Final answer:
The decrease in retained earnings due to the dividends declared by Ivanhoe Company is $4,138,500. This accounts for a 13% stock dividend valued at $3,788,200 and a recalculated cash dividend of $350,300 after accounting for the new share count post-stock dividend.
Step-by-step explanation:
To determine the decrease in retained earnings due to the dividends declared by Ivanhoe Company, we must first assess both the stock and cash dividends. First, for the 13% stock dividend, since the market price per share is $47, the value of the stock dividend is 0.13 × 620,000 × $47 = $3,788,200. This amount is transferred from retained earnings to paid-in capital and does not affect cash. Second, for the cash dividend of $0.50 per share, the total cash dividend is 620,000 × $0.50 = $310,000. This is the amount actually paid out to shareholders, and it will reduce both cash and retained earnings. Therefore, the total decrease in retained earnings is the sum of the amounts related to the stock dividend and the cash dividend, which is $3,788,200 for the stock dividend plus $310,000 for the cash dividend, equaling $4,098,200.
However, it should be noted that after the stock dividend the share count will increase. The new share count will be 620,000 + (0.13 × 620,000) = 700,600 shares. The cash dividend should be recalculated based on the new share count, which results in 700,600 × $0.50 = $350,300. The revised total decrease in retained earnings should thus be $3,788,200 + $350,300 = $4,138,500.