On May 31, 2011, James Logan Company had a cash balance per books of $6,781.50. The bank statement from Farmers State Bank on that date showed a balance of $6,404.60. A comparison of the statement with the cash account revealed the following facts.

The statement included a debit memo of $40 for the printing of additional company checks.
Cash sales of $836.15 on May 12 were deposited in the bank. The cash receipts journal entry and the deposit slip were incorrectly made for $886.15. The bank credited Logan Company for the correct amount.
Outstanding checks at May 31 totaled $576.25. Deposits in transit were $1,916.15.
On May 18, the company issued check No. 1181 for $685 to Barry Trest, on account. The check, which cleared the bank in May, was incorrectly journalized and posted by Logan Company for $658.
A $2,500 note receivable was collected by the bank for Logan Company on May 31 plus $80 interest. The bank charged a collection fee of $20. No interest has been accrued on the note.
Included with the cancelled checks was a check issued by Bridgetown Company to Tom Lujak for $800 that was incorrectly charged to Logan Company by the bank.
On May 31, the bank statement showed an NSF charge of $680 for a check issued by Sandy Grifton, a customer, to Logan Company on account.

a. Prepare the bank reconciliation at May 31, 2011
b. Prepare the necessary adjusting entries for Logan Company at May 31, 2011

a. To prepare the bank reconciliation at May 31, 2011, we need to compare the cash balance per books to the cash balance per the bank statement and make adjustments for any differences. Let's go through the given facts and calculate the adjusted balances.

1. Cash balance per books: $6,781.50
2. Cash balance per bank statement: $6,404.60

Now let's analyze the differences:
- Debit memo: The bank statement includes a debit memo of $40 for the printing of additional company checks. This means the bank reduced Logan Company's cash balance by $40.

Adjusted cash balance per bank statement: $6,404.60 - $40 = $6,364.60

- Incorrectly recorded deposit: The cash receipts journal entry and the deposit slip were incorrectly made for $886.15, but the bank credited Logan Company for the correct amount, which is $836.15. This means there is an overstatement of $50.

Adjusted cash balance per books: $6,781.50 - $50 = $6,731.50

- Outstanding checks: There are outstanding checks at May 31 totaling $576.25. These checks have been issued but have not yet cleared the bank, so we need to deduct this amount from the adjusted cash balance per bank statement.

Adjusted cash balance per bank statement: $6,364.60 - $576.25 = $5,788.35

- Deposits in transit: There are deposits in transit of $1,916.15. These are deposits made by Logan Company but have not yet been credited by the bank, so we need to add this amount to the adjusted cash balance per bank statement.

Adjusted cash balance per bank statement: $5,788.35 + $1,916.15 = $7,704.50

- Incorrectly recorded check: Check No. 1181 for $685 to Barry Trest was incorrectly recorded as $658 by Logan Company. This means there is an understatement of $27.

Adjusted cash balance per books: $6,731.50 + $27 = $6,758.50

- Collection of note receivable: The bank collected a $2,500 note receivable for Logan Company on May 31, plus $80 interest and charged a $20 collection fee. This means the bank increased Logan Company's cash balance by $2,500 + $80 - $20 = $2,560.

Adjusted cash balance per bank statement: $7,704.50 + $2,560 = $10,264.50

- Incorrectly charged check: The bank incorrectly charged Logan Company for a check issued by Bridgetown Company to Tom Lujak for $800. Since this is not Logan Company's transaction, we need to deduct $800 from the adjusted cash balance per bank statement.

Adjusted cash balance per bank statement: $10,264.50 - $800 = $9,464.50

- NSF charge: The bank charged a $680 NSF fee for a check issued by Sandy Grifton to Logan Company. This means the bank reduced Logan Company's cash balance by $680.

Adjusted cash balance per bank statement: $9,464.50 - $680 = $8,784.50

The final adjusted cash balances are:
Cash balance per books: $6,758.50
Cash balance per bank statement: $8,784.50

b. To prepare the necessary adjusting entries for Logan Company at May 31, 2011, we need to record any adjustments needed to bring the cash balances per books and the cash balances per the bank statement into agreement.

1. Adjusting entry for bank balance:
Debit: Cash (per bank) $2,026 (the difference between cash balance per bank statement and cash balance per books)
Credit: Adjustments to reconcile cash $2,026

2. Adjusting entry for book balance:
Debit: Adjustments to reconcile cash $2,026
Credit: Cash (per books) $2,026

These adjusting entries will bring the cash balances per books and the cash balances per the bank statement into agreement.

Note: Depending on the specific accounts used by Logan Company, it is essential to adjust the appropriate accounts to reflect the reconciled cash balances. This may include accounts such as Accounts Receivable, Discounts/Allowances, or Bank Fees, among others.