Press down arrow, enter 11,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 21,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 24,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –4074.01, which is the present value of the inflow. Solution: –$4,074. Based on the negative net present value, the project should not be undertaken. 14. Risk-adjusted discount rate (LO13-3) Dixie Dynamite Company is evaluating two methods of blowing up old buildings for commercial purposes over the next five years. Method one (implosion) is relatively low in risk for this business and will carry a 12 percent discount rate. Method two (explosion) is less expensive to perform but more dangerous and will call for a higher discount rate of 16 percent. Either method will require an initial capital outlay of $75,000. The inflows from projected business over the next five years are given next. Which method should be selected using net present value analysis? Years Method 1 Method 2 1 $18,000 $20,000 2 24,000 25,000 3 34,000 35,000 4 26,000 28,000 5 14,000 15,000 13-14. Solution: Dixie Dynamite Co. Method 1 Method 2 Year Inflows PVIF @ 12% PV Inflows PVIF @ 16% PV 1 $18,000 .893 $16,074 $20,000 .862 $17,240 2 24,000 .797 19,128 25,000 .743 18,575 3 34,000 .712 24,208 35,000 .641 22,435 4 26,000 .636 16,536 28,000 .552 15,456 5 14,000 .597 7,938 15,000 .476 7,140 PV of Inflows $83,884 $80,846 Investment –75,000 –75,000 NPV $ 8,884 $ 5,846 Select Method 1 Calculator solution: Method 1: Find the PV of cash inflow using a financial calculator at 12 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 75,000 and press +|–, press the Enter key. Press down arrow, enter 18,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 24,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 34,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 14,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 8,872.06, which is the present value of the inflow. Method 2: Find the PV of cash inflow using a financial calculator at 16 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 75,000 and press +|–, press the Enter key. Press down arrow, enter 20,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 35,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 28,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 16 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 5,849.32, which is the present value of the inflow. Solution: Select Method 1 15. Discount rate and timing (LO13-1) Fill in the following table from Appendix B. Does a high discount rate have a greater or lesser effect on long-term inflows compared to recent ones? Discount Rate Years 5% 20% 1 _______ _______ 10 _______ _______ 20 _______ _______ 13-15. Solution: Discount Rate Years 5% 20% 1 .952 .833 10 .614 .162 20 .377 .026 The impact of a high discount rate is much greater on long-term value. For example, after the first year, the high rate discount value produces an answer that is 87.5 percent of the low discount rate (.833/.952). However, after the 20th year, the high rate discount rate is only 6.90 percent of the low discount rate (.026/.377). 16. Expected value with net present value (LO13-1) Debby’s Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $27,900. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby’s cost of capital is 15 percent. Cash Flow Probability $4,570 .1 5,550 .3 7,400 .4 9,930 .2 a. What is the expected value of the cash flow? The value you compute will apply to each of the five years. b. What is the expected net present value? c. Should Debby buy the new equipment? 13-16. Solution: Debby’s Dance Studios a. Expected Cash Flow Cash Flow P $4,570 × .1 $ 457 5,550 × .3 1,665 7,400 × .4 2,960 9,930 × .2 1,986 $7,068 b. Net Present Value (Appendix D) $7,068 × 3.352 (PVIFA @ 15%, n = 5) = $23,692 Present Value of Inflows 27,900 Present Value of Outflows $(4,208) Net Present Value c. Debby should not buy this new equipment because the net present value is negative. Calculator solution: b. Find the PV of cash inflow using a financial calculator at 15 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 27,900 and press +|–, press the Enter key. Press down arrow, enter 7,068, and press Enter. Press down arrow, enter 5, and press Enter. Press NPV; the calculator shows I = 0; enter 15 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –4,206.97 is the present value of the inflow. Solution: –$4,207. Based on the negative net present value, the project should not be undertaken. 17. Deferred cash flows and risk-adjusted discount rate Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,649,000 and will produce $353,000 per year in years 5 through 15 and $503,000 per year in years 16 through 25. The U.S. gold mine will cost $2,054,000 and will produce $282,000 per year for the next 25 years. The cost of capital is 13 percent. a. Which investment should be made? (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Australian mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.) b. If the Australian mine justifies an extra 2 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of cash flows, does the investment decision change? 13-17. Solution: Highland Mining and Minerals Co. a. Calculate the net present value for each project. The Australian Mine Years Cash Flow n Factor PVIFA@13% Present Value 5–15 $353,000 (15 – 4) (6.462 – 2.974) $1,231,264 16–25 $503,000 (25 – 15) (7.330 – 6.462) $ 436,604 Present Value of Inflows $1,667,868 Present Value of Outflows $1,649,000 Net Present Value $ 18,868 The U.S. Mine Years Cash Flow n Factor PVIFA@13% Present Value 1–25 $282,000 (25) 7.330 $2,067,060 Present Value of Inflows $2,067,060 Present Value of Outflows $2,054,000 Net Present Value $ 13,060 Select the Australian Mine. While both mines have a positive net present value, the Australian mine adds more value to the company for a smaller investment. b. Recalculate the net present value of the Australian Mine at a 15 percent discount rate. Years Cash Flow n Factor PVIFA @ 15% Present Value 5–15 $353,000 (15 – 4) (5.847 – 2.855) $ 1,056,176 16–25 $503,000 (25 – 15) (6.464 – 5.847) $ 310,351 Present Value of Inflows $1,366,527 Present Value of Outflows $1,649,000 Net Present Value $ (282,473) Now the decision should be made to reject the purchase of the Australian Mine and purchase the U.S. Mine. 18. Coefficient of variation and investment decision (LO13-1) Mr. Sam Golff desires to invest a portion of his assets in rental property. He has narrowed his choices down to two apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the present owners, Mr. Golff has developed the following estimates of the cash flows for these properties. Palmer Heights Crenshaw Village Yearly Aftertax Cash Inflow (in thousands) Probability Yearly Aftertax Cash Inflow (in thousands) Probability $70 .2 $75 .2 75 .2 80 .3 90 .2 90 .4 105 .2 100 .1 110 .2 a. Find the expected cash flow from each apartment complex. b. What is the coefficient of variation for each apartment complex? c. Which apartment complex has more risk? 13-18. Solution: a. Mr. Sam Golff Palmer Heights Crenshaw Village D P DP D P DP 70 .2 $14.0 75 .2 $ 15.0 75 .2 15.0 80 .3 24.0 90 .2 18.0 90 .4 36.0 105 .2 21.0 100 .1 10.0 110 .2 22.0 Expected Cash Flow $90.0 (thousands) Expected Cash Flow $85.0 (thousands) b. First find the standard deviation and then the coefficient of variation. Palmer Heights D P P $70 $90 $–20 $400 .20 80 75 90 –15 225 .20 45 90 90 0 0 .20 0 105 90 +15 225 .20 45 110 90 +20 400 .20 80 250 V = $15.81/$90 = .176 Crenshaw Village D P P $75 $85 $–10 $100 .20 20.0 80 85 –5 25 .30 7.5 90 85 +5 25 .40 10.0 100 85 +15 225 .10 22.5 $60.0 V =$7.75/$85 = .091 c. Based on the coefficient of variation, Palmer Heights has more risk (.176 versus .091). 19. Decision-tree analysis (LO13-4) Allison’s Dresswear Manufacturers is preparing a strategy for the fall season. One alternative is to expand its traditional ensemble of wool sweaters. A second option would be to enter the cashmere sweater market with a new line of high-quality designer label products. The marketing department has determined that the wool and cashmere sweater lines offer the following probability of outcomes and related cash flows. Expand Wool Sweaters Line Enter Cashmere Sweaters Line Expected Sales Probability Present Value of Cash Flows from Sales Probability Present Value of Cash Flows from Sales Fantastic .5 $221,000 .3 $341,000 Moderate .2 192,000 .4 272,000 Low .3 88,600 .3 0 The initial cost to expand the wool sweater line is $142,000. To enter the cashmere sweater line, the initial cost in designs, inventory, and equipment is $102,000. a. Diagram a complete decision tree of possible outcomes similar to Figure 13-8. Note that you are dealing with thousands of dollars rather than millions. Take the analysis all the way through the process of computing expected NPV (the last column for each investment). b. Given the analysis in part a, would you automatically make the investment indicated? 13-19. Solution: b. The indicated investment, based on the expected NPV, is in the Cashmere sweater line. However, there is more risk in this alternative so further analysis may be necessary. It is not an automatic decision. 20. Probability analysis with a normal curve distribution (LO13-4) When returns from a project can be assumed to be normally distributed, such as those shown in Figure 13-6 (represented by a symmetrical, bell-shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations. For example, 68.26 percent of the distribution will fall within one standard deviation of the expected value ( ± 1σ). Similarly, 95.44 percent will fall within two standard deviations ( ± 2σ), and so on. An abbreviated table of areas under the normal curve is shown next. Number of σ’s from Expected Value + or – + and – 0.5 0.1915 0.3830 1.0 0.3413 0.6826 1.5 0.4332 0.8664 1.65 0.4505 0.9010 2.0 0.4772 0.9544 Assume Project A has an expected value of $24,000 and a standard deviation (σ) of $4,800. a. What is the probability that the outcome will be between $16,800 and $31,200? b. What is the probability that the outcome will be between $14,400 and $33,600? c. What is the probability that the outcome will be at least $14,400? d. What is the probability that the outcome will be less than $31,900? e. What is the probability that the outcome will be less than $19,200 or greater than $26,400? 13-20. Solution: a. Expected Value = $24,000, σ = $4,800 $16,800 > $24,000 $24,000 < $33,600 Expected Value ± 2.0 σ .9544 13-20. (Continued) c. At least $14,400 d. Less than $31,900 13-20. (Continued) e. Less than $19,200 or greater than $26,400 Area Distribution under the curve is .4672. 21. Increasing risk over time (LO13-1) The Oklahoma Pipeline Company projects the following pattern of inflows from an investment. The inflows are spread over time to reflect delayed benefits. Each year is independent of the others. Year 1 Year 5 Year 10 Cash Inflow Probability Cash Inflow Probability Cash Inflow Probability 55 .40 40 .30 20 .40 70 .20 70 .40 70 .20 85 .40 100 .30 120 .40 The expected value for all three years is $70. a. Compute the standard deviation for each of the three years. b. Diagram the expected values and standard deviations for each of the three years in a manner similar to Figure 13-6. c. Assuming 6 percent and 12 percent discount rates, complete the following table for present value factors. Year PVIF 6% PVIF 12% Difference 1 .943 .893 .050 5 ________ ________ ________ 10 ________ ________ ________ d. Is the increasing risk over time, as diagrammed in part b, consistent with the larger differences in PVIFs over time, as computed in part c? e. Assume the initial investment is $135. What is the net present value of the investment at a 12 percent discount rate? Should the investment be accepted? 13-21. Solution: Oklahoma Pipeline Company a. Standard deviation—year 1 D P P $55 70 –15 225 .40 90 70 70 0 0 .20 0 85 70 +15 225 .40 90 180 Standard deviation—year 5 D P P 40 70 –30 900 .30 270 70 70 0 0 .40 0 100 70 +30 900 .30 270 540 13-21. (Continued) Standard deviation—year 10 D P P 20 70 –50 2,500 .40 1,000 70 70 0 0 .20 0 120 70 +50 2,500 .40 1,000 2,000 b. Risk over time c. Year (1) PVIF (2) PVIF (3) PVIF 6% 12% Difference 1 .943 .893 .050 5 .747 .567 .180 10 .558 .322 .236 13-21. (Continued) d. Yes. The larger risk over time is consistent with the larger differences in the present value interest factors (PVIF) over time. In effect, future uncertainty is being penalized by a lower present value interest factor (PVIF). This is one of the consequences of using progressively higher discount rates to penalize for risk. Year Inflow PVIF (12%) PV 1 $70 .893 $ 62.51 5 70 .567 $ 39.69 10 70 .322 $ 22.54 PV of Inflows $124.74 Investment $135.00 NPV $ 10.26 e. Accept the investment. 22. Portfolio effect of a merger (LO13-5) Treynor Pie Company is a food company specializing in high-calorie snack foods. It is seeking to diversify its food business and lower its risks. It is examining three companies—a gourmet restaurant chain, a baby food company, and a nutritional products firm. Each of these companies can be bought at the same multiple of earnings. The following represents information about all the companies. Company Correlation with Treynor Pie Company Sales ($ millions) Expected Earnings ($ millions) Standard Deviation in Earnings ($ millions) Treynor Pie Company + 1.0 $126 $10 $4.0 Gourmet restaurant + .4 63 9 1.4 Baby food company + .3 52 5 1.6 Nutritional products company − .7 77 7 3.2 a. Using the last two columns, compute the coefficient of variation for each of the four companies. Which company is the least risky? Which company is the most risky? b. Discuss which of the acquisition candidates is most likely to reduce Treynor Pie Company’s risk? Explain why. 13-22. Solution: Treynor Pie Company a. (millions) Treynor Pie Company $4/$10 = .40 Gourmet Restaurant $1.4/$9 = .16 Baby Food $1.6/$5 = .32 Nutritional Products $3.2/$7 = .46 The Gourmet Restaurant chain is the least risky with a coefficient of variation of .16, while the nutritional products firm has the highest risk with a coefficient of variation of .46 b. Because the nutritional products firm is highly negatively correlated (–.7) with Treynor Pie Company, it is most likely to reduce risk. It would appear that the demand for high-calorie snack foods moves in the opposite direction as the demand for nutritional items. Thus, Treynor Pie Company would reduce its risk to the largest extent by acquiring the company with the highest coefficient of variation (.46) as computed in part a. This would appear to represent a paradox, but it is not. It simply reflects the fact that the interaction between two companies is much more important than the individual risk of the companies. 23. Portfolio effect of a merger (LO13-5) Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows: Outcomes ($ millions) Probability Recession $20 .30 Normal economy 40 .40 Strong economy 60 .30 After the acquisition, the expected outcomes for the firm would be: Outcomes ($ millions) Probability Recession $10 .3 Normal economy 40 .4 Strong economy 80 .3 a. Compute the expected value, standard deviation, and coefficient of variation before the acquisition. b. After the acquisition, these values are as follows: Expected value 43.0 ($ millions) Standard deviation 27.2 ($ millions) Coefficient of variation .633 Comment on whether this acquisition appears desirable to you. c. Do you think the firm’s stock price is likely to go up as a result of this acquisition? d. If the firm was interested in reducing its risk exposure, which of the following three industries would you advise it to consider for an acquisition? Briefly comment on your answer. (1) Chemical company (2) Oil company (3) Computer company 13-23. Solution: a. Hooper Chemical Co. D P PD $20 .30 6 40 .40 16 60 .30 18 $40 ($ million) D P P $20 40 –20 400 .30 120 40 40 0 0 .40 0 60 40 +20 400 .30 120 240 V = $15.5/$40 = .388 b. No, it does not appear to be desirable. Although the expected value is $3 million higher, the coefficient of variation is more than twice as high (.633 versus .388). The slightly added return probably does not adequately compensate for the added risk. c. Probably not. There may be a higher discount rate applied to the firm’s earnings to compensate for the additional risk. The stock price may actually go down. d. The oil company may provide the best risk reduction benefits. Since petroleum is used as part of the firm’s production process, an increase in the price of oil would normally hurt the chemical company, but this would be offset by the increased profits for the oil company. The same type of offsetting risk reduction benefits would take place if the price of oil were going down. 24. Efficient frontier (LO13-5) Ms. Sharp is looking at a number of different types of investments for her portfolio. She identifies eight possible investments. Return Risk Return Risk (a) 11% 2% (e) 14% 5.0% (b) 11 2.5 (f) 16 5.0 (c) 13 3.0 (g) 15 5.8 (d) 13 4.2 (h) 18 7.0 a. Graph the data in a manner similar to Figure 13-11. Use the axes that follow for your data. b. Draw a curved line representing the efficient frontier. c. What two objectives do points on the efficient frontier satisfy? d. Is there one point on the efficient frontier that is best for all investors? 13-24. Solution: Ms. Sharp a., b. c. Achieve the highest possible return for a given risk level. Allow the lowest possible risk at a given return level. d. No. Each investor must assess his or her own preferences about their risk and return trade-off. 25. Certainty equivalent approach (LO13-1) Sheila Goodman recently received her MBA from the Harvard Business School. She has joined the family business, Goodman Software Products Inc., as Vice-President of Finance. She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees to go along with her. Her approach is somewhat different than the risk-adjusted discount rate approach, but achieves the same objective. She suggests that the inflows for each year of a project be adjusted downward for lack of certainty and then be discounted back at a risk-free rate. The theory is that the adjustment penalty makes the inflows the equivalent of risk-less inflows, and therefore a risk-free rate is justified. A table showing the possible coefficient of variation for an inflow and the associated adjustment factor is shown next: Coefficient of Variation Adjustment Factor 0 – .25 .90 .26 – .50 .80 .51 – .75 .70 .76 – 1.00 .60 1.01 – 1.25 .50 Assume a $184,000 project provides the following inflows with the associated coefficients of variation for each year. Year Inflow Coefficient of Variation 1 $32,200 .12 2 59,500 .28 3 79,900 .45 4 59,200 .79 5 65,5600 1.15 a. Fill in the following table: Year Inflow Coefficient of Variation Adjustment Factor Adjusted Inflow 1 $32,200 .12 ____________ ____________ 2 59,500 .28 ____________ ____________ 3 79,900 .45 ____________ ____________ 4 59,200 .79 ____________ ____________ 5 65,600 1.15 ____________ ____________ b. If the risk-free rate is 5 percent, should this $184,000 project be accepted? Compute the net present value of the adjusted inflows. 13-25. Solution: Goodman Software Products a. Adjusted Inflows Year Inflow Coefficient of Variation Adjustment Factor Adjusted Inflow 1 $32,200 .12 .90 $28,980 2 59,500 .28 .80 47,600 3 79,900 .45 .80 63,920 4 59,200 .79 .60 35,520 5 65,600 1.15 .50 32,800 b. Net Present Value Year Adjusted Inflow PVIF at 5% Present Value 1 $28,980 .952 $ 27,589 2 47,600 .907 43,173 3 63,920 .864 55,227 4 35,520 .823 29,233 5 32,800 .784 25,715 Present Value of Adjusted Inflows $180,937 Present Value of Outflows 184,000 Net Present Value $ (3,063) Based on the positive net present value of –$3,063, the project should not be accepted. COMPREHENSIVE PROBLEMS Comprehensive Problem 1. Gibson Appliance Co. (portfolio effect of a merger) (LO13-5) Gibson Appliance Co. is a very stable billion-dollar company with a sales growth of about 7 percent per year in good or bad economic conditions. Because of this stability (a coefficient of correlation with the economy of +.4, and a standard deviation of sales of about 5 percent from the mean), Mr. Hoover, the Vice-President of Finance, thinks the company could absorb a small risky company that could add quite a bit of return without increasing the company’s risk very much. He is trying to decide which of the two companies he will buy, using the following figures. Gibson’s cost of capital is 12 percent. a. What is the expected cash flow from both companies? b. Which company has the lower coefficient of variation? c. Compute the net present value of each company. d. Which company would you pick, based on the net present values? e. Would you change your mind if you added the risk dimensions to the problem? Explain. f. What if Genetic Technology Co. had a coefficient of correlation with the economy of –.2, and Silicon Microchip Co. had one of +.5? Which of these companies would give you the best portfolio effects for risk reduction? g. What might be the effect of the acquisitions on the market value of Gibson Appliance Co.’s stock? CP 13-1 Solution: Portfolio Effect of a Merger Gibson Appliance Co. a. Genetic Technology Co. Silicon Microchip Co. D P DP D P DP $ 2 .2 .4 $ 5 .2 1.0 8 .3 2.4 7 .2 1.4 16 .2 3.2 18 .3 5.4 25 .2 5.0 24 .3 7.2 40 .1 4.0 Expected Value of Cash Flows $15.0 (million) Expected Value of Cash Flows $15.0 (million) b. Coefficient of variation for Genetic Technology Co. D P P $ 2 $15 $–13 $169 .2 $33.8 8 15 –7 49 .3 14.7 16 15 +1 1 .2 .2 25 15 +10 100 .2 20.0 40 15 +25 625 .1 62.5 $131.2 Coefficient of Variation = $11.45/$15 = .764 (million) CP 13-1. (Continued) Coefficient of variation for Silicon Microchip Co. D P P $ 5 $15 $–103 $100 .2 $20.0 7 15 –8 64 .2 12.8 18 15 +3 9 .3 2.7 24 15 +9 81 .3 24.3 $59.8 Coefficient of Variation = $7.73/$15 = .515 Silicon Microchip has a lower coefficient of variation, .515 < .764. c. For both companies, the annual expected value is $15 million for 10 years. The cost is $80 million for either company. Gibson has a cost of capital of 12 percent. $15 million × PVIFA (n = 10, i = 12%) (Appendix D) $15 × 5.650 = $84.750 PV of Inflows 80.000 PV of Outflows $ 4.750 Net Present Value (million) d. Based on present values, you could pick either company. e. The only way one will win out over the other is if risk factors are considered. Since Genetic Technology Co. has the higher coefficient of variation, we would select the lower risk company––Silicon Microchip. If Gibson Appliance Co. uses a risk-adjusted cost of capital concepts, it would use a higher cost of capital for the cash flows generated by Genetic Technology Co. and this would reduce its NPV. f. Since Gibson Appliance Co. has a correlation coefficient with the economy of +.4, the selection of Genetic Technology Co. would offer the most risk reduction because its correlation coefficient with the economy is –.2. g. Because Gibson Appliance Co. is a stable billion-dollar company, this investment of $80 million would probably not have a great impact on the stock price in the short run. There could be some positive movement in the stock price if investors perceive less risk from portfolio diversification. This would be particularly true for a merger with Genetic Technology Co. You can use this question to discuss risk-return trade-offs and market reactions. Comprehensive Problem 2. Kennedy Trucking Company (investment decision based on probability analysis) (LO13-1) Five years ago, Kennedy Trucking Company was considering the purchase of 60 new diesel trucks that were 15 percent more fuel-efficient than the ones the firm is now using. Mr. Hoffman, the president, had found that the company uses an average of 10 million gallons of diesel fuel per year at a price of $1.25 per gallon. If he can cut fuel consumption by 15 percent, he will save $1,875,000 per year (1,500,000 gallons times $1.25). Mr. Hoffman assumed that the price of diesel fuel is an external market force that he cannot control and that any increased costs of fuel will be passed on to the shipper through higher rates endorsed by the Interstate Commerce Commission. If this is true, then fuel efficiency would save more money as the price of diesel fuel rises (at $1.35 per gallon, he would save $2,025,000 in total if he buys the new trucks). Mr. Hoffman has come up with two possible forecasts shown next—each of which he feels has about a 50 percent chance of coming true. Under assumption number 1, diesel prices will stay relatively low; under assumption number 2, diesel prices will rise considerably. Sixty new trucks will cost Kennedy Trucking $5 million. Under a special provision from the Interstate Commerce Commission, the allowable depreciation will be 25 percent in year 1, 38 percent in year 2, and 37 percent in year 3. The firm has a tax rate of 40 percent and a cost of capital of 10 percent. a. First, compute the yearly expected price of diesel fuel for both assumption 1 (relatively low prices) and assumption 2 (high prices) from the forecasts that follow. Forecast for assumption 1 (low fuel prices): Probability (same for each year) Price of Diesel Fuel per Gallon Year 1 Year 2 Year 3 .1 $ .80 $ .90 $1.00 .2 1.00 1.10 1.10 .3 1.10 1.20 1.30 .2 1.30 1.45 1.45 .2 1.40 1.55 1.60 Forecast for assumption 2 (high fuel prices): Probability (same for each year) Price of Diesel Fuel per Gallon Year 1 Year 2 Year 3 .1 $1.20 $1.50 $1.70 .3 1.30 1.70 2.00 .4 1.80 2.30 2.50 .2 2.20 2.50 2.80 b. What will be the dollar savings in diesel expenses each year for assumption 1 and for assumption 2? c. Find the increased cash flow after taxes for both forecasts. d. Compute the net present value of the truck purchases for each fuel forecast assumption and the combined net present value (that is, weigh the NPV by .5). e. If you were Mr. Hoffman, would you go ahead with this capital investment? f. How sensitive to fuel prices is this capital investment? CP 13-2 Solution: Investment Decision Based on Probability Analysis Kennedy Trucking Company a. Assumption One: Yr.1 Yr.2 Yr.3 Probability D DP D DP D DP .1 $0.80 .08 $0.90 .09 $1.00 .10 .2 1.00 .20 1.10 .22 1.10 .22 .3 1.10 .33 1.20 .36 1.30 .39 .2 1.30 .26 1.45 .29 1.45 .29 .2 1.40 .28 1.55 .31 1.60 .32 Expected value $1.15/gallon $1.27/gallon $1.32/gallon Assumption Two: Yr.1 Yr.2 Yr.3 Probability D DP D DP D DP .1 $1.20 .12 $1.50 .15 $1.70 .17 .3 1.30 .39 1.70 .51 2.00 .60 .4 1.80 .72 2.30 .92 2.50 1.00 .2 2.20 .44 2.50 .50 2.80 .56 Expected value $1.67/gallon $2.08/gallon $2.33/gallon 13-CP 2. (Continued) b. Assumption One: Yr. Expected Cost/Gal. # of Gals. Without Efficiency = Cost % Savings with Efficiency Total $ Saved 1 $1.15 10 million $11,500,000 15% $1,725,000 2 1.27 12,700,000 1,905,000 3 1.32 13,200,000 1,980,000 Assumption Two: Yr. Expected Cost/Gal. # of Gals. without Efficiency = Cost % Savings with Efficiency Total $ Saved 1 $1.67 10 million $16,700,000 15% $2,505,000 2 2.08 20,800,000 3,120,000 3 2.33 23,300,000 3,495,000 c. First, compute annual depreciation. Then, proceed to the analysis. Year 1 25% × $5 mil. = 1.25 mil. Year 2 38% × $5 mil. = 1.90 mil. Year 3 37% × $5 mil. = 1.85 mil. Total saved equals an increase in EBDT. 13-CP 2. (Continued) Assumption One: Year 1 Year 2 Year 3 Increase in EBDT $1,725,000 $1,905,000 $1,980,000 – Depreciation 1,250,000 1,900,000 1,850,000 Increase in EBT 475,000 5,000 130,000 – Taxes 40 percent 190,000 2,000 52,000 Increase in EAT 285,000 3,000 78,000 + Depreciation 1,250,000 1,900,000 1,850,000 Increased Cash Flow $1,535,000 $1,903,000 $1,928,000 Assumption Two: Year 1 Year 2 Year 3 Increase in EBDT $2,505,000 $3,120,000 $3,495,000 – Depreciation 1,250,000 1,900,000 1,850,000 Increase in EBT 1,255,000 1,220,000 1,645,000 – Taxes 40 percent 502,000 488,000 658,000 Increase in EAT 753,000 732,000 987,000 + Depreciation 1,250,000 1,900,000 1,850,000 Increased Cash Flow $2,003,000 $2,632,000 $2,837,000 13-CP 2. (Continued) d. Present Value Assumption One: Year Cash Flow PVIF @ 10% Present Value 1 $1,535,000 .909 $1,395,315 2 1,903,000 .826 1,571,878 3 1,928,000 .751 1,447,928 PV of Inflows $4,415,121 PV of Outflows 5,000,000 NPV $ (584,879) Assumption Two: Year Cash Flow PVIF @ 10% Present Value 1 $2,003,000 .909 $1,820,727 2 2,632,000 .826 2,174,032 3 2,837,000 .751 2,130,587 PV of Inflows $6,125,346 PV of Outflows 5,000,000 NPV $1,125,346 Combined NPV: Outcome NPV Probability Assumption One –584,879 .5 –292,440 Assumption Two 1,125,346 .5 562.673 Expected Outcome $270,233 e. Yes—The combined expected value of the outcomes is positive. f. Quite sensitive when that many gallons are used per year. Solution Manual for Foundations of Financial Management Stanley B. Block, Geoffrey A. Hirt, Bartley R. Danielsen 9780077861612, 9781260013917, 9781259277160