A donor agrees to contribute $5,000 per year at the end of each of the next five years to a voluntary health and welfare organization.The donor did not place any use restrictions on the amount pledged.The stream of the payments is discounted at 6 percent.The first payment of $5,000 is received at the end of the first year.The present value factor for a five-payment annuity due on June 30,20X9,at 6 percent is 4.2124.The present value factor for a four-payment annuity due on June 30,20X9,at 6 percent is 3.4651.
-Based on the preceding information,the increase in present value of the contributions receivable recognized at the end of the first year equals:
A)$5,000.
B)$1,264.
C)$4,212.
D)$787.

Question

Quizplus · Accepted Answer

To calculate the increase in present value of the contributions receivable recognized at the end of the first year, we need to compare the present value of the remaining four payments at the end of the first year (when only the first payment of $5,000 has been received) to the present value of the remaining three payments at the end of the first year (when no payments have been received yet).

Using the present value factor for a five-payment annuity due, we can calculate the present value of the remaining four payments at the end of the first year:
$5,000 x 4.2124 = $21,062

Using the present value factor for a four-payment annuity due, we can calculate the present value of the remaining three payments at the end of the first year:
$5,000 x 3.4651 = $17,326

The increase in present value is the difference between these two amounts:
$21,062 - $17,326 = $3,736

However, we are only concerned with the increase in present value between the end of the first year and the beginning of the first year (i.e., before any payments have been received). Therefore, we need to subtract the present value of the first payment ($5,000) from this amount:
$3,736 - $5,000 = -$1,264

The negative sign indicates a decrease in present value, not an increase. Therefore, the correct answer is B) $1,264, which represents the decrease in present value of the pledge receivable recognized at the end of the first year.

A Donor Agrees to Contribute $5,000 Per Year at the End