Need help with number $3!!!$

Larissa has been talking with the company's directors about the future of East Coast Yachts.

To this point, the company has used outside suppliers for various key components of the

company's yachts, including engines. Larissa has decided that East Coast Yachts should

consider the purchase of an engine manufacturer to allow East Coast Yachts to better integrate

its supply chain and get more control over engine features. After investigating several possible

companies, Larissa feels that the purchase of Ragan Engines, Inc., is a possibility. She has

asked Dan Ervin to analyze Ragan's value.

Ragan Engines, Inc., was founded nine years ago by a brother and sister$-$Carrington and

Genevieve Ragan$-$and has remained a privately owned company. The company

manufactures marine engines for a variety of applications. Ragan has experienced rapid

growth because of a proprietary technology that increases the fuel efficiency of its engines with

very little sacrifice in performance. The company is equally owned by Carrington and

Genevieve. The original agreement between the siblings gave each $125,000$ shares of stock.

Larissa has asked Dan to determine a value per share of Ragan stock. To accomplish this,

Dan has gathered the following information about some of Ragan's competitors that are publicly

traded:

Nautilus Marine Engines' negative earnings per share $($EPS$)$ was the result of an accounting

write$-$off last year. Without the write$-$off, EPS for the company would have been $$1\mathrm{.}75.$ Last

year, Ragan had an EPS of $$4\mathrm{.}10$ and paid a dividend to$-$Carrington and Genevieve of

$$215,000$ each. The company also had a return on equity of $18$ percent. Larissa tells Dan that

a required return for Ragan of $13$ percent is appropriate.

Case Questions

Assuming the company continues its current growth rate, what is the stock price for the

company? $($Hint: To find firm value per share, you will need to estimate the following $($in

order$)$: The payout ratio, the retention rate $(=1-$ payout rate$),$ the growth rate $($g$)$; total

dividends paid next year $($D$1),$ and therefore total firm value today.$)$

Dan has examined the company's financial statements, as well as examining those of its

competitors. Although Ragan currently has a technological advantage, Dan's research

indicates that Ragan's competitors are investigating other methods to improve efficiency.

Given this, Dan believes that Ragan's technological advantage will last only for the next

five years. After that period, the company's growth will likely slow to the industry average.

Additionally, Dan believes that the required return the company uses is too low. He

believes the industry average required return is more appropriate. Under Dan's

assumptions, what is the estimated stock price? $($Hint$\text{'}$ to answer this question, you will

have to estimate or use the following $($in order$)$: the $($average$)$ industry growth rate $($g$),$

the $($average$)$ industry required return $($R$)$; the new stream of dividends to be paid, i$.$e$.$

under the revised assumptions$).$

What is the industry average price$-$earnings ratio? What is Ragan's price$-$earnings ratio?

Compare your estimates of the industry average PE ratio to Ragan's PE ratio estimates,

calculated from information you used in Q$1($original assumption$),$ and Q$2($revised

assumption$),$ respectively. Comment on any differences and explain why they may exist.