A company is considering a $250 million investment in land that it will hold for 25 years. The pretax net cash flows are $40 million per year and land prices are expected to rise at a rate of 7% per year. The opportunity cost of capital is 13%, inflation is 2% and tax rate is 45%. What is the NPV of this project?
To calculate the Net Present Value (NPV) of the project, you will need to discount the future cash flows to their present value and then subtract the initial investment.
Here are the steps to calculate the NPV:
1. Calculate the present value of the annual net cash flows over the 25-year period:
NPV = (CF₁ / (1 + r)¹) + (CF₂ / (1 + r)²) + ... + (CFn / (1 + r)^n)
Where:
CF₁ = yearly net cash flow in the first year
r = discount rate (opportunity cost of capital)
n = number of years
In this case, the net cash flow is $40 million per year, the discount rate is 13%, and the project lasts for 25 years. So let's calculate the present value of the cash flows:
PV_CF = (40 / (1 + 0.13)¹) + (40 / (1 + 0.13)²) + ... + (40 / (1 + 0.13)^25)
2. Calculate the present value of the future resale value of the land:
PV_Resale_Value = Resale_Value / (1 + r)^n
The future resale value is the initial investment ($250 million) multiplied by the expected annual increase in land prices (7%) over the 25-year period. So:
PV_Resale_Value = (250 * (1 + 0.07)^25) / (1 + 0.13)^25
3. Calculate the total present value of all cash flows:
Total_PV = PV_CF + PV_Resale_Value
4. Subtract the initial investment from the total present value:
NPV = Total_PV - Initial_Investment
In this case, the initial investment is $250 million.
Now, let's plug in the numbers and calculate the NPV:
PV_CF = (40 / (1 + 0.13)¹) + (40 / (1 + 0.13)²) + ... + (40 / (1 + 0.13)^25)
= (40 / 1.13) + (40 / 1.13²) + ... + (40 / 1.13^25)
PV_Resale_Value = (250 * (1 + 0.07)^25) / (1 + 0.13)^25
Total_PV = PV_CF + PV_Resale_Value
NPV = Total_PV - Initial_Investment
Plug in the numbers and calculate the NPV.