Final answer:
The projected increase in retained earnings for Garza & Gray Realty next year is $2,746.61. This is calculated by adjusting for a 3 percent decrease in sales and increasing the dividend payout ratio by 2.5 percent while keeping the net profit margin constant.
Step-by-step explanation:
To calculate the projected increase in retained earnings for next year for Garza & Gray Realty, we must first determine the projected sales and net income. With a 3 percent decrease in sales from $68,900, the projected sales for next year would be $68,900 - (0.03 × $68,900) = $66,833. Net income is a result of the net profit margin, which remains constant. If we retain the same net profit margin, the projected net income will be proportional to the projected sales. Therefore, the projected net income is $4,900 / $68,900 × $66,833 = $4,755.61 (approximated to two decimal places).
Next, we consider the dividend payout ratio. An increase of 2.5 percent on the current dividends means the new dividends will be $1,960 + (0.025 × $1,960) = $2,009. Retained earnings are the portion of net income that is not paid out as dividends. So the projected retained earnings for next year would be the projected net income minus the new dividend payout, which is $4,755.61 - $2,009 = $2,746.61.
Therefore, the projected increase in retained earnings for next year is $2,746.61.