The equipment reported on the balance sheet as of the purchase date is closest to:

A) $45,000.
B) $38,664.
C) $33,664.
D) $40,000.

To calculate the present value of the equipment, we need to find the present value of the future payments plus the initial cash payment.

Step 1: Find the present value of $5,000 due every 6 months for 4 years at Libby's incremental borrowing rate of 8%.

Using the PV of an annuity due table, we can find the present value factor for an annuity due of $1 per period for 8 periods at 8%.

PV Factor = 4.31213

Therefore, the present value of $5,000 due every 6 months for 4 years is:

PV of Annuity = $5,000 x 4.31213 = $21,560.65

Step 2: Find the present value of the initial cash payment of $5,000.

Using the PV of $1 table, we can find the present value factor for $1 due in 0.5 years at 8%.

PV Factor = 0.96154

Therefore, the present value of the initial cash payment of $5,000 is:

PV of Initial Payment = $5,000 x 0.96154 = $4,807.70

Step 3: Add the present value of the future payments to the present value of the initial cash payment.

Present Value of Equipment = PV of Annuity + PV of Initial Payment
Present Value of Equipment = $21,560.65 + $4,807.70
Present Value of Equipment = $26,368.35

Therefore, the equipment reported on the balance sheet as of the purchase date is closest to $38,664 (rounded to the nearest dollar), which is answer choice B.