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

Chapter 13 Discussion Questions 13-1. 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. 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. The standard deviation is an absolute measure of dispersion, while the coefficient of variation is a relative measure that 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. 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, may also be used. 13-5. 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. 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. A discount rate combines the effects of risk and time value of money in one evaluation tool. A certainty equivalent deals first with risk by converting uncertain cash flows to ‘certainty equivalents’, and then discounts at the risk free rate to consider the time value of money. 13-8. 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. 13-9. Sensitivity analysis only adjusts one variable at a time. In all likelihood variables are interdependent and if one changes the others will likely change as well. Sensitivity analysis misses this dynamism. As well sensitivity analysis does not assess risk, it only points out possible outcomes and we are left to assign probabilities. With today’s ease of spreadsheet production on the PC one can turn out endless analysis, which, without a plan will become meaningless. 13-10. Decision trees help lay out the sequence of decisions that are to be made and present a tabular or graphical comparison resembling the branches of a tree which highlights the difference between investment choices. 13-11. 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. 13-12. 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 shares. Only by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market. 13-13. It depends! If the firm is well diversified beta risk would probably be more important. However if the firm is not well diversified or if a project is particularly significant in size to the firm then total risk (unique and systematic) would be more appropriate, as measured by the standard deviation of the project. Internet Resources and Questions 1. www.standardandpoors.com/home/en/us www.bankofcanada.ca http://pages.stern.nyu.edu/~adamodar/New_Home_Page/data.html Problems 13-1. Coefficient of Variation A B C $900/ $1,800 = 0.50 $1,400/ $2,000 = 0.70 $500/ $1,500 = 0.33 13-2. Pabst Dental Supplies D = ∑ DP a. D 20 40 65 80 P .10 .20 .40 .30 60 DP 2 8 26 24 = D σ = ∑ (D − D ) P 2 b. D 20 40 65 80 D 60 60 60 60 (D– D ) – 40 – 20 + 5 + 20 (D– D )2 1,600 400 25 400 σ = 370 = 19.24 P .10 .20 .40 .30 (D– D )2P 160 80 10 120 370 13-3. Northern Wind Power D = ∑ DP a. D 50 70 90 140 P .10 .40 .20 .30 DP 5 28 18 42 93 = D σ = ∑ (D − D ) P 2 b. D 50 70 90 140 D 93 93 93 93 (D– D ) – 43 – 23 + 3 + 47 (D– D )2 1,849 529 9 2209 σ = 1,061 = 32.57 P .10 .40 .20 .30 (D– D )2P 184.9 211.6 1.8 662.7 1,061.0 13-4. Monarch King Size Beds Ltd. D = ∑ DP a. D 20 30 70 P .20 .50 .30 DP 4 15 21 40 = D σ = ∑ (D − D ) P 2 b. D 20 30 70 D 40 40 40 (D– D ) – 20 – 10 + 30 (D– D )2 400 100 900 P .20 .50 .30 σ = 400 = 20 Coefficient of variation (V ) = σ D = 20 = 0.5 40 (D– D )2P 80 50 270 400 13-5. Sam Sung D = ∑ DP a. D 80 124 340 P .30 .50 .20 DP 24 62 68 154 = D σ = ∑ (D − D ) P 2 b. D 80 124 340 (D– D ) (D– D )2 – 74 5,476 – 30 900 + 186 34,596 D 154 154 154 P .30 .50 .20 (D– D )2P 1,642.8 450.0 6,919.2 9,012.0 σ = 9,012 = 94.93 Coefficient of variation (V ) = 13-6. σ D = 94.93 = 0.616 154 Five alternatives Coefficient of variation (V ) = A B C D E $200/ $1,000 $300/ $3,000 $400/ $3,000 $700/ $5,000 $900/ $10,000 = .20 = .10 = .13 = .14 = .09 σ D Ranking from lowest to highest E (.09) B (.10) C (.13) D (.14) A (.20) 13-7. You would not need to use the coefficient of variation. Since B and C have the same expected value, they can be evaluated based solely on their standard deviations of return. C has a larger standard deviation and so is riskier than B for the same expected return. 13-8. Another five alternatives Coefficient of variation (V ) = A $300/ $1,200 B $600/ $800 C $450/ $5,000 D $430/ $1,000 E $13,200/ $60,000 = .25 = .75 = .09 = .43 = .22 13-9. σ D Ranking from lowest to highest C (.09) E (.22) A (.25) D (.43) B (.75) Digital Technology a. Year Profits: Expected Value Standard Deviation Coefficient of Variation 1 3 6 9 180 240 300 400 54 104 166 260 .30 .43 .55 .65 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. 13-10. Tom Fears and Sonny Outlook Coefficient of variation Stocks $4,000/ $7,000 0.57 Bonds $1,560/ $5,000 0.31 Commodities $15,100/ $12,000 1.26 Options $8,850/ $8,000 1.11 a. Tom should select bonds, which have the least risk. b. Sonny should select commodities, which have the greatest risk. 13-11. Project A B C D Tomcat Oil and HiC Construction $96,600/ $183,400 $282,100/ $471,800 $75,600/ $61,600 $144,900/ $87,500 Coefficient of variation 0.53 0.60 1.23 1.66 a. Tomcat Oil should select project D, which has the greatest risk. b. HiC Construction should select project A, which has the least risk. 13-12. Alternative 1 D × P = DP $50 .2 $10 80 .4 32 120 .4 48 D = $90 Three Investment Alternatives Alternative 2 D × P = DP $90 .3 $27 160 .5 80 200 .2 40 D = $147 Alternative 3 D × P = DP $80 .4 $32 200 .5 100 400 .1 40 D = $172 Standard Deviation: Alternative 1: D D $50 90 80 90 120 90 (D– D ) – 40 – 10 + 30 (D– D )2 1,600 100 900 P .20 .4 .4 (D– D )2P $320 40 360 $720 P .3 .5 .2 (D– D )2P $974.70 84.50 561.80 $1,621.00 P .4 .5 .1 (D– D )2P $3,385.60 392.00 5,198.40 $8,976.00 σ = 720 = 26.83 Alternative 2: D D $90 $147 160 147 200 147 (D– D ) – 57 + 13 + 53 (D– D )2 3,249 169 2,809 σ = 1,621 = 40.26 Alternative 3: D D $80 $172 200 172 400 172 (D– D ) $-92 +28 +228 (D– D )2 $8,464 784 51,984 σ = 8,976 = 94.74 Rank by Coefficient of Variation: least risk to most Alternative 2 (V ) = σ = 40.26 = 0.274 147 Alternative 1 (V ) = σ = 26.83 = 0.298 90 Alternative 3 (V ) = σ = 94.74 = 0.551 172 D D D 13-13. Mary Beth Clothes Standard Deviations of Sites A and B Site A D $50 100 110 135 D $100 100 100 100 (D– D ) ─ $50 0 +10 +35 (D– D )2 $2,500 0 100 1,225 P .20 .30 .30 .20 (D– D )2P $ 500 0 30 245 $ 775 P .10 .20 .40 .20 .10 (D– D )2P $ 640 500 0 500 640 $2,280 σ = 775 = $27.84 Site B D $20 50 100 150 180 D $100 100 100 100 100 (D– D ) ─ $80 ─ 50 0 +50 +80 (D– D )2 $6,400 2,500 0 2,500 6,400 σ = 2,280 = $47.75 VA VB = = $27.84/$100 $47.75/$100 = = .2784 .4775 Site A is the preferred site since it has the smaller 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. 13-14. Waste Industries The coefficient of variation suggests a discount rate of 14%. Year 1 2 3 4 5 Cash flow $11,000 16,000 21,000 24,000 30,000 PV of cash flows Investment NPV PV@14% $ 9,649 12,311 14,174 14,210 15,581 65,925 70,000 ─ $4,075 Based on a negative NPV, the project should not be undertaken. 13-15. Western Dynamite Co. Method 1 Year Cash flow 1 $25,000 2 30,000 3 38,000 4 31,000 5 19,000 PV of Inflows Investment NPV Method 2 PV@10% $22,727 24,793 28,550 21,173 11,798 $109,041 100,000 $ 9,041 Year 1 2 3 4 5 Cash flow $28,000 32,000 39,000 33,000 25,000 PV@15% $24,348 24,197 25,643 18,868 12,429 $105,485 100,000 $ 5,485 Select Method 1 The instructor may wish to point out that Method 2 has higher undiscounted total cash flows than Method 1 (the numbers are $157,000 versus $143,000), but has a lower NPV because of the higher discount rate. 13-16. Larry’s Athletic Lounge a. Expected Cash Flow Cash Flow $2,400 4,800 6,000 7,200 × × × × P .2 .4 .3 .1 $ 480 1,920 1,800 720 $4,920 b. NPV (Net Present Value) $4,920 (%I/Y = 14%, n = 5) = $16,891 $ 16,891 20,000 $(3,109) Present value of inflows Present value of outflows Net present value IRR (Internal Rate of Return) Calculator: Compute: PV = $20,000 %I/Y =? %I/Y = 7.32% FV = 0 N=5 PMT = $4,920 c. Larry should not buy this new equipment because the net present value is negative and the internal rate of return is less than the cost of capital. The answer assumes that Larry’s probability distribution of the possible outcomes is accurate. 13-17. Canadian Metal, Mining and Petroleum Company a. Calculate the net present value for each project. Oil Wells Years Cash Flow 1-4 $ 0 5-10 100,000,000 11-20 200,000,000 Present value of inflows Present value of outflows NPV (Net present value) Present Value @ 12% $ 0 261,287,368 $363,844,119 $625,131,487 $500,000,000 $125,131,487 Aluminum Smelter Years Cash Flow 1 $ 0 2-20 87,000,000 Present value of inflows Present value of outflows NPV (Net present value) Present Value @ 12% $ 0 572,163,024 $572,163,024 500,000,000 $ 72,163,024 Both projects are attractive based on positive NPVs. Select the Oil Well if projects are mutually exclusive. b. Recalculate the NPV of the Oil Wells at a 16% discount rate. Oil Wells (risk factor) Years Cash Flow 1-4 $0 5-10 100,000,000 11-20 200,000,000 Present value of inflows Present value of outflows NPV (Net Present Value) Present Value @ 16% $ 0 203,504,684 219,122,684 $422,627,368 $500,000,000 $ (77,372,632) Reject the Oil Mills. Purchase the Smelter. 13-18. John Backster a. D = ∑ DP Windy Acres D P 10 .10 15 .20 30 .40 45 .20 50 .10 Expected cash flow (thousands) Hillcrest DP $1 3 12 9 5 $30 D P 15 .20 25 .30 35 .40 45 .10 Expected cash flow (thousands) DP $ 3.0 7.5 14.0 4.5 $29.0 b. Find the standard deviation. Then the coefficient of variation. D $10 15 30 45 50 D $30 30 30 30 30 Windy Acres (D– D ) (D– D )2 ─ $20 $400 ─ 15 225 0 0 +15 225 +20 400 P .10 .20 .40 .20 .10 (D– D )2P $ 40 45 0 45 40 $170 σ = 170 = 13.04 thousands Coefficient of variation (V ) = σ D = $13.04 = 0.4347 $30 D $15 25 35 45 Hillcrest (D– D ) (D– D )2 $-14 196 -4 16 +6 36 +16 256 D $29 29 29 29 (D– D )2P $39.2 4.8 14.4 25.6 $84.0 P .20 .30 .40 .10 σ = 84 = 9.17 thousands Coefficient of variation (V ) = σ D = $9.17 = 0.3162 $29 Based on the coefficient of variation, Windy Acres has more risk (0.4347 vs. 0.3162). 13-19. John Backster (Continued) a. Risk-adjusted net present value Expected cash flow IF PVA (n = 10) Present value of inflows Present value of outflows Net present value Windy Acres Hillcrest With V = 0.4347, With V = 0.3162, discount rate = 16% discount rate = 12% $30,000 $29,000 $144,997 100,000 $ 44,997 $163,856 100,000 $ 63,856 b. If these two investments are mutually exclusive, he should accept Hillcrest because it has a higher net present value. If the investments are non-mutually exclusive and no capital rationing is involved, they both should be undertaken. 13-20. a. (1) Wardrobe Clothing Manufacturers (2) (3) (4) Present Value of cash flows Probability from sales Initial cost .40 $240,000 $100,000 Enter Expected Sales Fantastic New Coat Moderate .20 Market Dismal .40 180,000 0 (5) (3) – (4) $140,000 (6) Expected NPV (2) × (5) $56,000 100,000 80,000 16,000 100,000 (100,000) (40,000) Expected NPV $32,000 Enter Fantastic .20 $120,000 $60,000 $60,000 $12,000 Blazer Moderate .60 75,000 60,000 15,000 9,000 Market Dismal .20 65,000 60,000 (5,000) (1,000) Expected NPV $20,000 b. The indicated investment, based on the expected NPV, is in the new coat market. However, there is more risk in this alternative so further analysis may be necessary. It is not an automatic decision. 13-21. Probability calculations Expected value = $30,000, σ = $6,000 a. $24,000 to $36,000 expected value + 1 σ 0.6826 = 68.26% b. $21,000 to $39,000 expected value + 1.5 σ 0.8664 = 86.64% c. greater than $18,000 $18,000 Compare to expected value: $18,000 − $30,000 − $12,000 = = −2 $6,000 $6,000 This represents 0.4772 or 48% Total distribution under the curve: .4772 .5000 .9772 = 97.72% d. Less than $41,760 $41,760 Compare to expected value: $41,760 − $30,000 $11,760 = = +1.96 (Represents 0.4750 or 48%) $6,000 $6,000 Total distribution under the curve: .4750 .5000 .9750 = 97.50% e. Less than $27,000 or greater than $39,000 $27,000 $39,000 Compare to expected value: $27,000 − $30,000 − $3,000 = = −.5 (Represents 0.1915 or 19%) $6,000 $6,000 $39,000 − $30,000 $9,000 = = +1.5 (Represents 0.4332 or 43%) $6,000 $6,000 Total distribution under the curve, in the tails: 0.5000 – 0.1915 = 0.3085 + 0.5000 – 0.4332 = 0.0668 = 0.3753 = 37.53% 13-22. Caribou Pipeline Company a. Standard deviation: year 1 D 65 80 95 D 80 80 80 (D– D ) – 15 0 + 15 (D– D )2 225 0 225 P .20 .60 .20 (D– D )2P 45 0 45 90 P .25 .50 .25 (D– D )2P 225 0 225 450 P .30 .40 .30 (D– D )2P 480 0 480 960 σ = 90 = 9.49 Standard deviation: year 5 D 50 80 110 D 80 80 80 (D– D ) –30 0 + 30 (D– D )2 900 0 900 σ = 450 = 21.21 Standard deviation: year 10 D 40 80 120 D 80 80 80 (D– D ) – 40 0 + 40 (D– D )2 1,600 0 1,600 σ = 960 = 30.98 b. Risk over time Dollars Expected Cash flow ($80) $80 1 yr. 5 yr. 10 yr. c. Table: (1) PV IF (2) PV IF (3) PV IF 6% 12% Difference 1 .943 .893 .050 5 .747 .567 .180 10 .558 .322 .236 Year d. Yes. The larger risk over time is consistent with the larger differences in the present value interest factors (PV IF s) over time. In effect, future uncertainty is being penalized by a lower present value interest factor (PV IF ). This is one of the consequences of using progressively higher discount rates to penalize for risk. e. NPV Year Inflow PV @ 12% 1 $80 $ 71.4 5 80 45.4 10 80 25.8 PV of inflows Investment NPV Accept the investment. $142.6 135.0 $ 7.6 13-23. General Munchies a. Purchase of the Toy Company would provide some reduction in risk because of the low correlation with General Munchies, while purchase of Fast Foods would do very little to reduce portfolio risk because of the high correlation coefficient. A combination with the Lumber Company would provide a fairly large degree of risk reduction. b. Students may or may not calculate the coefficient of variation to get some idea about the riskiness of each project. If they do, they will find the following: V GM = $2/ $10 = 0.2 V Toy = $5/ $10 = 0.5 V FF = $3/ $10 = 0.3 V LC = $6/ $10 = 0.6 Although the Lumber Company has the highest risk as measured by the coefficient of variation, its negative correlation coefficient of – 0.5 should provide the best risk reduction for General Munchies. This is an example of a risky company being added to a portfolio but reducing total risk. Buy the Lumber Company. c. Since the Fast Food Company is most like General Munchies, its selection would provide the least amount of risk reduction. Therefore, add the Toy Company to the Lumber Company selected in part (b). The Toy Company offers the next best risk reduction after the Lumber Company because of its low positive correlation coefficient. You might also want to know more about the relationship of the other companies to each other. 13-24. Transoceanic Airlines a. Before acquisition: D $30 .30 50 .40 70 .30 D = ∑ DP P DP 9 20 21 $50($ millions) σ = ∑ (D − D ) P 2 D $30 50 70 D 50 50 50 (D– D ) – 20 0 + 20 (D– D )2 400 0 400 P .30 .40 .30 (D– D )2P 120 0 120 240 σ = 240 = 15.49 Coefficient of variation After the acquisition: (V ) = σ D = 15.49 = 0.310 50 Expected value 53.0 ($ millions) Standard deviation 34.9 ($ millions) Coefficient of variation 0.658 b. No, it doesn’t appear desirable. Although the expected value is $3 million higher, the coefficient of variation is more than twice as high (.658 vs. 310). 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 share price may actually go down. d. The oil company may provide the best diversification benefits. The performance of oil companies and airlines tend to go in opposite directions. If oil prices are high, oil companies’ benefit, but airlines are hurt. The opposite effect is true when oil prices are low. A major travel agency or gambling casino would probably not provide much in the way of risk reduction benefits. They are both closely associated with entertainment and travel. 13-25. Jimmy a. Investment D is riskier by itself with the higher standard deviation (5.2% vs. 4.1%), and D is also riskier in a portfolio context as its beta is higher (1.25 vs. 0.94). b. D = 0.4 × 0.18 + 0.60 × 0.14 = 0.072 + 0.084 = .156 = 15.6% σ DE = 0.4 2 × 0.052 2 + 0.6 2 × 0.0412 + 2 × 0.55 × 0.052 × 0.041 × 0.4 × 0.6 c. σ DE = 0.0400081 = 4.0% d. Β = 0.4 × 1.25 + 0.6 × 0.94 = 1.064 e. The standard deviation of the portfolio is less than either investment individually. The key variable in determining the portfolio standard deviation is the correlation coefficient (how the two investments move together). The portfolio beta is an easier calculation of risk than the portfolio standard deviation. 13-26. Astrid a. Investment N is riskier by itself with the higher standard deviation (3.9% vs. 3.1%). However M is also riskier in a portfolio context as its beta is higher (1.40 vs. 0.85). b. D = 0.55 × 0.12 + 0.45 × 0.19 = 0.066 + 0.0855 = .1515 = 15.15% σ DE = 0.55 2 × 0.0312 + 0.45 2 × 0.039 2 + 2 × 0.30 × 0.031 × 0.039 × 0.55 × 0.45 c. σ DE = 0.027897 = 2.79% d. Β = 0.55 × 1.40+ 0.45 × 0.85 = 1.1525 e. The standard deviation of the portfolio is less than either investment individually. The key variable in determining the portfolio standard deviation is the correlation coefficient (how the two investments move together). Beta is an easier calculation of risk than the portfolio standard deviation. 13-27. Mrs. Markowitz a. b. Return (percent) 17 H 16 F 15 G 14 E 13 C D 12 11 B 10 A 0 1 2 3 4 5 6 Risk (percent) 7 8 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. Comprehensive Problems 13-28. Gibson Appliance Company Portfolio Effect of a Merger a. Genetic Technology Company D P DP $ 2 .2 $0.4 8 .3 2.4 16 .2 3.2 25 .2 5.0 40 .1 4.0 Expected cash flow $15.0 (millions) Silicon Microchip Company D $ 5 7 18 24 P .2 .2 .3 .3 Expected cash flow (millions) DP $1.0 1.4 5.4 7.2 $15.0 b. Expected coefficient of variation for Genetic Technology Company D $2 8 16 25 40 D $15 15 15 15 15 (D– D ) $ –13 – 7 + 1 + 10 + 25 (D– D )2 $ 169 49 1 100 625 P .2 .3 .2 .2 .1 (D– D )2P $33.8 14.7 0.2 20.0 62.5 $131.2 σ = 131.2 = $11.45 million Coefficient of variation (V ) = σ D = $11.45 = 0.763 $15 Coefficient of variation for Silicon Microchip Company D $ 5 7 18 24 D $15 15 15 15 (D– D ) $–10 –8 +3 +9 (D– D )2 $100 64 9 81 P .2 .2 .3 .3 (D– D )2P $20.0 12.8 2.7 24.3 $59.8 σ = 59.8 = $7.73 million Coefficient of variation (V ) = σ D = $7.73 = 0.515 $15 Silicon Microchip has a lower coefficient of variation, 0.515 < 0.763. c. For both companies the annual expected value is $15million for 10 years. The cost is $80 million for either company. Gibson has a cost of capital of 12%. $15 million(n = 10, %I/Y = 12%) = $84.753 PV of inflows 80.000 PV of outflows $ 4.753 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 has the higher coefficient of variation, we would select the lower risk company; Silicon Microchip. If Gibson Appliance Company uses risk-adjusted cost of capital concepts, it would use a higher cost of capital for the cash flows generated by Genetic Technology and this would reduce its NPV. f. Since Gibson Appliance has a correlation coefficient with the economy of +.4, the selection of Genetic Technology would offer the most risk reduction because its correlation coefficient with the economy is – 0.2. g. Because Gibson Appliance is a stable billion-dollar company, this investment of $80 million would probably not have a great impact on the share price in the short run. There could be some positive movement in the share price if investors perceive less risk from portfolio diversification. This would be particularly true for a merger with Genetic Technology. You can use this question to discuss risk-return trade-offs and market reactions. 13-29. Ace Trucking Company a. Assumption One: Yr. 1 Yr. 2 Yr. 3 Probability D DP D DP D DP .1 $0.68 .068 $0.81 .081 $0.95 .095 .2 .81 .162 .95 .190 1.08 .216 .3 .95 .285 1.08 .324 1.22 .366 .2 1.08 .216 1.22 .244 1.35 .270 .2 1.22 .244 1.35 .270 1.49 .298 Expected value $0.975/litre $1.109/litre $1.245/litre Assumption Two: Yr. 1 Yr. 2 Yr. 3 Probability D DP D DP D DP .1 $1.22 .122 $1.35 .135 $1.76 .176 .3 1.35 .405 1.49 .447 2.03 .609 .4 1.76 .704 2.03 .812 2.43 .972 .2 2.03 .406 2.30 .460 2.70 .540 Expected value $1.637/litre $1.854/litre $2.297/litre b. Assumption One: #of litres % savings Expected without with Year cost/ gal. efficiency = Cost efficiency 1 $0.975 30 million $29,250,000 15% 2 1.109 33,270,000 3 1.245 37,350,000 Total $ saved $4,387,500 4,990,500 5,602,500 Assumption Two: #of litres % savings Expected without with Year cost/ gal. efficiency = Cost efficiency 1 $1.637 30 million $49,110,000 15% 2 1.854 55,620,000 3 2.297 68,910,000 Total $ saved $7,366,500 8,343,000 10,336,500 c. Compute annual CCA (amortization): Then proceed to the analysis. Year 1 30% (1/2) × 13.25 mil. = 1.9875 mil. Year 2 30% × 11.2625 mil. = 3.37875 mil. Year 3 30% × 7.88375 mil. = 2.365125 mil. Total saved equals increase in EBAT (earnings before amortization or CCA and taxes) Assumption One Increase in EBAT – CCA Increase in EBT – Taxes (30%) Increase in EAT + CCA Increased cash flow Year 1 $4,387,500 1,987,500 2,400,000 720,000 1,680,000 1,987,500 $3,667,500 Year 2 $4,990,500 3,378,750 1,611,750 483,525 1,128,225 3,378,750 $4,506,975 Year 3 $5,602,500 2,365,125 3,237,375 971,213 2,266,162 2,365,125 $4,631,288 Assumption Two Increase in EBDT – CCA Increase in EBT – Taxes (30%) Increase in EAT + CCA Increased Cash Flow Year 1 Year 2 $7,366,500 1,987,500 5,379,000 1,613,700 3,765,300 1,987,500 $5,752,800 $8,343,000 3,378,750 4,964,250 1,489,275 3,474,975 3,378,750 $6,853,725 Year 3 $10,336,500 2,365,125 7,971,375 2,391,413 5,579,962 2,365,125 $7,945,088 d. #1 Year 1 2 3 Cash Flow $3,667,500 4,506,975 4,631,288 PV of inflows PV of outflows NPV Present Value @ 11% $ 3,304,054 3,657,962 3,386,358 $ 10,348,374 13,250,000 $(2,901,626) #2 Year 1 2 3 Cash Flow $5,752,800 6,853,725 7,945,088 PV of inflows PV of outflows NPV Present Value @ 11% $5,182,703 5,562,637 5,809,380 $16,554,720 13,250,000 $3,304,720 Combined NPV: Outcome NPV Assumption One (2,901,626) Assumption Two 3,304,720 Expected Outcome Probability .5 (1,450,813) .5 1,652,360 $201,547 e. Yes: The combined expected value of the outcomes is positive. f. Quite sensitive when that many litres are used per year. 13-30. Grit Ltd. a. Cost of capital the same for all three projects @ 12% Project A Cash flow per year Number of years Present value = Cost NPV Project B Cash flow per year Number of years Present value = Cost NPV Project C Cash flow per year Number of years Present value = Cost NPV $30,000 10 $169,507 160,000 $ 9,507 $26,000 10 $146,906 150,000 $ (3,094) $29,000 10 $163,856 175,000 $(11,144) Only project A has a positive NPV, when using the cost of capital as the evaluation criteria. b. The CAPM attempts to match the risk of a project with its required return. K j = R f + β j (R m – R f ) Project A K j = 5% + 1.5 (12% – 5%) = 5% + 10.5% = 15.5% Present value = Cost NPV Project B K j = 5% +.9 (12% – 5%) = 5% + 6.3% = 11.3% Present value = Cost NPV Project C $147,737 160,000 $(12,263) $151,213 150,000 $ 1,123 K j = 5% + .6 (12% – 5%) = 5% + 4.2% = 9.2% Present value = Cost NPV $184,485 175,000 $ 9,485 Based on the risk-return criteria of the CAPM, project A is no longer acceptable. Project C now has the highest positive NPV. 13-31. The Hour Winehouse a. Cost of capital = 0.50 × .08 (1 − .28) + 0.50 × .15 = .50 × 0.0576 + .075 = 0.0288 +0.075 = 0.1038 = 10.38% CAPM Kj = R f + β j (R m – R f ) = 0.029 + 1.3 (0.07) = 0.121 = 12.1% b. The Hour Winehouse could use one of two discount rates, depending on the perceived risk of the project. If the risk is the same as current projects the cost of capital based on current market values is appropriate. If the risk is different the CAPM is probably justified, in an attempt to match risk and required return. In this case the analysis suggests that the project is ‘quite unlike’ any of its existing projects. Therefore the CAPM rate of 12% is probably justified for use as the discount rate. c. Year 0 0 1-6 6 6 n=8 Event T = 28% r = 12% Expected Cash Flow d = 30% Aftertax Cash Flow Investment $(500,000) − Current liabilities 30,000 − Revenues 150,000 108,000 Salvage 55,000 − Current lia. reversed 30,000 [500,000 − 27,865] (.30)(.28)  1 + .5(.12)   .12 + .30  1 + .12  472,135(.020 )(.946428571) = NPV = Proceed! Present Value @ 12% $(500,000) 30,000 444,032 27,865 (15,199) 89,368 $76,066 13-32. Ivan Skavinsky Skavar Project a. Cost of capital = .40 × 9% (1 − .40) + 60% × 17% = .40 × 5.4 + 10.2% = 0.0216 +0.1020 = 0.1236 = 12.36% CAPM Kj = R f + β j (R m – R f ) = 0.06 + 1.5 (0.08) = 0.180 = 18% b. Abdul Abubu Amir could use one of two discount rates, depending on the perceived risk of the project. If the risk is the same as current projects the cost of capital based on current market values is appropriate. If the risk is different the CAPM is probably justified, in an attempt to match risk and required return. In this case the analysis suggests that the project is ‘quite unlike’ any of its existing projects. Therefore the CAPM rate of 18% is probably justified for use as the discount rate. c. Year 0 0 1-3 4-7 7 7 n=7 Event T = 40% r = 18% d = 30% Expected Aftertax Cash Flow Cash Flow $(400,000) − (40,000) − 135,000 81,000 160,000 96,000 35,000 − 40,000 [400,000 − 10,987] (.30)(.40)  1 + .5(.18)   .18 + .30  1 + .18  389,013(.0250 )(.9237288) = NPV = The Skavar W. C. Revenues Revenues Salvage WC recovery Enjoy Ivan Skavinsky Skvar. Present Value @ 18% $(400,000) (40,000) 176,116 157,176 10,987 12,557 89,836 $6,672 d. If instead of a firm beta we have an equity beta we will have to calculate the cost of capital based on a weighting of debt and equity. The cost of equity capital: CAPM K j = R f + β j (R m – R f ) = 0.06 + 2.0 (0.08) = 0.220 = 22% Overall cost of capital = .40 × 0.09 (1 − .40) + 60% × 0.22 = .40 × 0.0540 + 0.1320 = 0.0216 +0.1320 = 0.1536 = 15.36% n=7 Year 0 0 1-3 4-7 7 7 Event T = 38% r = 13.24% d = 30% Expected Aftertax Present Value Cash Flow Cash Flow @ 15.36% $(400,000) − (40,000) − 135,000 81,000 160,000 96,000 35,000 − 40,000 − [400,000 − 12,873] (.30)(.40)  1 + .5(.1536)   .1536 + .30  1 + .1536  387,127(.26455)(.93343) = NPV = The Skavar W. C. Revenues Revenues Salvage WC recovery The Skavar should be accepted. Its value is higher. $(400,000) (40,000) 183,843 177,237 12,873 14,712 95,596 $44,261 MINI CASES Churchill's Muffins (Investment Decision with NPV and Risk Analysis) Standard (company-owned) P .30 .40 .30 D 1,450 630 – 200 × × × × D 627 627 627 NPV 1,450 630 (200) D = = = = 435 252 (60) 627 (D– D ) (D– D )2 823 677,329 3 9 – 827 683,929 (D– D )2P 203,199 4 205,179 408,382 P .30 .40 .30 σ = 408,382 = 639 Coefficient of variation (V ) = σ D = 639 = 1.02 627 Expanded (company-owned) P .30 .40 .30 D 3,812 740 – 900 × × × × D 1,170 1,170 1,170 NPV 3,812 740 (900) D = 1,144 = 296 = (270) = 1,170 (D– D ) (D– D )2 2,642 6,980,164 430 184,900 – 2,070 4,284,900 P .3 .4 .3 (D– D )2P 2,094,049 73,960 1,285,470 3,453,479 σ = 3,453,479 = 1,858 Coefficient of variation (V ) = σ D = 1,858 = 1.59 1,170 The numeric analysis indicates that, on an expected values NPV basis, the expanded size alternative is far superior. The risk measure, on the other hand, certainly favors the standard size alternative. Note that the return advantage of the expanded alternative rests entirely with the enormous potential under the "very favorable" outcome. The downside risk is also very high under this alternative. The franchisee alternative offers lower potential returns but very little risk since the investment by the firm in case of poor franchisee performance will come mostly in the way of additional managerial troubleshooting efforts and the necessity to forgo royalties in order to ensure the survival of a franchisee under adverse conditions. In real life, Churchill's (disguised name) actually elected for the standard, franchised alternative. Under this one the franchisee still stood to make a reasonable return with lower risk to himself and also to the company (less investment for the company plus better experience historically under the franchisee option). Importantly, this allowed John's dad to begin withdrawing funds from the firm for the purpose of reducing the mortgage and thus removing his home from being at risk if the business failed. Phillips Toy Company (Capital Budgeting and Cash Flow) Purpose: The case gives the student a good opportunity to do cash flow analysis. The use of variable discount rates based on project risk gives insight into how some corporations adjust for risk exposure. Also, the use of an appropriate time horizon for analysis is highlighted. Some students may take a special interest in the case because of the discussion of the profitable world of hockey card collecting. Though the case is closely related to Chapter 12, it should probably follow after Chapter 13 because of the risk dimensions in the discussion Given the case information, the expected value for sales in 2006 would be calculated as: P × .25 .40 .20 .15 × × × × Sales (in $ thousands) 1,100 2,000 3,750 4,500 D = = = = = 275 800 750 675 2,500 The standard deviation and coefficient of variation of the estimated probable outcomes are: D $1,100 2,000 3,750 4,500 D $2,500 2,500 2,500 2,500 (D− D ) −$1,500 −500 1,250 2,000 (D− D )2 1,960,000 250,000 1,562,500 4,000,000 P .25 .40 .20 .15 (D− D )2P $490,000 100,000 312,500 600,000 $1,502,500 σ = 1,502,500 = 1,226 Coefficient of variation = $1,226/ $2,500 = 0.49 Yet table 2 would indicate 14% as the appropriate discount rate. The 2006 timing for the first sales might be confusing for the students because they have to make an assumption about when in 2005 the equipment would be delivered and paid for. In actuality, the equipment, because of order lead times, will not be deliverable until late in 2005 and thus uncertainties will arise in any analysis on how soon it can be up and running smoothly and then how long it will take to produce an adequate starting inventory. A pre-sales investment period would add to the initial investment. Note however that the standard analysis assumes the cash flows (earnings) occur at the end of each year, not throughout the year, which builds in a conservative bias. Barnes produced (the company's actual estimate for tax rate was 40 percent, not stated in the case) the following calculations: In thousands Operating Projected Expenses EAT Sales (.70) = EBT × (1 ─ .40) Year 1 2 3 4 5 6 $2,500 3,000 3,600 4,320 4,752 5,227 $1,750 2,100 2,520 3,024 3,326 3,659 $ 750 900 1,080 1,296 1,426 1,568 Present Value @ 14% $450.0 540.0 648.0 777.6 855.6 940.8 $ 394.7 415.5 437.4 460.4 444.4 428.6 $2,581.0 PV of CCA tax shield [2,800,000] (.20)(.40)  1 + .5(.14)   .14 + .20  1 + .14  2,800,000(0.235294 )0(.938596 ) = 618,369 (assuming asset pool continues) and no salvage value Summary: PV of cash flows PV of CCA tax shields Initial working capital investment Initial investment Recovery of working capital (n=6) NPV = $2,581.0 618.4 (200.0) (2,800.0) 91.1 $ 290.5 Based on the positive net present value NPV, the project appears to be feasible. The firm would be justified in going ahead with the investment. A six-year time horizon may be too short a time frame to fully assess the project. It assumes there will be no cash flows from the seventh year on. While many firms utilize a time frame of 5 to 10 years for conservative purposes, this may sometimes result in the rejection of a potentially profitable project that requires a longer time period for analysis. In this particular case, this was not a problem for the Phillips Toy Company as the project had a positive net present value over six years. Nevertheless, it could lead to an inappropriate decision for a long-life project in the future. Finally, there is the question of what discount rate to use for the calculations. Given the historical practice, we can take comfort that the coefficient of variation comes in right in the middle of one of the seemingly normal ranges. However, not knowing how or when those ranges were set up should make Barnes somewhat uncomfortable. Up until now estimates have resulted in a positive net present value for the new product. However, if a discount rate of 16 to 18 percent were really more appropriate that 14 percent, the investment would not be attractive. This may not be a concern given lower yields in the capital markets. Solution Manual for Foundations of Financial Management Stanley B. Block, Geoffrey A. Hirt, Bartley Danielsen, Doug Short, Michael Perretta 9780071320566, 9781259268892, 978125926101