On question 2 after the industry growth, where does D1, D2, D3, D4, D5, and P5 come from?

Mini 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 in 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. The get started, they have gathered the following information about their main competitors:

RaganIncorporation, Competitors

EPS ($)

DPS ($)

Stock Price ($)

ROE (%)

R (%)

Arctic Cooling, Inc.

0.79

0.20

14.18

10.00

10.00

National Heating & Cooling

1.38

0.62

11.87

13.00

13.00

Expert HVAC Corp.

-0.48

0.38

13.21

14.00

12.00

Industry Average

0.56

0.40

13.09

12.33

11.67

Expert HVAC Corporation's negative earnings 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 $63,000 each. The company also had a return on equity of 25%. The siblings believe that 20% is an appropriate required return for the company.

Question 1

Assuming the company continues its current growth rate, what is the value per share of the company's stock?

Total of shares outstanding = 50,000units 2 (Carrington & Genevieve)

= 100,000units

Total dividend paid by the company = $63,000 2 (Carrington & Genevieve)

= $126,000

Earnings per share =

4.54 =

Net income = 4.54 100,000

Net income = $454,000

Dividend payout ratio =

=

= 0.28

Retention ratio = 1 - Dividend payout ratio

= 1 - 0.28

= 0.72

Growth (g) = Return on equity (ROE) Retention ratio

= 0.25 0.72

= 0.18 or 18%

Value per share (V0) =

=

= $74.34

Therefore the value per share of the company's stock is $74.34.

Question 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 examining 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 this 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 too high. He believes the industry average required return is more appropriate. Under this growth rate assumption, what is your estimate of the stock price?

Industry average earning per share (EPS) =

= $1.08

Industry average payout ratio =

=

= 0.37

Industry retention ratio = 1 - Industry payout ratio

= 1 - 0.37

= 0.63

Industry growth (g) = Industry average return on equity Industry retention ratio

= 0.1233 0.63

= 0.078 or 7.8%

Stock Price, (P0) = D1/(1+R)2 + D2/(1+R)2 + D3/(1+R)2 +D4/(1+R)2 + D5/(1+R)2 + P5/(1+R)2

= 1.49/(1.1167)2 + 1.75/(1.1167)2 + 2.07/(1.1167)2 + 2.44/(1.1167)2 + 3.4/(1.1167)2 + 87.85/(1.1167)2

= $58.34

Thus, estimate stock price is $58.34.