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 determine the Net Present Value (NPV) of the project, follow these steps:
1. Calculate the annual cash flows net of taxes:
The pretax net cash flows are given as $40 million per year. Since the tax rate is 45%, the after-tax cash flows can be calculated as follows:
Annual Cash Flow = Pretax Net Cash Flow * (1 - Tax Rate)
Annual Cash Flow = $40 million * (1 - 0.45)
Annual Cash Flow = $40 million * 0.55
Annual Cash Flow = $22 million
2. Adjust the cash flows for inflation:
Since the inflation rate is given as 2%, adjust the cash flows to reflect the expected purchasing power in real terms. To do this, divide the annual cash flows by (1 + inflation rate):
Inflation-Adjusted Cash Flow = Annual Cash Flow / (1 + Inflation Rate)
Inflation-Adjusted Cash Flow = $22 million / (1 + 0.02)
Inflation-Adjusted Cash Flow = $22 million / 1.02
Inflation-Adjusted Cash Flow = $21.57 million (rounded to two decimal places)
3. Calculate the present value of each cash flow:
To calculate the present value of each cash flow, use the formula: Present Value = Cash Flow / (1 + Cost of Capital)^t, where t is the time period.
Year 1:
Present Value Year 1 = $21.57 million / (1 + 0.13)^1
Present Value Year 1 = $21.57 million / 1.13
Present Value Year 1 = $19.08 million (rounded to two decimal places)
Year 2:
Present Value Year 2 = $21.57 million / (1 + 0.13)^2
Present Value Year 2 = $21.57 million / 1.2769
Present Value Year 2 = $16.89 million (rounded to two decimal places)
Year 3:
Present Value Year 3 = $21.57 million / (1 + 0.13)^3
Present Value Year 3 = $21.57 million / 1.4477
Present Value Year 3 = $14.90 million (rounded to two decimal places)
Repeat this calculation for each year until Year 25, or alternatively, use a financial calculator or spreadsheet software to calculate the present value of each year.
4. Sum up the present values:
Add up the present values of all the cash flows to get the net present value:
NPV = Present Value Year 1 + Present Value Year 2 + ... + Present Value Year 25
Alternatively, you can use the formula:
NPV = Cash Flow Year 1 / (1 + Cost of Capital)^1 + Cash Flow Year 2 / (1 + Cost of Capital)^2 + ... + Cash Flow Year 25 / (1 + Cost of Capital)^25
Calculate the NPV based on the present values you calculated in Step 3.
Considering the calculations required for each year, it may be more efficient to use spreadsheet software or a financial calculator to calculate the NPV.