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:

Blue Ribbon Motors Corp :

EPS: $$1\mathrm{.}13$

DPS: $$\mathrm{.}35$

Stock Price: $$18\mathrm{.}25$

ROE: $11\mathrm{.}00\%$

R: $14\mathrm{.}00\%$

Bon Voyage Marine Inc. :

EPS: $$1\mathrm{.}41$

DPS: $$\mathrm{.}43$

Stock Price: $$15\mathrm{.}31$

ROE: $14\mathrm{.}00\%$

R: $17\mathrm{.}00\%$

Nautilus Marine Engines:

EPS: $$-\mathrm{.}23$

DPS: $$\mathrm{.}61$

Stock Price: $$28\mathrm{.}72$

ROE: N$/$A

R: $13\mathrm{.}00\%$

Industry Average:

EPS: $$\mathrm{.}77$

DPS: $$\mathrm{.}46$

Stock Price: $$20\mathrm{.}76$

ROE: $12\mathrm{.}59\%$

R: $14\mathrm{.}67\%$

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.

$1.$ 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.$)$

EPS $=$ $$4\mathrm{.}10$

Dividends $($each$)$ $$215,000$

$$125,000$ shares of stock to each sibling

Total no: of outstanding shares$=$ $$125,000$ X $2=$ $$250,000$

Required Return $13\%$

Return on Equity $18\%$

Industry Average for R: $14\mathrm{.}67\%$

D$=$Total dividends$/$ Total Number of Shares Outstanding

$($$$215,000$ X $2)/$ $$250,000$

$$430,000/$ $$250,000$

D $=$ $$1\mathrm{.}72$

Payout Ratio:

Retention Rate $=1-($total dividends$/$ net income$)$

$1-($$$430,000/($$$4\mathrm{.}10$ x $$250,000))$

$1-($$$430,000/$ $$1,025,000)$

$1-0\mathrm{.}41951$

Retention Rate $=0\mathrm{.}5804$ or $58\%$

Growth Rate $($if Ragan maintains their current growth rate$)$

Growth Rate $=$ Return on Equity x Retention rate

$0\mathrm{.}18$ X $0\mathrm{.}58$

Growth Rate $($G$)=0\mathrm{.}10$ or $10\%$

Total equity value $=$ D$1/($R$-$G$)$

D$1=$ D$0(1+$ G$)$

$$430,000(1+0\mathrm{.}10)=$ $$473,000$

$$473,000/(\mathrm{.}01467-\mathrm{.}10)$

$$473,000/0\mathrm{.}0467$

$$10,128,479\mathrm{.}70$

Total value$/$number of share $=$ $$10,128,479\mathrm{.}70/$ $$250,000$

$$40\mathrm{.}51=$ stock price

$2.$ 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: 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$).$

Industry average EPS is $$\mathrm{.}77($recalculate for write off$)=$ $$1\mathrm{.}13+$ $$1\mathrm{.}41+1\mathrm{.}75/3=$ $$1\mathrm{.}43$

Industry average dividend is $$\mathrm{.}46$

Payout Ratio of industry $=$ DPS $/$ EPS

$0\mathrm{.}46/1\mathrm{.}43=0\mathrm{.}2898$

Retention Ratio of industry $=1-0\mathrm{.}2898=0\mathrm{.}7102$

g $=$ ROE x Retention Ratio

$12\mathrm{.}50\%$ X $0\mathrm{.}7102=0\mathrm{.}8877$

Values for the next six years:

D$1=$ $$430,000$ X $1\mathrm{.}1=$ $$473,000$

D$2=$ $$473,000$ X $1\mathrm{.}1=$ $$520,300$

D$3=$ $$520,300$ X $1\mathrm{.}1=$ $$572,330$

D$4=$ $$572,330$ X $1\mathrm{.}1=$ $$629,563$

D$5=$ $$629,563$ X $1\mathrm{.}1=$ $$692,519\mathrm{.}3$

In year $6$ we use the industry average for R $(1+14\mathrm{.}67\%)$

D$6=$ $$692,519\mathrm{.}3$ X $1\mathrm{.}14=$ $$789,472$

Stock value in $5$th year $=$

$$789,472/0\mathrm{.}15-(1-1\mathrm{.}14)=$ $$789,472/0\mathrm{.}29$

$$2,722\mathrm{.}317\mathrm{.}24$

Today$-$Value of Stock $=$

Estimated average industry growth rate $($g$)$

average industry required return $$

the new stream of dividends to be paid

Estimate Stock P