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 Corporations 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, Siddle Inc. had an EPS of $3.75 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. COMPETITORS

	EPS	DPS	STOCK PRICE	ROE	R
ARCTIC COOLING INC.	$1.3	$0.15	$25.34	9%	10%
NATIONAL HEATING&COOLING	$1.95	$0.22	$29.85	11%	13%
EXPERT HVAC CORP.	$-0.37	$0.12	$22.13	10%	12%
INDUSTRY AVERAGE	$0.96	$0.16	$25.77	10%	11.67%

Questions

4. Wendy and Peter are unsure how to interpret the P/E ratio. After some head scratching, theyve come up with the following expression for the P/E ratio: P 0/ E 1 = (1 b) / R (ROE b) 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 companys ROE?