Chapter 13 Discussion Questions If corporate managers are risk-averse, does this mean they will not take risks? 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 for risk taki 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 d ivide the or measure of dIsp n)by the mean. We also may measure risk in terms of beta, in which we determine the volatility of returns on an ind ividual 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 Icient of variation is a better measure o 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 bud geting Risk may be introduced into the capital bud geting 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 use S-477 Copyright C2005 by The McGramw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-477 Chapter 13 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
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 New b. New market c. Repair of old machinery d. New product in a foreign market e. New product in a related market f. Add ition to a new product line Referring to Table 13-3, the following order would be correct repair old machinery(c) new equipment(a) addition to normal product line(f) new product in related market(e) completely new market(b) new product in foreign market(d) 13-6 Assume a company, correlated with the economy, is evaluating six projects, of hich 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 om alyze the risk-return trade-off for portfolios of 20 projects. How should it ceed 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 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 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 by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market CopyrightC 2005 by The McGray-Hill Companies, Inc. S-478
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-478 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 new product line. Referring to Table 13-3, the following order would be correct: repair old machinery (c) new equipment (a) addition to normal product line (f) new product in related market (e) completely new market (b) new product in 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
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 S-479 CopyrightC2005 by The McGramw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-479 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
Problems 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 below Market reaction in units Probabilities 20 10 Moderate a. What is the expected value of unit sales for the new product? b. What is the standard deviation of unit sales? Solution: ers business systems D=∑DP P DP 20 10 2 40 30 12 40 22 70 20 b D-DIP )(D-D) (D-D)"P 2050 900 10 90 4050 10 100 30 30 550 25 20 400 0 210 210=1449 by The McGraw-Hill Compa
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-480 Problems 13-1. 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 below. 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? Solution: Myers Business Systems a. D = DP D 20 40 55 70 P .10 .30 .40 .20 DP 2 12 22 14 50 = D b. (D D) P 2 = − D D (D− D) 2 (D − D) P (D D) P 2 − 20 50 –30 900 .10 90 40 50 –10 100 .30 30 55 50 +5 25 .40 10 70 50 +20 400 .20 80 210 210 =14.49 =
2 Monarck King Size Beds, Inc, is evaluating a new promotional campaign that could increase sales. Possible outcomes and probabilities of the outcomes are shown below. Compute the coefficient of variation Additiona Possible outcomes Sales in Units Probabilities Ineffective campaign 20 Normal response emely Solution: Monarck King Size Beds, Inc Coefficient of variation()=standard deviation/expected value D=∑DP DP 20 30 50 21 σ=∑(D-D)P D D-D)(D-D)2 P D-D)2P 2040 20 400 20 80 3040 50 7040+30 900 270 400 400=20=a 20 50 by The M
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-481 13-2. Monarck King Size Beds, Inc., is evaluating a new promotional campaign that could increase sales. Possible outcomes and probabilities of the outcomes are shown below. Compute the coefficient of variation. Possible Outcomes Additional Sales in Units Probabilities Ineffective campaign 20 .20 Normal response 30 .50 Extremely effective 70 .30 Solution: Monarck King Size Beds, Inc. Coefficient of variation (V) = standard deviation/expected value. D = DP D 20 30 70 P .20 .50 .30 DP 4 15 21 40 = D (D D) P 2 = − D D (D− D) 2 (D − D) P (D D) P 2 − 20 40 –20 400 .20 80 30 40 –10 100 .50 50 70 40 +30 900 .30 270 400 .50 40 20 V 400 20 = = = =
Al Bundy is evaluating a new advertising program that could increase shoe sales Possible outcomes and probabilities of the outcomes are shown below. Compute the coefficient of variation Additiona Possible outcomes Sales in Units Probabilities Ineffective campaign 40 Normal response emely Solution: Al Bundy Coefficient of variation()=standard deviation/expected value D=∑DP DP 20 8 50 30 140 42 √∑D-DP (D-D)(D-D)2 P (D-D)2P 4080 40 1600 20 320 400 200 1408 +60 1.080 1.600 600=40 40 50 80 CopyrightC 2005 by The McGray-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-482 13-3. Al Bundy is evaluating a new advertising program that could increase shoe sales. Possible outcomes and probabilities of the outcomes are shown below. Compute the coefficient of variation. Possible Outcomes Additional Sales in Units Probabilities Ineffective campaign 40 .20 Normal response 60 .50 Extremely effective 140 .30 Solution: Al Bundy Coefficient of variation (V) = standard deviation/expected value. D = DP D 40 60 140 P .20 .50 .30 DP 8 30 42 80 = D (D D) P 2 = − D D (D− D) 2 (D − D) P (D D) P 2 − 40 80 –40 1,600 .20 320 60 80 –20 400 .50 200 140 80 +60 3,600 .30 1,080 1,600 .50 80 40 V 1,600 40 = = = =
Possible outcomes for three investment alternatives and their probabilities of occurrence are given below Alternative 1 Alternative 2 Alternative 3 Outcomes Probability Outcomes Probability Outcomes Probability Acceptable 160 Successful 120 244 200 20 Rank the three alternatives in terms of risk from lowest to highest(compute the coefficient of variation Solution: Alternative 1 Alternative 2 Alternative 3 DⅹP=DP DⅹP=DP DⅹP=DP $502$10$903$27$804$32 80432 160580 200 100 120448 200240400140 D=$90 D=$147 D=$172 Standard Deviation alternative 1 D (D-D)(D-D D-D)P $50$90$-40 $1.600 $320 10 100 4 40 12090+30 900 $720 720=$2683=a by The M
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-483 13-4. Possible outcomes for three investment alternatives and their probabilities of occurrence are given below. Alternative 1 Alternative 2 Alternative 3 Outcomes Probability Outcomes Probability Outcomes Probability Failure 50 .2 90 .3 80 .4 Acceptable 80 .4 160 .5 200 .5 Successful 120 .4 200 .2 400 .1 Rank the three alternatives in terms of risk from lowest to highest (compute the coefficient of variation). Solution: Alternative 1 D x P = DP Alternative 2 D x P = DP Alternative 3 D x P = DP $ 50 .2 $10 80 .4 32 120 .4 48 D = $90 $ 90 .3 $ 27 160 .5 80 200 .2 40 D = $147 $ 80 .4 $ 32 200 .5 100 400 .1 40 D = $172 Standard Deviation Alternative 1 D D (D− D) 2 (D − D) P (D D) P 2 − $ 50 $90 $–40 $1,600 .2 $320 80 90 –10 100 .4 40 120 90 +30 900 .4 360 $720 720 = $26.83 =
13-4. Continued Alternative 2 ①D-D)(D-D) D-D)P $90$147$-57 $3,249 3$974.70 160147 13 169 84.50 200147 53 2,809 561.80 √1621=$40.26=a Alternative 3 D D-D (D-D (D-D)P $80$172$-92 $8464 4$3,38560 200172 28 784 9200 400172+228 51984 15.19840 8,97600 8,976=$9474=σ Rank by Coefficient of Variation Coefficient of Variation(V)=Standard Deviation/Expected value 40.26 Alternative 2 =.274 147 $26.83 Alternative 1 =.298 94.74 Alternative 3 172 CopyrightC 2005 by The McGray-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-484 13-4. Continued Alternative 2 D D (D− D) 2 (D − D) P (D D) P 2 − $ 90 $147 $–57 $3,249 .3 $ 974.70 160 147 +13 169 .5 84.50 200 147 +53 2,809 .2 561.80 $1,621.00 1,621 = $40.26 = Alternative 3 D D (D− D) 2 (D − D) P (D D) P 2 − $ 80 $172 $–92 $ 8,464 .4 $3,385.60 200 172 +28 784 .5 392.00 400 172 +228 51,984 .1 5,198.40 $8,976.00 8,976 = $94.74 = Rank by Coefficient of Variation Coefficient of Variation (V) = Standard Deviation/Expected Value V Alternative 2 .274 147 40.26 = Alternative 1 .298 90 $26.83 = Alternative 3 .551 172 94.74 =
Five investment alternatives have the following returns and standard deviations of returns Alternative Returns: Standard Expected value Deviation ABCDE 4.000 600 4,000 8.000 3,200 10.000 900 Using the coefficient of variation, rank the five altematives from lowest risk to highest risk 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 13-6 In problem 5, if you were to choose between Alternative B and C only, would you need to use the coefficient of variation? why? Solu Since b and c have the same expected value they can be evaluated based on their standard de ofreturn C has a I deviation and so is riskier than b for the same expected return S-485 by The M
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-485 13-5. 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. 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 E $3,200/$8,000 = .40 $900/$10,000 = .09 A (.24) D (.40) 13-6. In problem 5, if you were to choose between Alternative B and C only, would you need to use the coefficient of variation? Why? Solution: Since B and C have the same expected value, they can be evaluated based on their standard deviations of return. C has a larger standard deviation and so is riskier than B for the same expected return
Tom Fears is highly risk-averse while Sonny Outlook actually enjoys taking a a. Which one of the four investments should Tom choose? Compute the coefficients of variation to help you in your choice b. Which one of the four investments should Sonny choose? Returns Standard Investments Expected valu Deviatio 7000 Buy bonds 5.000 1.560 Buy commodity futures 12000 15.100 Buy options 8.000 8.850 Solution: Coefficient of variation(V)=standard deviation/expected value Buy stocks $4.000/$7,000=571 Buy bonds $l560/$5,000=312 BI dity futures $15,100/$12,000=1.258 Buy options $8.850/$8.000=1.106 a. Tom should buy the bonds because bonds have the lowest coefficient of variation b. Sonny should buy the commodity futures because they have the highest coefficient of variation by The McGraw-Hill Compa
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-486 13-7. Tom Fears is highly risk-averse while Sonny Outlook actually enjoys taking a risk. a. Which one of the four investments should Tom choose? Compute the coefficients of variation to help you in your choice. b. Which one of the four investments should Sonny choose? Investments Returns – Expected Value Standard Deviation Buy stocks $ 7,000 $ 4,000 Buy bonds 5,000 1,560 Buy commodity futures 12,000 15,100 Buy options 8,000 8,850 Solution: Coefficient of variation (V) = standard deviation/expected value. Buy stocks $4,000/$7,000 = .571 Buy bonds $1,560/$5,000 = .312 Buy commodity futures $15,100/$12,000 = 1.258 Buy options $8,850/$8,000 = 1.106 a. Tom should buy the bonds because bonds have the lowest coefficient of variation. b. Sonny should buy the commodity futures because they have the highest coefficient of variation
