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Libby Company purchased equipment by paying $6,700 cash on the purchase date and agreed to pay $6,700 every six months during the next four years. The first payment is due six months after the purchase date. Libby's incremental borrowing rate is 6%. The equipment reported on the balance sheet as of the purchase date is closest to _________?

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Answer:

The answer is $53,732.

Explanation:

The value of the equipment reported on Libby Company's balance sheet is equal to:

Cash payment at purchase + Present value of 8 equal semiannual payment, $6,700 each discounted at 3% ( because semiannual payment is made for 4 years so we have 2 x4 = 8 payments; and annual borrowing rate is 6% so we have discount rate = 6% /2 = 3%).

with:

Cash payment at purchase = $6,700;

Present value of 8 equal semiannual payment, $6,700 each discounted at 3% = (6,700/3%) x ( 1 - 1.03^(-8) ) = $47,032 ( that is, apply the formula to find present value of annuity).

we have:

The value of the equipment reported on Libby Company's balance sheet = 6,700 + 47,032 = $53,732.

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