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Chapter 6 Solutions

Chapter 6 Solutions - 6 1 Year Sales (millions Inflation...

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Unformatted text preview: 6- 1 Year Sales (millions) Inflation Change in Real GDP a. Nominal Sales Growth Rate a. Real Sales Growth Rate c. Weights Weighted Nominal Growth Rate d. Real Sales/Real GDP - 6 \$5.30 - 5 \$5.70 3.00% 1.00% - 4 \$5.50 2.00% - 2.00% - 3 \$6.30 5.00% 2.00% - 2 \$7.50 3.00% 3.00% - 1 \$8.00 4.00% 1.00% Average 7.5% - 3.5% 14.5% 19.0% 6.7% 8.9% 4.5% - 5.5% 9.5% 16.0% 2.7% 5.5% 1/15 2/15 1/5 4/15 1/3 Sum 0.5% - 0.5% 2.9% 5.1% 2.2% 10.2% 4.55 2.75 4.77 5.35 2.67 4.02 a. The average annual growth rate in nominal sales is 8.9%, which gives a forecast of Year 0 sales of \$8.0 x 1.089 = \$8.71 million. b. The average annual growth rate in real sales is 5.5%. With expected inﬂaLon of 2.0%, the expected nominal growth rate for Year 0 is 7.5%, which gives a forecast of Year 0 nominal sales of \$8.0 x 1.075 = \$8.6 million. c. Using weighted nominal growth rates, the Year 0 growth rate will be 10.2%, which gives a forecast of Year 0 nominal sales of \$8.0 x 1.102 = \$8.82 million. d. For the historical period, the raLo of real sales growth to real GDP growth has been approximately four Lmes. With real GDP growth in Year 0 forecast at 2.5%, real sales growth would be 10% (2.5% x 4). Adding the expected inﬂaLon of 2.0% produces an expected nominal growth rate for Year 0 of 12.0%, and a forecast of Year 0 nominal sales of \$8.0 x 1.12 = \$8.96 million. e. Method d) is probably the most reliable because it incorporates esLmates of both real GDP growth and inﬂaLon. 6- 2 Year Sales (millions) Inflation Change in Real GDP - 6 \$1.2 - 5 \$1.8 6% 3% - 4 \$1.6 4% - 2% - 3 \$2.3 5% 2% - 2 \$2.8 3% 1% - 1 \$2.6 1% - 1% Average 50.0% - 11.1% 43.8% 21.7% - 7.1% 19.4% 44.0% - 15.1% 38.8% 18.7% - 8.1% 15.6% 1/15 2/15 1/5 4/15 1/3 Sum 3.3% - 1.5% 8.8% 5.8% - 2.4% 14.0% 14.67 7.56 19.38 18.74 8.14 13.70 a. Nominal Sales Growth Rate a. Real Sales Growth Rate c. Weights Weighted Nominal Growth Rate d. Real Sales/Real GDP a. The average annual growth rate in nominal sales is 19.4%, which gives a forecast of Year 0 sales of \$2.6 x 1.194 = \$3.10 million and a Year 1 sales forecast of \$3.10 x 1.194 = \$3.71 million. b. The average annual growth rate in real sales is 15.6%. With expected inﬂaVon of 2.0%, the expected nominal growth rate for Years 0 and 1 is 17.6%, which gives a forecast of Year 0 nominal sales of \$2.6 x 1.176 = \$3.06 million and a Year 1 sales forecast of \$3.06 x 1.176 = \$3.60 million. c. Using weighted nominal growth rates, the Years 0 and 1 growth rate will be 14.0%, which gives a forecast of Year 0 nominal sales of \$2.6 x 1.14 = \$2.96 million and a Year 1 sales forecast of \$2.96 x 1.14 = \$3.38 million. d. For the historical period, in the years with posiVve real GDP growth, the raVo of real sales growth to real GDP growth has been approximately 13.70 Vmes. With real GDP growth in Year 0 and Year 1 forecast at 1.5% and 2% respecVvely, real sales growth would be 20.54% (1.5% x 13.70%) and 27.39% (2.0% x 13.70%) in Year 0 and Year 1. Adding the expected inﬂaVon of 2.0% produces expected nominal growth rates of 22.54% for Year 0 and 29.39% for Year 1. The resultant forecast of Year 0 nominal sales is \$2.6 x 1.2254 = \$3.19 million and of Year 1 nominal sales is \$3.19 x 1.2739 = \$4.12 million e. Given that real sales growth rates are highly correlated with real GDP growth rates, method (d) is probably the most reliable because it incorporates esVmates of both real GDP growth and inﬂaVon. a. extrapolation based on nominal percentage growth rates of sales Year Sales (millions) Sales Growth Avg. Percent Increase Inflation Change in Real GDP - 6 \$1.20 b. extrapolation based on real percentage growth rates in sales - 5 \$1.80 50.00% - 4 \$1.60 - 11.11% - 3 \$2.40 50.00% - 2 \$2.80 16.67% - 1 \$2.60 - 7.14% 6.00% 3.00% 4.00% - 2.00% 5.00% 2.00% 3.00% 1.00% 1.00% - 1.00% 0 \$2.60 1 \$2.60 19.68% - - - - 6- 2 Year Sales (millions) Sales Growth Inflation Real Sales Growth Change in Real GDP - 6 \$1.20 - 5 \$1.80 50.00% 6.00% 44.00% 3.00% - 4 \$1.60 - 11.11% 4.00% - 15.11% - 2.00% - 3 \$2.40 50.00% 5.00% 45.00% 2.00% - 2 \$2.80 16.67% 3.00% 13.67% 1.00% - 1 \$2.60 - 7.14% 1.00% - 8.14% - 1.00% - 3 \$2.40 50.00% 3/15 10.00% 5.00% 2.00% - 2 \$2.80 16.67% 4/15 4.44% 3.00% 1.00% - 1 \$2.60 - 7.14% 5/15 - 2.38% 1.00% - 1.00% 0 1 \$3.01 \$3.49 - - - - 15.88% - 15.88% - c. extrapolation applied to nominal sales, with greater weight on the more recent data Year Sales (millions) Sales Growth Weight Factor Weighted Sales Growth Inflation Change in Real GDP - 6 \$1.20 - 5 \$1.80 50.00% 1/15 3.33% 6.00% 3.00% - 4 \$1.60 - 11.11% 2/15 - 1.48% 4.00% - 2.00% 0 1 \$2.96 \$3.37 - - - - 13.92% - - 13.92% - - d. extrapolation based on the relationship between the real sales gowth rate and the annual change in real GDP. The forecast of real GDP for year zero is 2.5%, and for year one, it is the average from the past five years. Year Sales (millions) Sales Growth Inflation Real Sales Growth Change in Real GDP - 6 \$1.20 - 5 \$1.80 50.00% 6.00% 44.00% 3.00% - 4 \$1.60 - 11.11% 4.00% - 15.11% - 2.00% - 3 \$2.40 50.00% 5.00% 45.00% 2.00% - 2 \$2.80 16.67% 3.00% 13.67% 1.00% - 1 \$2.60 - 7.14% 1.00% - 8.14% - 1.00% 0 1 \$2.60 \$2.60 - - - - 0.00% 2.50% 0.00% 0.60% 6- 3 Year - 6 Sales Growth (%) Alpha Growth Forecast Alpha Growth Forecast Alpha Growth Forecast Alpha Growth Forecast Year - 5 Year - 4 Year - 3 Year - 2 Year - 1 223% 127% 174% 59% 90% Year 0 43% 0.2 223% 223.0% 203.8% 197.8% 170.1% 154.1% 131.8% 223.0% 184.6% 180.4% 131.8% 115.1% 86.3% 223.0% 165.4% 170.6% 103.6% 95.4% 64.0% 223.0% 146.2% 168.4% 80.9% 88.2% 52.0% 0.4 223% 0.6 223% 0.8 223% With the growth rate decreasing over Cme, exponenCal smoothing tends to forecast rates that are too high. The problem is minimized by emphasizing the most recent actual growth rate (alpha = 0.8 in this example), but the bias sCll is posiCve and informaCon contained in the growth trend is diminished in importance in the forecast. The naive approaches illustrated in the chapter generally have similar problems in forecasCng growth rates that are secularly rising or secularly declining. One way to try to address the problem is to try to forecast the change in the growth rate, rather than the growth rate itself. Perhaps the growth rates in each period tends to be a ﬁxed percentage of the previous growth rate. If so, then forecasCng the change in the rate could produce a beTer esCmate of the expected growth rate. AlternaCve, non- naive approaches can be tried. 6- 4 Subscribers (000s) Annual Revenue (millions) Annual Revenue/ subscriber Rev/ subscriber/ month Company Year Services* Market Penetration Tri- County Cable 1997 TV 32% 45 \$27.7 \$615.56 \$51.30 Digicast Inc. 2000 TV,INT 41% 5 \$3.1 \$620.00 \$51.67 Sky Signal Inc. 2008 TV,INT,T 50% 143 \$187.7 \$1,312.59 \$109.38 MidTel Cable Co. 2009 TV,INT,T 58% 58 \$72.8 \$1,255.17 \$104.60 Fairway Communications 2010 TV,INT,T 62% 741 \$1,058.0 \$1,427.80 \$118.98 * - TV = television; INT = internet; T = telephone a. Use the data above to estimate the potential annual revenue of the new venture. Use Sky, MidTel, and Fairway Average Market Penetration Average Revenue / Subscriber 57% \$110.99 /month DSI Target Market 25,000 households Subscribers 14,166 (assumes average penetration) Average Annual Revenue/Subsc. Estimated Annual Revenue \$1,331.85 \$ 18,867,035 b. What assumptions are critical to your estimate? How might you validate them? The most critical assumption is the ability of DSI to achieve the 57% market penetration. To validate this assumption, DSI could do market research including consumer surveys and focus groups. Also, if the yardsticks are not equally likely to be good for DSI it could make sense to ignore some of them or to weight them differently. 6- 5 a. Use the data above to estimate the potential annual revenue of the new venture. Total Market Population % Targeted DSI Target Market % Converted to Subscribers 25,000 households 40% 10,000 households 75% Estimated Subscribers 7,500 Average Monthly Revenue/Subsc. \$ 160 Estimated Monthly Revenue \$ 1,200,000 Estimated Annual Revenue \$ 14,400,000 b. What assumptions are critical to your estimate? How might you validate them? The most critical assumption is the ability of DSI to convert 75% of the targeted customers to subscribers. Market research, e.g., focus groups or consumer surveys, might help DSI have more confidence in this assumption. 6- 6 Total Population % Targeted DSI Target Market % Converted to Subscribers 25,000 households 40% 10,000 households 75% Estimated Subscribers 7,500 Average Monthly Revenue/Subsc. \$ 160 Estimated Monthly Revenue \$ 1,200,000 Estimated Annual Revenue \$ 14,400,000 \$ 14,400,000 \$130 \$140 \$150 \$160 \$170 \$180 \$190 60% \$ 9,360,000 \$ 10,080,000 \$ 10,800,000 \$ 11,520,000 \$ 12,240,000 \$ 12,960,000 \$ 13,680,000 65% \$ 10,140,000 \$ 10,920,000 \$ 11,700,000 \$ 12,480,000 \$ 13,260,000 \$ 14,040,000 \$ 14,820,000 70% \$ 10,920,000 \$ 11,760,000 \$ 12,600,000 \$ 13,440,000 \$ 14,280,000 \$ 15,120,000 \$ 15,960,000 75% \$ 11,700,000 \$ 12,600,000 \$ 13,500,000 \$ 14,400,000 \$ 15,300,000 \$ 16,200,000 \$ 17,100,000 80% \$ 12,480,000 \$ 13,440,000 \$ 14,400,000 \$ 15,360,000 \$ 16,320,000 \$ 17,280,000 \$ 18,240,000 85% \$ 13,260,000 \$ 14,280,000 \$ 15,300,000 \$ 16,320,000 \$ 17,340,000 \$ 18,360,000 \$ 19,380,000 90% \$ 14,040,000 \$ 15,120,000 \$ 16,200,000 \$ 17,280,000 \$ 18,360,000 \$ 19,440,000 \$ 20,520,000 6- 7 Scenario (a) Total Population % Targeted DSI Target Market % Converted to Subscribers 25,000 households 55% 13,750 households 80% Estimated Subscribers 11,000 Average Monthly Revenue/Subsc. \$ 170 Estimated Monthly Revenue \$ 1,870,000 Estimated Annual Revenue \$ 22,440,000 Scenario (b) Total Population % Targeted DSI Target Market % Converted to Subscribers 25,000 households 40% 10,000 households 50% Estimated Subscribers 5,000 Average Monthly Revenue/Subsc. \$ 140 Estimated Monthly Revenue \$ 700,000 Estimated Annual Revenue \$ 8,400,000 6- 10 MONTH Units Sold Price/unit Revenue 4 5,000 \$2.99 15% 1 0 2 0 3 0 4 0 \$0 \$0 \$0 \$0 5 5,000 \$2.99 \$14,950 6 5,750 \$2.99 \$17,193 7 6,613 \$2.99 \$19,771 8 7,604 \$2.99 \$22,737 9 8,745 \$2.99 \$26,148 10 10,057 \$2.99 \$30,070 Revenue \$50,000 Monthly Revenue Take Five Systems Development Month Initial Unit Sales Selling Price Sales Growth (Months 5- 12) \$40,000 \$30,000 \$20,000 \$10,000 \$0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Month 11 11,565 \$2.99 \$34,580 12 13,300 \$2.99 \$39,767 13 14 15 16 17 18 13,300 13,300 13,300 13,300 13,300 13,300 \$2.99 \$2.99 \$2.99 \$2.99 \$2.99 \$2.99 \$39,767 \$39,767 \$39,767 \$39,767 \$39,767 \$39,767 6- 11 Take Five Systems Development Month Initial Unit Sales Selling Price Sales Growth (Months 5- 12) 4 5,000 \$2.99 15% Monthly Growth Rate Sensitivity Analysis \$39,767 9% 11% 13% 15% 17% 19% 21% 2,500 \$13,664 \$15,518 \$17,584 \$19,884 \$22,434 \$25,260 \$28,384 3,000 \$16,397 \$18,622 \$21,100 \$23,860 \$26,919 \$30,310 \$34,062 3,500 \$19,130 \$21,725 \$24,620 \$27,837 \$31,407 \$35,363 \$39,740 4,000 \$21,863 \$24,829 \$28,136 \$31,814 \$35,892 \$40,416 \$45,415 Initial Unit Sales 4,500 5,000 5,500 \$24,596 \$27,329 \$30,061 \$27,933 \$31,036 \$34,140 \$31,652 \$35,171 \$38,688 \$35,790 \$39,767 \$43,744 \$40,380 \$44,868 \$49,353 \$45,466 \$50,519 \$55,572 \$51,093 \$56,771 \$62,449 6,000 \$32,794 \$37,243 \$42,204 \$47,720 \$53,841 \$60,622 \$68,124 6,500 \$35,527 \$40,350 \$45,720 \$51,697 \$58,329 \$65,675 \$73,802 7,000 \$38,260 \$43,454 \$49,239 \$55,674 \$62,814 \$70,728 \$79,480 7,500 \$40,993 \$46,557 \$52,756 \$59,651 \$67,302 \$75,779 \$85,158 6- 12 Take Five Systems - Scenario (a) Development Month Initial Unit Sales Selling Price Sales Growth (Months 3- 12) MONTH Units Sold Price/unit Revenue 2 4,000 \$3.99 17% 1 0 2 0 \$0 \$0 3 4 5 6 7 4,000 4,680 5,476 6,406 7,496 \$3.99 \$3.99 \$3.99 \$3.99 \$3.99 \$15,960 \$18,673 \$21,848 \$25,562 \$29,907 8 8,770 \$3.99 \$34,991 9 10,261 \$3.99 \$40,940 10 12,005 \$3.99 \$47,900 11 14,046 \$3.99 \$56,043 12 16,434 \$3.99 \$65,570 13 16,434 \$3.99 \$65,570 14 16,434 \$3.99 \$65,570 15 16,434 \$3.99 \$65,570 16 16,434 \$3.99 \$65,570 17 16,434 \$3.99 \$65,570 18 16,434 \$3.99 \$65,570 14 5,315 \$1.99 \$10,576 15 5,315 \$1.99 \$10,576 16 5,315 \$1.99 \$10,576 17 5,315 \$1.99 \$10,576 18 5,315 \$1.99 \$10,576 Monthly Revenue \$70,000 Take Five Systems - Scenario (b) Development Month Initial Unit Sales Selling Price Sales Growth (Months 9- 12) MONTH Units Sold Price/unit Revenue \$60,000 \$50,000 \$40,000 \$30,000 Revenue (a) \$20,000 Revenue (b) \$10,000 \$0 7 3,000 \$1.99 10% 1 0 2 0 3 0 4 0 5 0 6 0 7 0 \$0 \$0 \$0 \$0 \$0 \$0 \$0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Month 8 3,000 \$1.99 \$5,970 9 3,300 \$1.99 \$6,567 10 3,630 \$1.99 \$7,224 11 3,993 \$1.99 \$7,946 12 4,392 \$1.99 \$8,741 13 4,832 \$1.99 \$9,615 ...
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