Hawaiian Electric Industries Inc.’s earnings rose sharply in the second quarter, largely reflecting the timing of a rate increase at its main utility subsidiary that wasn’t in effect for the comparable quarter a year earlier.

HEI earned $38.8 million, or 40 cents a share in the April-to-June quarter, up from $27.1 million, or 28 cents a share during the same period a year earlier, the company reported today.

Hawaiian Electric Co. and affiliates Maui Electric Co. and Hawaii Electric Light Co. earned a combined $29.4 million in the second quarter, up 73 percent from the $17.0 million they earned during the second quarter of 2011.

Today’s financial report included results for American Savings Bank that HEI originally reported on Tuesday. American Savings earned $14.2 million in the second quarter compared with $15.2 million in the year-earlier period.