Rachel Corporation purchased a building by paying $90,000 cash on the purchase date, agreeing to pay $50,000 every year for the next nine years and one payment of $100,000 ten years from the purchase date. The first payment is due one year after the purchase date. Rachel's incremental borrowing rate is 10%. The building reported on the balance sheet as of the purchase date is closest to:

The amount at which the building reported on the balance sheet as of the purchase date is closest to $416,505.52.

Explanation:

This can be caclulated using the following 3 steps:

Step 1: Calculation of the present value of $50,000 every year for the next nine years

Since the first payment is due one year after the purchase date, this can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV50 = present value of $50,000 every year for the next nine years = ?

P = Annual payment = $50,000

r = incremental borrowing rate = 10%, or 0.10

n = number of years = 9

Substitute the values into equation (1), we have:

PV50 = $50,000 * ((1 - (1 / (1 + 0.10))^9) / 0.10)

PV50 = $287,951.19

Step 2: Calculation of the present value of one payment of $100,000 ten years from the purchase date

This can be calculated using th present value formula as follows:

PV100 = FV100 / (1 + r)^n (2)

Where;

PV100 = present value of one payment of $100,000 ten years from the purchase date = ?

FV100 = Future value or the one payment of $100,000 ten years from the purchase date = $100,000

r = incremental borrowing rate = 10%, or 0.10

n = number of years = 10

Substitute the values into equation (2), we have:

PV100 = $100,000 / (1 + 0.10)^10

PV100 = $38,554.33

Step 3: Calculation of the amount at which the building reported on the balance sheet as of the purchase date

This can be calculated as follows

Amount reported = Cash paid on the purchase date + PV50 + PV100 = $90,000 + $287,951.19 + $38,554.33 = $416,505.52

Therefore, the amount at which the building reported on the balance sheet as of the purchase date is closest to $416,505.52.

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