Stock Valuation at Siddle Inc.Siddle Inc. was founded nine years ago by brother and sister Wendy and Peter Siddle. The company manufactures and installs commercial heating, ventilation, and cooling $($HVAC$)$ units. Siddle Inc. has experienced rapid growth because of a proprietary technology that increases the energy efficiency of its units. The company is equally owned by Wendy and Peter. 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 information about their main competitors, summarized in the table below.In addition, they found that 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 $$1\mathrm{.}10.$Last year, Siddle Inc. had an EPS of $$3\mathrm{.}75$ and paid a dividend to Wendy and Peter of $$48,000$ each. The company also had a return on equity of $17\%.$ The siblings believe that $14\%$ is an appropriate required return for the company.Siddle Inc. CompetitorsEPSDPSStock PriceROEArctic Cooling Inc.$$1\mathrm{.}30$$$0\mathrm{.}15$$$25\mathrm{.}349\%10\%$National Heating & Cooling$1\mathrm{.}950\mathrm{.}2229\mathrm{.}8513$Expert HVAC Corp.$=0370\mathrm{.}1222\mathrm{.}131012$Industry Average$$0\mathrm{.}96$SO$\mathrm{.}16$$$25\mathrm{.}7710\mathrm{.}00\%11\mathrm{.}67\%$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, Wendy and Peter have hired David Boon as a consultant. David was previously an equity analyst and covered the HVAC industry. David has examined the company's financial statements, as well as its competitors. Although Siddle Inc. currently has a technological advantage, his research indicates that other companies are investigating methods to improve efficiency. Given this, David 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, David 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?$3.$ What is the industry average P$/$E ratio? What is the P$/$E ratio for Siddle Inc.? Is this the relationship you would expect between the two ratios? Why?$4.$ Wendy and Peter are unsure how to interpret the P$/$E ratio. After some head scratching, they've come up with the following expression for the P$/$E ratio:$1-$ b$2=$R$-$ROEXBeginning 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?$5.$ 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?Page $2946.$ After discussing the stock value with David, Wendy and Peter 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?