13-8. Bridget's Modeling Studios is considering opening a new location in Miami. An aftertax cash flow of $120 per day(expected value)is projected for each of the two locations being evaluated Which of these sites would you select based on the distribution of these cash flows(use the coefficient of variation as your measure of risk) Site B Probability Cash Flows Probability Cash Flows 30 140 120 220 20 160 Expected value l20 Expected value $120 Solution: Bridgets Modeling Studios Standard Deviations of Sites a and B Site a D D-D)(D P(D-D $80$120$-40 $1,600 $240 110120 100 50 50 140120+20 400 30 120 220120+100 10,000 05 500 $910 910=$3017= ght C 2005 by The McGramr-Hill Co
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-487 13-8. Bridget’s Modeling Studiosis considering opening a new location in Miami. An aftertax cash flow of $120 per day (expected value) is projected for each of the two locations being evaluated.. Which of these sites 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 .15............ $ 80 .10 ............ $ 50 .50............ 110 .20 ............ 80 .30............ 140 .40 ............ 120 .05............ 220 .20 ............ 160 Expected value $120 .10 ............ Expected Value 190 $120 Solution: Bridget’s Modeling Studios Standard Deviations of Sites A and B Site A D D (D− D) 2 (D − D) P (D D) P 2 − $ 80 $120 $–40 $ 1,600 .15 $240 110 120 –10 100 .50 50 140 120 +20 400 .30 120 220 120 +100 10,000 .05 500 $910 17 A 910 = $30. =
13-8. Continued Site B D (D-D)(D-D (D-D)+P $50$120 $4,900.10$490 80120 40 160020 320 120120 40 160120+40 1,60020 320 190120+70 4.900 490 $1.620 √1620=$40.25= VA=$30.17/$120=2514 $40.25/$120=.3354 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 CopyrightC 2005 by The McGray-Hill Companies, Inc. S-488
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-488 13-8. Continued Site B D D (D− D) 2 (D − D) P (D D) P 2 − $ 50 $120 $–70 $4,900 .10 $ 490 80 120 –40 1,600 .20 320 120 120 –0– –0– .40 –0– 160 120 +40 1,600 .20 320 190 120 +70 4,900 .10 490 $1,620 1,620 = $40.25 = VA = $30.17/$120 = .2514 VB = $40.25/$120 = .3354 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
Waste Industries is evaluating a $70,000 project with the following cash flows Year Cash Flows $11,000 16,000 21,000 24.000 30,00 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 Discount of variation Rate 6% 51-.75 10 76-1.00 1.01-125 Solution: Waste industries Year Inflows PVIF @ 14% P $11,000 877 $9,647 2 16,000 .769 12.304 21.000 67: 14.175 4 24.000 592 14,208 30.000 519 5570 Pv of Inflows $65,904 Investment 70000 NPV (4096) Based on the positive net present value, the project should not be undertaken S-489 Copyright C2005 by The McGramw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-489 13-9. 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 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 positive net present value, the project should not be undertaken
13-10 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 below. Which method should be selected using net present value Y Method 1 Method 2 $18,000 $20,000 24.000 25.000 2345 34,000 35.000 26.000 14,000 15000 Solution: Dixie Dynamite Co. Method 1 Method 2 PVE PVE Year Inflows 12% Inflows 16% P $18,000893$16,074 $20,000862$17,240 224.00079719,128 25,00074318,575 3400071224,208 35,00064122435 26.000636 16.536 280055215,456 514,0005977938 15,0004762 PV ofInflows $83.884 $80846 Investment 75000 75000 NPV $8,884 $5,846 Select method 1 CopyrightC 2005 by The McGray-Hill Companies, Inc. S-490
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-490 13-10. 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 below. Which method should be selected using net present value analysis? Year 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 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 Select Method 1 $ 5,846
Fill in the table below from Append ix B. Does a high discount rate have a greater or lesser effect on long-term inflows compared to recent ones? Discount rate ears 20% Solution: Discount rate Y 5% 20% 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 produce an answer that is 87.5% of the low discount rate(833/952).However after the 20th year the high rate discount rate is only 6. 90% of the low discount rate(.026/377) ght C 2005 by The McGramr-Hill Co
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-491 13-11. Fill in the table below 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....................... ______ ______ 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 produce an answer that is 87.5% of the low discount rate (.833/.952). However, after the 20th year, the high rate discount rate is only 6.90% of the low discount rate (.026/.377)