How do you calculate the stock price for both scenarios? 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. Ms. Firewater asked two questions immediately. First, what should she assume about investment and growth? Mr. Breezeway suggested two valuations, one assuming more rapid expansion (as in the top panel of Table 3.8) and another just projecting past growth (as in the bottom panel of Table 3.8). Second, what rate of return should she use? Mr. Breezeway said that 15 percent, Prairie Home?s usual return on book equity, sounded right to him, but he referred her to an article in the Journal of Finance indicating that investors in rural supermarket chains, with risks similar to Prairie Home Stores, expected to earn about 11 percent on average. Rapid-Growth Scenario 1 2 3 4 5 6 Book value, start of year 80 92 105.8 121.7 139.9 146.9 Earnings 12 13.8 15.9 18.3 21 22 Dividends 0 0 0 0 14 14.7 Retained Earnings 12 13.8 15.9 18.3 7 7.4 Book value, end of year 92 105.8 121.7 140 146.9 154.3 Constant-Growth Scenario 1 2 3 4 5 6 Book value, start of year 80 84 88.2 92.6 97.2 102.1 Earnings 12 12.6 13.2 13.9 14.6 15.3 Dividends 8 8.4 8.8 9.3 9.7 10.2 Retained Earnings 4 4.2 4.4 4.6 4.9 5.1 Book value, end of year 84 88.2 92.6 97.2 102.1 107.2 Notes: 1. Both panels assume earnings equal to 15 percent of start-of-year book value. This profitability rate is constant. 2. The top panel assumes all earnings are reinvested from 2005 to 2009. In 2010 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. Solution Valuation based on constant growth scenario Growth Rate = Return on Equity x Plowback ratio = 15% x 1/3 = 5% Value of the equity =DIVx(1+g)/ (r-g) =$10.2 million x (1+0.05)/(15%- 5%) =$10.71 million/ 10% = 107.10 million Value per share = Value of the equity / No. of shares Common Shares Outstanding = = $107.10 million /400,000 = $267.75 per share Valuation based on rapid growth scenario Plowback ratio is 1 as the entire income is reinvested for the next five years. Value of equity = DIV 2010 x (1+g) / r-g (Assume same as in constant growth scenario) = $14.7 million x (1+.05) / (15%- 5% ) = 154.35 milion Value per share = $154.35 / 400,000 = $385.875 Rapid growth scenario is preferable as the value of per share is greater in rapid growth scenario..

1. How do you calculate the stock price for both scenarios? 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. Ms. Firewater asked two questions immediately. First, what should
she assume about investment and growth? Mr. Breezeway suggested two valuations, one
assuming more rapid expansion (as in the top panel of Table 3.8) and another just projecting past
growth (as in the bottom panel of Table 3.8). Second, what rate of return should she use? Mr.
Breezeway said that 15 percent, Prairie Home?s usual return on book equity, sounded right to
him, but he referred her to an article in the Journal of Finance indicating that investors in rural
supermarket chains, with risks similar to Prairie Home Stores, expected to earn about 11 percent
on average. Rapid-Growth Scenario 1 2 3
4 5 6 Book value, start of year 80 92 105.8 121.7 139.9 146.9 Earnings
12 13.8 15.9 18.3 21 22 Dividends 0 0 0 0 14
14.7 Retained Earnings 12 13.8 15.9 18.3 7 7.4 Book value, end of year
92 105.8 121.7 140 146.9 154.3 Constant-Growth Scenario
1 2 3 4 5 6 Book value, start of year 80 84 88.2
92.6 97.2 102.1 Earnings 12 12.6 13.2 13.9 14.6 15.3 Dividends
8 8.4 8.8 9.3 9.7 10.2 Retained Earnings 4 4.2 4.4 4.6
4.9 5.1 Book value, end of year 84 88.2 92.6 97.2 102.1 107.2
Notes: 1. Both panels assume earnings equal to 15 percent of start-of-year
book value. This profitability rate is constant. 2. The top panel assumes all earnings are
reinvested from 2005 to 2009. In 2010 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.
Solution
Valuation based on constant growth scenario
Growth Rate = Return on Equity x Plowback ratio = 15% x 1/3 = 5%
Value of the equity =DIVx(1+g)/ (r-g) =$10.2 million x (1+0.05)/(15%- 5%) =$10.71 million/
10%
= 107.10 million
Value per share = Value of the equity / No. of shares Common Shares Outstanding =
= $107.10 million /400,000
= $267.75 per share
Valuation based on rapid growth scenario

2. Plowback ratio is 1 as the entire income is reinvested for the next five years.
Value of equity = DIV 2010 x (1+g) / r-g (Assume same as in constant growth scenario)
= $14.7 million x (1+.05) / (15%- 5% )
= 154.35 milion
Value per share = $154.35 / 400,000
= $385.875
Rapid growth scenario is preferable as the value of per share is greater in rapid growth scenario.