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Chapter Case . Stock Valuation at Ragan, Inc. Ragan, Inc., was founded nine years ago by brother and sister Carrington and Genevieve Ragan. The company manufactures and installs commercial heating, ventilation, and cooling (HVAC) units. Ragan, Inc. has experienced rapid growth because of a proprietary technology that increases the energy efficiency of its units. The company is equally owned by Carrington and Genevieve. The original partnership agreement between the siblings gave each 50,000 shares of stock. In the event either wished to sell stock, the shares first had to be offered to the other at a discounted price. Although neither sibling wants to sell, they have decided they should value their holdings in the company. To get started, they have gathered the following information about their main competitors: Ragan, Inc.—Competitors EPS Div. Stock Price ROE R Arctic Cooling, Inc. $87 $20 $15.18 10.00% 10.00% National Heating & Cooling. 138 62 1287 13.00 13.00 Expert HVAC Corp. = 38 1421 1400 1200 Industry average $60 $40 $14.09 12.33% 1.67% Expert HVAC Corporation's negative eamings per share were the result of an accounting write-off last year. Without the write-off, earnings per share for the company would have been $1.06. Last year, Ragan, Inc., had an EPS of $4.54 and paid a dividend to Carrington and Genevieve of $60,000 each. The company also had a return on equity of 16 percent. The siblings believe that 14 percent is an appropriate required return for the company. QUESTIONS 1. Assuming the company continues its current growth rate, what is the value per share of the company’s stock? 2. To verify their calculations, Carrington and Genevieve have hired Josh Schlessman as a consultant. Josh was previously an equity analyst and covered the HVAC industry. Josh has examined the company’s financial statements, as well as those of its competitors. Although Ragan, Inc. currently has a technological advantage, his research indicates that other companies are investigating methods to improve efficiency. Given this, Josh believes that the company’s technological advantage will last only for the next five years. After that period, the company’s growth will likely slow to the industry growth average. Additionally, Josh believes that the required return used by the company is 100 high. He believes the industry average required return is more appropriate. Under this growth rate assumption, what is your estimate of the stock price?

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Uploaded ImageChapter Case . Stock Valuation at Ragan, Inc. Ragan, Inc., was founded nine years ago by brother and sister Carrington and Genevieve Ragan. The company manufactures and installs commercial heating, ventilation, and cooling (HVAC) units. Ragan, Inc. has experienced rapid growth because of a proprietary technology that increases the energy efficiency of its units. The company is equally owned by Carrington and Genevieve. The original partnership agreement between the siblings gave each 50,000 shares of stock. In the event either wished to sell stock, the shares first had to be offered to the other at a discounted price. Although neither sibling wants to sell, they have decided they should value their holdings in the company. To get started, they have gathered the following information about their main competitors: Ragan, Inc.—Competitors EPS Div. Stock Price ROE R Arctic Cooling, Inc. $87 $20 $15.18 10.00% 10.00% National Heating & Cooling. 138 62 1287 13.00 13.00 Expert HVAC Corp. = 38 1421 1400 1200 Industry average $60 $40 $14.09 12.33% 1.67% Expert HVAC Corporation's negative eamings per share were the result of an accounting write-off last year. Without the write-off, earnings per share for the company would have been $1.06. Last year, Ragan, Inc., had an EPS of $4.54 and paid a dividend to Carrington and Genevieve of $60,000 each. The company also had a return on equity of 16 percent. The siblings believe that 14 percent is an appropriate required return for the company. QUESTIONS 1. Assuming the company continues its current growth rate, what is the value per share of the company’s stock? 2. To verify their calculations, Carrington and Genevieve have hired Josh Schlessman as a consultant. Josh was previously an equity analyst and covered the HVAC industry. Josh has examined the company’s financial statements, as well as those of its competitors. Although Ragan, Inc. currently has a technological advantage, his research indicates that other companies are investigating methods to improve efficiency. Given this, Josh believes that the company’s technological advantage will last only for the next five years. After that period, the company’s growth will likely slow to the industry growth average. Additionally, Josh believes that the required return used by the company is 100 high. He believes the industry average required return is more appropriate. Under this growth rate assumption, what is your estimate of the stock price?

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Asked by: Veera manikanta
Created at: 2025-08-03 20:49:21

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Let's break down the questions with the information provided: --- ## **Question 1: Value Per Share Using Current Growth Rate** ### **Given:** - **Last year EPS:** $4.54 - **Dividend paid:** $60,000 to each sibling, total $120,000 - **Shares outstanding:** 100,000 shares (50,000 each) - **ROE:** 16% - **Required return (R):** 14% - **Retained earnings = Earnings - Dividends** ### **Step 1: Calculate Dividend Per Share (D₀):** \[ \text{Dividend per share} = \frac{\text{Total dividends}}{\text{Shares outstanding}} = \frac{120,000}{100,000} = \$1.20 \] ### **Step 2: Calculate Growth Rate (g):** \[ \text{Retention ratio (b)} = 1 - \frac{\text{Dividends per share}}{\text{EPS}} = 1 - \frac{1.20}{4.54} = 1 - 0.264 = 0.736 \] \[ \text{Growth rate (g)} = \text{Retention ratio} \times \text{ROE} = 0.736 \times 0.16 = 0.1178 = 11.78\% \] ### **Step 3: Use Dividend Discount Model (Gordon Growth Model):** \[ P_0 = \frac{D_1}{R - g} \] Where: - \( D_1 = D_0 \times (1 + g) = 1.20 \times 1.1178 = \$1.341 \) - \( R = 14\% \) - \( g = 11.78\% \) \[ P_0 = \frac{1.341}{0.14 - 0.1178} = \frac{1.341}{0.0222} = \$60.41 \] **Value per share: \(\boxed{\$60.41}\)** --- ## **Question 2: Value Per Share Using Industry Growth Rate & Required Return** ### **Given:** - **Technological advantage lasts 5 years at current growth, then slows to industry average.** - **Industry average growth rate (g):** 5% (from the table). - **Industry required return (R):** 11.67% (from the table). ### **Step 1: Calculate Dividends for Next 5 Years** - \( D_0 = \$1.20 \) - Growth for next 5 years = 11.78% \[ D_1 = 1.20 \times 1.1178 = 1.341 \] \[ D_2 = 1.341 \times 1.1178 = 1.500 \] \[ D_3 = 1.500 \times 1.1178 = 1.677 \] \[ D_4 = 1.677 \times 1.1178 = 1.875 \] \[ D_5 = 1.875 \times 1.1178 = 2.097 \] ### **Step 2: Calculate Terminal Value at Year 5 (Start Growing at 5%)** \[ P_5 = \frac{D_6}{R - g_{industry}} \] \[ D_6 = D_5 \times (1 + g_{industry}) = 2.097 \times 1.05 = 2.202 \] \[ P_5 = \frac{2.202}{0.1167 - 0.05} = \frac{2.202}{0.0667} = 33.01 \] ### **Step 3: Discount Dividends & Terminal Value Back to Present** - Use \( R = 11.67\% \) \[ P_0 = \frac{D_1}{(1+R)^1} + \frac{D_2}{(1+R)^2} + \frac{D_3}{(1+R)^3} + \frac{D_4}{(1+R)^4} + \frac{D_5 + P_5}{(1+R)^5} \] Calculate each term: - \( (1+R) = 1.1167 \) - \( (1+R)^2 = 1.247 \) - \( (1+R)^3 = 1.393 \) - \( (1+R)^4 = 1.556 \) - \( (1+R)^5 = 1.738 \) \[ \frac{1.341}{1.1167} = 1.201 \] \[ \frac{1.500}{1.247} = 1.203 \] \[ \frac{1.677}{1.393} = 1.204 \] \[ \frac{1.875}{1.556} = 1.205 \] \[ \frac{2.097 + 33.01}{1.738} = \frac{35.107}{1.738} = 20.20 \] \[ P_0 = 1.201 + 1.203 + 1.204 + 1.205 + 20.20 = \$25.01 \] **Value per share under new assumptions: \(\boxed{\$25.01}\)** --- ## **Summary Table** | Scenario | Value per Share | |-------------------------------------|-----------------| | Current growth rate & required return | \$60.41 | | Industry growth rate & required return | \$25.01 | --- Let me know if you'd like to see the calculations in more detail!

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