4. Carrington and Genevieve are unsure how to interpret the priceearnings ratio. After some head scratching, they have come up with the following expression for the price-earnings ratio:

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 shares and the company’s ROE?

Sydney Heating Company was founded nine years ago by brother and sister Carrington and Genevieve Sydney. The company manufactures and installs commercial heating, ventilation and cooling (HVAC) units. Sydney Heating 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. In the event either wished to sell shares, 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 information about their main competitors in the table below.
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. The ROE for Expert HVAC is based on profit for the year excluding the write-off.

Transcribed Image Text:

Po 1-b E R- (ROE b)