1) Which rate of return should be used to discount the future dividends of Prairie Home Stores? Justify your answer. 2) Calculate the sustainable growth rate based on both the rapid growth scenario and the constant growth scenario in Table 7.7. 3) What is the value per share based on the constant growth scenario? Show your calculations. 4) What is the value per share based on the rapid growth scenario? Show your calculations. TABLE 7.6 Financial data for Prairie Home Stores, 2022-2026 (figures in millions) Book value, start of year Earnings Dividends Retained earnings Book value, end of year Notes: 2022 $62.7 9.7 6.3 3.4 66.1 1. Prairie Home Stores has 400,000 common shares. 2. The company's policy is to pay cash dividends equal to 10% of start-of-year book value. 2023 $66.1 9.5 6.6 2.9 69.0 2024 $69.0 11.8 6.9 4.9 73.9 2025 $73.9 11.0 7.4 2.6 76.5 2026 $76.5 11.2 7.7 3.5 80.0 Mr. Breezeway was proud of this record, although he wished that Prairie Home could have grown more rapidly. He had passed up several opportunities to build new stores in adjacent counties. Prairie Home was still just a family company. Its common stock was distributed among 15 grandchildren and nephews of Jacob Breezeway, most of whom had come to depend on generous regular dividends. The commitment to high dividend payout 8 had reduced the earnings available for reinvestment and thereby constrained growth. Mr. Breezeway believed the time had come to take Prairie Home public. Once its shares were traded in the public market, the Page 233 Breezeway descendants who needed (or just wanted) more cash to spend could sell off part of their holdings. Others with more interest in the business could hold on to their shares and be rewarded by higher future earnings and stock prices. But if Prairie Home did go public, what should its shares sell for? Mr. Breezeway worried that shares would be sold, either by Breezeway family members or by the company itself, at too low a price. One relative was about to accept a private offer for $200, the current book value per share, but Mr. Breezeway had intervened and convinced the would-be seller to wait. Prairie Home's value depended not just on its current book value or earnings but on its future prospects, which were good. One financial projection (shown in the top panel of Table 7.7) called for growth in earnings of more than 100% by 2033. Unfortunately, this plan would require reinvestment of all of Prairie Home's earnings from 2027-2030. After that, the company could resume its normal dividend payout and growth rate. Mr. Breezeway believed this plan was feasible. TABLE 7.7 Financial projections for Prairie Home Stores, 2027-2032 (figures in millions) 2027 2029 Book value, start of year Earnings Dividends Retained earnings Book value, end of year Book value, start of year Earnings Dividends Retained earnings Book value, end of year Notes: $80 12 0 12 92 $80 12 8 4 84 2028 $ 92.0 13.8 0 13.8 105.8 $84.0 12.6 8.4 4.2 88.2 2030 Rapid-Growth Scenario $121.7 18.3 0 18.3 139.9 Constant-Growth Scenario $105.8 15.9 0 15.9 121.7 $88.2 13.2 8.8 4.4 92.6 $92.6 13.9 9.3 4.6 97.2 2031 $139.9 21.0 14.0 7.0 146.9 $ 97.2 14.6 9.7 4.9 102.1 2032 $146.9 22.0 14.7 7.4 154.3 $102.1 15.3 10.2 5.1 107.2 1. Both panels assume earnings equal to 15% of start-of-year book value. This profitability rate is constant. 2. The top panel assumes all earnings are reinvested from 2027-2032. In 2031 and later years, two-thirds of earnings are paid out as dividends and one-third reinvested. 3. The bottom panel assumes two-thirds of earnings are paid out as dividends in all years. 4. Columns may not add up because of rounding. He was determined to step aside for the next generation of top management. But before retiring, he had to decide whether to recommend that Prairie Home Stores "go public"-and before that decision he had to know what the company was worth. The next morning, he rode thoughtfully to work. He left his horse at the south corral and ambled down the dusty street to Mike Gordon's Saloon, where Francine Firewater, the company's CFO, was having her usual steak-and-beans breakfast. He asked Ms. Firewater to prepare a formal report to Prairie Home stockholders, valuing the company on the assumption that its shares were publicly traded. 1) Which rate of return should be used to discount the future dividends of Prairie Home Stores? Justify your answer. 2) Calculate the sustainable growth rate based on both the rapid growth scenario and the constant growth scenario in Table 7.7. 3) What is the value per share based on the constant growth scenario? Show your calculations. 4) What is the value per share based on the rapid growth scenario? Show your calculations. TABLE 7.6 Financial data for Prairie Home Stores, 2022-2026 (figures in millions) Book value, start of year Earnings Dividends Retained earnings Book value, end of year Notes: 2022 $62.7 9.7 6.3 3.4 66.1 1. Prairie Home Stores has 400,000 common shares. 2. The company's policy is to pay cash dividends equal to 10% of start-of-year book value. 2023 $66.1 9.5 6.6 2.9 69.0 2024 $69.0 11.8 6.9 4.9 73.9 2025 $73.9 11.0 7.4 2.6 76.5 2026 $76.5 11.2 7.7 3.5 80.0 Mr. Breezeway was proud of this record, although he wished that Prairie Home could have grown more rapidly. He had passed up several opportunities to build new stores in adjacent counties. Prairie Home was still just a family company. Its common stock was distributed among 15 grandchildren and nephews of Jacob Breezeway, most of whom had come to depend on generous regular dividends. The commitment to high dividend payout 8 had reduced the earnings available for reinvestment and thereby constrained growth. Mr. Breezeway believed the time had come to take Prairie Home public. Once its shares were traded in the public market, the Page 233 Breezeway descendants who needed (or just wanted) more cash to spend could sell off part of their holdings. Others with more interest in the business could hold on to their shares and be rewarded by higher future earnings and stock prices. But if Prairie Home did go public, what should its shares sell for? Mr. Breezeway worried that shares would be sold, either by Breezeway family members or by the company itself, at too low a price. One relative was about to accept a private offer for $200, the current book value per share, but Mr. Breezeway had intervened and convinced the would-be seller to wait. Prairie Home's value depended not just on its current book value or earnings but on its future prospects, which were good. One financial projection (shown in the top panel of Table 7.7) called for growth in earnings of more than 100% by 2033. Unfortunately, this plan would require reinvestment of all of Prairie Home's earnings from 2027-2030. After that, the company could resume its normal dividend payout and growth rate. Mr. Breezeway believed this plan was feasible. TABLE 7.7 Financial projections for Prairie Home Stores, 2027-2032 (figures in millions) 2027 2029 Book value, start of year Earnings Dividends Retained earnings Book value, end of year Book value, start of year Earnings Dividends Retained earnings Book value, end of year Notes: $80 12 0 12 92 $80 12 8 4 84 2028 $ 92.0 13.8 0 13.8 105.8 $84.0 12.6 8.4 4.2 88.2 2030 Rapid-Growth Scenario $121.7 18.3 0 18.3 139.9 Constant-Growth Scenario $105.8 15.9 0 15.9 121.7 $88.2 13.2 8.8 4.4 92.6 $92.6 13.9 9.3 4.6 97.2 2031 $139.9 21.0 14.0 7.0 146.9 $ 97.2 14.6 9.7 4.9 102.1 2032 $146.9 22.0 14.7 7.4 154.3 $102.1 15.3 10.2 5.1 107.2 1. Both panels assume earnings equal to 15% of start-of-year book value. This profitability rate is constant. 2. The top panel assumes all earnings are reinvested from 2027-2032. In 2031 and later years, two-thirds of earnings are paid out as dividends and one-third reinvested. 3. The bottom panel assumes two-thirds of earnings are paid out as dividends in all years. 4. Columns may not add up because of rounding. He was determined to step aside for the next generation of top management. But before retiring, he had to decide whether to recommend that Prairie Home Stores "go public"-and before that decision he had to know what the company was worth. The next morning, he rode thoughtfully to work. He left his horse at the south corral and ambled down the dusty street to Mike Gordon's Saloon, where Francine Firewater, the company's CFO, was having her usual steak-and-beans breakfast. He asked Ms. Firewater to prepare a formal report to Prairie Home stockholders, valuing the company on the assumption that its shares were publicly traded