w3-homework
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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:
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.
Questions:
1. Assuming the company continues its current growth rate, what is the value per share of the company’s stock?
The total dividend paid by the company is 126,000.
Total earnings are:100,000x4.54=454,000
Therefore, payout ratio is 126,000/454,000=0.28
Retention ratio=1-0.28=0.72
It is easy to calculate g=ROExb=0.25x0.72=0.18
D0=63,000/50,000=1.26
Therefore, P0= D1/(R-g)=1.26(1.2)/(0.2-0.18)=75.6
In conclusion, the value per share of the company’s stock is 75.6 dollars
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 equired 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?
Since the Expert HCAC has a write-off to affect the real answer, we need to recalculate it. Industry EPS=(0.79+1.38+1.06)/3=1.08
Industry payout ratio=0.4/1.08=0.37
Industry retention ratio=1-0.37=0.63
Therefore, g=0.1233x0.63=0.078
The company will continue to grow in five years
So, D1=1.26(1.18)=1.4868
D2=1.4868(1.18)=1.754424
D3=1.754424(1.18)=2.07
D4=2.07(1.18)=2.44286
D5=2.44286(1.18)=2.8825
D6=2.8825(1.18)=3.4
The stock price in year 5 with the industry required return will be:
Stock value in year 5 =3.4/(0.1167-0.078)=87.85
It is easy to calculate the total value today is：53 dollars
3. What is the industry average price-earnings ratio? What is the price-earnings ratio for Ragan, Inc.? Is this the relationship you would expect between the two ratios? Why?
industry average price-earnings ratio=0.51/13.09=0.0389
price-earnings ratio for Ragan, Inc.=4.54/53=0.0856
the relationship between the two ratios is：Positive correlation which means that with the rise of industry average price-earnings ratio, the price-earnings ratio for Ragan, Inc. will rise. Because industry average measures the average level of the Arctic Cooling, Inc , National Heating & Cooling and Expert HVAC Corp. If industry average rise, means the average level of the Arctic Cooling, Inc , National Heating & Cooling and Expert HVAC Corp has risen, therefore, price-earnings ratio for Ragan, Inc will rise for its business are the same to the three subjects above.
4. Carrington and Genevieve are unsure how to interpret the price-earnings ratio. After some head scratching, they’ve come up with the following expression for the price-earnings ratio:
Beginning with the constant dividend growth model, verify this result. What does this expression imply about the relationship between the dividend payout ratio, the required return on the stock, and the company’s ROE?
As we known b is Retention ratio which equals 1- payout ratio
Therefore, P/E= D/(R-g)E=1-b/R-(ROExb)
D/E=(R-g)(1-b)/R-(ROExb)
R=(DxROE+Dxb-Exg-Exgxb)/(D-E+b)
So,the company’s ROE and R has positive correlation.
5. Assume the company’s growth rate slows to the industry average in five years. What future return on equity does this imply, assuming a constant payout ratio?
It implies that the value of the stock price of Ragan, Inc will get lower because of the lower growth rate. We can get the answer with the formula we have used above.
6.After discussing the stock value with Josh, Carrington and Genevieve agree that they would
like to increase the value of the company stock. Like many small business owners, they want to retain control of the company, but they do not want to sell stock to outside investors.
They also feel that the company’s debt is at a manageable level and do not want to borrow more money. How can they increase the price of the stock? Are there any conditions under which this strategy would not increase the stock price?
We can increase the price of the stock by issuing more dividends. As we know, we calculate the stock price by the formula D/(R-g).But, when the growth rate of Ragan, Inc get lower, this strategy would not increase the stock price. We can also get the answer with the formula above ,and if dividends are not paid in cash such as shares, this strategy would also not increase the stock price.
唐庆飞11210690142 金融工程管理