Final answer:
The present value of the investment with annual payments of $8,000 for three years, with a nominal discount rate of 7.5% and inflation rate of 2.9%, is $22,007.69.
Step-by-step explanation:
To calculate the present value (PV) of an investment with multiple cash flows under inflation and nominal discount rate, you must first adjust the nominal rate to get the real discount rate.
To do this, you can use the Fisher Equation which states that (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Solving for the real rate gives you the formula (1 + nominal rate) / (1 + inflation rate) - 1.
In this case, the nominal rate is 7.5% and the inflation rate is 2.9%, which results in a real discount rate of approximately 4.44%.
Now, apply this real discount rate to each of the $8,000 payments to get their present values:
PV of Year 1 = $8,000 / (1 + 0.0444) = $7,661.17
PV of Year 2 = $8,000 / (1 + 0.0444)^2 = $7,332.63
PV of Year 3 = $8,000 / (1 + 0.0444)^3 = $7,013.89
Add these three present values together to get the total present value of the investment:
Total PV of Investment = $7,661.17 + $7,332.63 + $7,013.89 = $22,007.69