An office building is purchased with the following projected cash flows:
-NOI is expected to be $180,000 in year 1 with 3 percent annual increases.
-The purchase price of the property is $820,000.
-100% equity financing is used to purchase the property
-The property is sold at the end of year 4 for $780,000 with selling costs of 6 percent.
-The required unlevered rate of return is 12 percent.
Calculate the unlevered net present value (NPV).
I had this question on one of my real estate principles exams and the correct answer, according to my professor, was $215,399.
Not sure how she arrived at this answer yet.
To calculate the unlevered net present value (NPV), we need to discount the projected cash flows to their present value and then subtract the initial investment.
1. Calculate the net operating income (NOI) for each year, considering the 3 percent annual increases:
Year 1 NOI = $180,000
Year 2 NOI = $180,000 + ($180,000 * 0.03)
Year 3 NOI = Year 2 NOI + (Year 2 NOI * 0.03)
Year 4 NOI = Year 3 NOI + (Year 3 NOI * 0.03)
2. Calculate the present value (PV) of the projected cash flows using the required unlevered rate of return (12 percent):
PV = Cash Flow / (1 + R)^n
Where:
- PV is the present value
- Cash Flow is the projected cash flow
- R is the required unlevered rate of return
- n is the year
For example:
PV Year 1 = Year 1 NOI / (1 + 0.12)^1
PV Year 2 = Year 2 NOI / (1 + 0.12)^2
PV Year 3 = Year 3 NOI / (1 + 0.12)^3
PV Year 4 = (Year 4 NOI + Selling Price - Selling Costs) / (1 + 0.12)^4
3. Calculate the NPV by summing up the present values of the cash flows:
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 - Initial Investment
Given that the initial investment (purchase price) is $820,000 and the selling costs are 6 percent of the selling price, which is $780,000 * 0.06 = $46,800, we can substitute the values into the equation.
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 - $820,000
Calculate each PV value for the corresponding year and substitute those values into the NPV equation to find the final result.