Libby Company purchased equipment by paying $5,000 cash on the purchase date and agreeing to pay $5,000 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 8%. 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.

$38,664

Explanation:

To solve this we shall use the Present Value of an Annuity Formula because the cost is the present value of all the payments.

The formula is as follows,

PV of an Annuity = C [ (1 – (1+i)^-n) / i ]

Where,

C is the cash flow per period

i is the rate of interest

n is the frequency of payments

They'll be paying twice a year for 4 years so n = 8

Since it is semi annually, the rate should be 8%/2, = 4%

Calculating we have,

= 5,000 ( 1 - ( 1 + 4%) ^-8 ) / 4%)

=$ 33,663.72

Then we add the $5,000 on purchase day to get,

= 5,000 + 33,663.72

= 38,663.72

= $38,664

The equipment reported on the balance sheet as of the purchase date is closest to $38,664

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