Terence Breezeway, the CEO of Prairie Home Stores, wondered what retirement would be like. It was almost 20 years to the day since hisuncle Jacob Breezeway, Prairie Home's founder, had asked him to take responsibility for managing the company. Now it was time to spendmore time riding and fishing on the cld Lazy Beta Ranch.U'nder Mr. Breezeway's leadership, Prairie Home had grown slowty but steadily and was solidly profitable. (E Table 7.6 shows earnings.dividends, and book asset values for the last 5 years.) Most of the company's supermarkets had been modernized, and its brand name waswell known.Table 7.6 Financial data for Prairie Home Stores, 2019-2023 (figures in millions)20192020202120222023Book value, start of year$62.7$73.9$66.1$69.0$76.5Earnings9.79.511.811.011.2Dividends6.36.66.97.47.7Retained earnings3.42.94.92.63.5Book value, end of year66.169.073.976.580.0Note1. Prairie Home Stores has 400,000 common shar2. The company's poley ia to pury cash dividends equal to 10s of start-af-year boak valunMr. Breezeway was proud of this record, although he wished that Prairie Home could have grown more rapidly. He had passed up severalopportunities to build new stores in adjacent counties. Prairie Home was still just a family company. Its common stock was distributedamong 15 grandchildren and nephews of Jacob Breezeway, most of whom had come to depend on generous regular dividends. Thecommitment 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, theBreezeway descendants who needed (or just wanted) more cash to spend could sell off part of their holdings. Others with moreinterest in the business could hold on to their shares and be rewarded by higher future earnings and stock prices.Page 237But if Prairie Home did go public, what should its shares sell for? Mr. Breezeway worried that shares would be sold, either by Breezewayfamily members or by the company itself, at too low a price. One relative was about to accept a private ofer for $200, the current book valueper 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 financialprojection (shown in the top panel of e Table 7.7) called for growth in earnings of more than 100% by 2030. Uafortunately, this plan wouldrequire reinvestment of all of Prairie Home's earnings from 2024-2027. After that, the company could resume its normal dividend payoutand growth rate. Mr. Breezeway believed this plan was feasible. Table 77 Financial projections for Prairie Home Stores, 2024-2029 (figures in millions)202420252026202720282029Rapid-Growth ScenarioBook value, start of year$80$ 92.0$105.8$121.7$139.9$146.9Earnings1213.815.918.321.022.0Dividends14.014.7Retained earnings1213.815.918.37.07.4Book value, end of year92105.8121.7139.9146.9154.3Constant-Growth ScenarioBook value, start of year$80$ 84.0$ 8.2$ 92.6$ 97.2$102.1Earnings1212.613.213.914.615.3Dividends8.48.89.39.710.2Retained earnings44.24.44.64.95.1Book value, end of year8488.292.697.2102.1107.2Note1. Both panes assume eamings equal to 15% of start-of-year book value. This profitability rate is constant.2. The top panel assumes all earnings are reinvested from 2024-2027. In 2028 and later years, two-thirds of earnings are pald out as dividends and one-thirdreinvested.3. The bottom panel assumes two-thirds of earnings are pald out as dividends In all years.4. Columns may not add up becnuse of rounding.He was determined to step aside for the next generation of top management. But before retiring, he had to decide whsther to recommendthat 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'sSalcon, where Francine Firewater, the company's CFO, was having her usual steakand-beans breakfast. He asked Ma. Firewater to prepare aformal report to Prairie Home stockholders, valuing the company on the assumption that its shares were publicly traded.Ms. Firewater asked two questions immediately. First, what should she assume about investment and growth? Mr. Breezeway suggested twovaluations, one assuming more rapid expansion (as in the top panel of Table 7.7) and another just projecting past growth (as in thebottom panel of4 Table 7.7).Second, what rate of return should she use? Mr. Breezeway said that 15%, Prairie Home's usual return on book equity, sounded right to him,but he referred her to an article in the Jounal of Finanos indicating that investors in rural supermarket chains, with risks similar to PrairieHome Stores, expected to earn about 11% on average.

Question

Terence Breezeway, the CEO of Prairie Home Stores, wondered what retirement would be like. It was almost 20 years to the day since hisuncle Jacob Breezeway, Prairie Home's founder, had asked him to take responsibility for managing the company. Now it was time to spendmore time riding and fishing on the cld Lazy Beta Ranch.U'nder Mr. Breezeway's leadership, Prairie Home had grown slowty but steadily and was solidly profitable. (E Table 7.6 shows earnings.dividends, and book asset values for the last 5 years.) Most of the company's supermarkets had been modernized, and its brand name waswell known.Table 7.6 Financial data for Prairie Home Stores, 2019-2023 (figures in millions)20192020202120222023Book value, start of year$62.7$73.9$66.1$69.0$76.5Earnings9.79.511.811.011.2Dividends6.36.66.97.47.7Retained earnings3.42.94.92.63.5Book value, end of year66.169.073.976.580.0Note1. Prairie Home Stores has 400,000 common shar2. The company's poley ia to pury cash dividends equal to 10s of start-af-year boak valunMr. Breezeway was proud of this record, although he wished that Prairie Home could have grown more rapidly. He had passed up severalopportunities to build new stores in adjacent counties. Prairie Home was still just a family company. Its common stock was distributedamong 15 grandchildren and nephews of Jacob Breezeway, most of whom had come to depend on generous regular dividends. Thecommitment 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, theBreezeway descendants who needed (or just wanted) more cash to spend could sell off part of their holdings. Others with moreinterest in the business could hold on to their shares and be rewarded by higher future earnings and stock prices.Page 237But if Prairie Home did go public, what should its shares sell for? Mr. Breezeway worried that shares would be sold, either by Breezewayfamily members or by the company itself, at too low a price. One relative was about to accept a private ofer for $200, the current book valueper 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 financialprojection (shown in the top panel of e Table 7.7) called for growth in earnings of more than 100% by 2030. Uafortunately, this plan wouldrequire reinvestment of all of Prairie Home's earnings from 2024-2027. After that, the company could resume its normal dividend payoutand growth rate. Mr. Breezeway believed this plan was feasible. Table 77 Financial projections for Prairie Home Stores, 2024-2029 (figures in millions)202420252026202720282029Rapid-Growth ScenarioBook value, start of year$80$ 92.0$105.8$121.7$139.9$146.9Earnings1213.815.918.321.022.0Dividends14.014.7Retained earnings1213.815.918.37.07.4Book value, end of year92105.8121.7139.9146.9154.3Constant-Growth ScenarioBook value, start of year$80$ 84.0$ 8.2$ 92.6$ 97.2$102.1Earnings1212.613.213.914.615.3Dividends8.48.89.39.710.2Retained earnings44.24.44.64.95.1Book value, end of year8488.292.697.2102.1107.2Note1. Both panes assume eamings equal to 15% of start-of-year book value. This profitability rate is constant.2. The top panel assumes all earnings are reinvested from 2024-2027. In 2028 and later years, two-thirds of earnings are pald out as dividends and one-thirdreinvested.3. The bottom panel assumes two-thirds of earnings are pald out as dividends In all years.4. Columns may not add up becnuse of rounding.He was determined to step aside for the next generation of top management. But before retiring, he had to decide whsther to recommendthat Prairie Home Stores &#34;go public&#34;-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'sSalcon, where Francine Firewater, the company's CFO, was having her usual steakand-beans breakfast. He asked Ma. Firewater to prepare aformal report to Prairie Home stockholders, valuing the company on the assumption that its shares were publicly traded.Ms. Firewater asked two questions immediately. First, what should she assume about investment and growth? Mr. Breezeway suggested twovaluations, one assuming more rapid expansion (as in the top panel of Table 7.7) and another just projecting past growth (as in thebottom panel of4 Table 7.7).Second, what rate of return should she use? Mr. Breezeway said that 15%, Prairie Home's usual return on book equity, sounded right to him,but he referred her to an article in the Jounal of Finanos indicating that investors in rural supermarket chains, with risks similar to PrairieHome Stores, expected to earn about 11% on average.

Accepted Answer

Valuation of the company:

Rapid Growth Scenario

There are several methods that can be used to…