This question requires the calculation of the Present Value (PV) of a future lump sum payment. The appropriate discount rate is the agency's opportunity rate of 12%, which represents the return the agency could earn on its investments. The inflation rate of 3% is extraneous information for this specific calculation. The formula for Present Value is: PV = FV / (1 + r)^n, where FV is the Future Value ($500,000), r is the periodic discount rate (0.12), and n is the number of periods (10 years).

Calculation:

PV = $500,000 / (1 + 0.12)^10

PV = $500,000 / 3.105848

PV ≈ $160,986

B. $186,023: This result is inconsistent with the standard present value calculation using the provided opportunity rate and time period.

C. $440,000: This figure results from an incorrect, non-compounded, single-period discount ($500,000 × (1 - 0.12)), failing to account for the 10-year time horizon.

D. $485,000: This incorrectly uses the inflation rate as a simple one-year discount ($500,000 × (1 - 0.03)) instead of the appropriate opportunity rate and compounding period.

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1. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.

Chapter 2, Section 2-1, "Calculating Present Value": This chapter explicitly defines the formula for present value as PV = Ct / (1 + r)^t. It states, "The rate r is called the discount rate, hurdle rate, or opportunity cost of capital. It is the return that is foregone by investing in the project rather than investing in financial markets." This directly supports using the 12% opportunity rate as the discount rate 'r'.

2. U.S. Office of Management and Budget (OMB). (2023). Circular A-94, Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs.

Section 5, "Basic Precepts of Benefit-Cost Analysis": This official government source states, "The conceptually correct discount rate for a given program is the opportunity cost of the resources that it displaces." It further clarifies that future values must be discounted to their present value. This establishes the principle of using an opportunity cost rate for discounting in a governmental context.

3. Massachusetts Institute of Technology (MIT) OpenCourseWare. (2008). 15.401 Finance Theory I, Lecture Notes, Lecture 2: The Time Value of Money.

Page 3, "Present Value": The notes provide the formula PV = C / (1+r)^t and define 'r' as the "discount rate" or "opportunity cost of capital." This academic source confirms the fundamental formula and the correct application of the opportunity rate for calculating the present value of a future cash flow. Available at: https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/resources/mit15401f08lec02/