A student will receive a $25,000 grant at the beginning of every year for the next five years. Assuming an annual interest rate of 4% is appropriate, the present value of an ordinary annuity is 4.4518 * $25,000 = $111,295, and the present value of an annuity due is 4.62990 * $25,000 = $115,748. What is the fair value of the grant payments according to the Financial Accounting Standards Board (FASB)?

Rationale

The fair value of the grant payments is $115,748.

The present value of the annuity due, calculated as 4.62990 * $25,000, represents the fair value of the grant payments according to the FASB. This accounts for the fact that the payments are received at the beginning of each year, thus earning interest for the full year.

A ($130,000) YOUR ANSWER

This amount does not reflect the present value of the grant payments since it exceeds the calculated values for both the ordinary annuity and the annuity due. It overlooks the impact of the annual interest rate on the present value of the cash flows.

B ($115,748) CORRECT

This is the correct answer, representing the present value of the annuity due, which is calculated using the appropriate interest factor for cash flows received at the beginning of each period. It accurately reflects the fair value of the grant payments over the five-year period.

C ($125,000) YOUR ANSWER

This choice is incorrect as it does not correlate to any present value calculation associated with the grant payments. It assumes a value that is neither the present value of an ordinary annuity nor of an annuity due, failing to consider the specific discounting factors involved.

D ($111,295) YOUR ANSWER

This value corresponds to the present value of an ordinary annuity, where payments are received at the end of each year. However, since the payments for the grant are due at the beginning of each year, this option does not accurately represent the fair value of the grant payments.

Conclusion

The fair value of the grant payments, according to the FASB, is determined by the present value of an annuity due, which takes into account the timing of the cash flows. With a calculated present value of $115,748, this reflects the appropriate valuation for the grant payments over the specified period, adhering to the principles of financial accounting.

The fair value of the grant payments is $115,748.

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