What Are We Solving For?
We are determining the present value (PV) of a $500,000 lump sum payment to be received in 10 years, using anopportunity rate of 12%. Inflation is not relevant here because the opportunity rate already reflects the expected return, including inflation adjustments.
Formula for Present Value:
The present value (PV) is calculated using the formula:
PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}PV=(1+r)nFV
Where:
FVFVFV = Future Value = $500,000
rrr = Opportunity rate = 12% or 0.12
nnn = Number of years = 10
Calculation:
PV=500,000(1+0.12)10PV = \frac{500,000}{(1 + 0.12)^{10}}PV=(1+0.12)10500,000 PV=500,000(1.12)10PV = \frac{500,000}{(1.12)^{10}}PV=(1.12)10500,000 PV=500,0003.10585PV = \frac{500,000}{3.10585}PV=3.10585500,000 PV≈160,986PV ≈ 160,986PV≈160,986
Why Inflation Is Not Included:
The opportunity rate already incorporates the expected inflation. Using it ensures the PV reflects the real purchasing power of the future lump sum payment.
Why Other Options Are Incorrect:
B. $186,023, C. $440,000, D. $485,000:These values result from incorrect calculations or the misuse of inflation in the formula.
References and Documents:
GAO Financial Analysis Guide:Recommends using present value calculations with opportunity rates for investment decision-making.
AICPA Financial Management Guide:Provides detailed examples of calculating present value for lump sum payments.
