Question

Stock valuation at Rayari, 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 of 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. To get started, they have gathered the following information about their main competitors: Ragan, Inc. - Competitors EPS Div. Stock Price ROE R Arctic Cooling, Inc. $1.30 $.16 $25.34 8.50% 10.00% National Heating & Cooling 1.95 23 29.85 10.50 13.00 Expert HVAC Corp. -.37 .14 22.13 9.78 12.00 Industry average $.96 $.18 $25.77 9.59% 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 $1.10. Last year, Ragan, Inc., had an EPS of $3.15 and paid a dividend to Carrington and Genevieve of $45,000 each. The company also had a return on equity of 17 percent. The siblings believe that 14 percent is an appropriate required return for the company.

Answer 1

1. Calculation of Value of Share of Ragan Inc.

As per Gordon's model (i.e. Growth model)

D1 P= ke-9

where P is Fair value of Share, D1 is dividend at the end of year 1, ke is cost of equity & g is growth rate

Or

DO(1 +9) P= 1 ke - 9

Ke =14% (given in question) , Put the value of D0 & g from working note 1 & 2 respectively.

P = 0.90(1 +.1214) .14 - .1214

P= 1.00926 .0186

P=54.26

Working notes:

1. Calculation of retention ratio:

Dividend paid last year = $45000 * 2 = $90000 ($45000 to each shareholder)

No. of shares outstanding = 50000 * 2 shares = 100000 shares (50000 shares each are held by both shareholders)

Dividend per share = Dividend paid/ No. of shares outstanding

DPS (d0) = $90000/100000

=$0.90 per share

EPS of last year = $3.15 per share (given in question)

Dividend payout ratio = DPS/ EPS

Dividend payout ratio = 0.90/3.15

=0.2857

Retention ratio = 1 - dividend payout ratio

Retention ratio = 1 - .2857

=0.7143

2. Calculation of current growth rate of the Ragan Inc.

Growth rate = b x r

where b is retention ratio & r is rate of return on investment

Growth rate = 0.7143 (note 2) * 0.17 (given in question i.e. return on equity)

Growth rate = .1214 or 12.14%

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