Question

A company has the option to purchase a building for $500,000 at the begining of year one. This building is larger than needed; however, the excess space can be sublet for 12 years at a net annual rental of $8,000. Rental payments will be received at the end of each year and the risk associated with this investment is 10%. Calculate the present value of the investment in the building.

Answer 1

Given information:

1. Cost of building = $500,000
2. Time period = 12 years
3. Annual rental/cash inflows = $8,000
4. Interest rate = 10%

To calculate the present value of the investment in the building, the following steps need to be followed:

STEP 1: Prepare a table (like above) and jot down the cash inflows (in this case annual rentals of $8,000) at the end of each year (as stated in the image - column 1 & 2)

STEP 2: Calculation of Present Value Factor (PVF) i.e. Column 3 in the above image

The formula to calculate the present value factor (PVF) is as follows:

where r = rate of interest and n = number of years/periods

In this question, r = 10% or 0.10, and n keeps changing as per the years. For e.g.

Now for year 1,

For year 2, and similarly computed for all the 12 years (column 3 of the image represent this PV factor @10%.

STEP 3: Calculation of the Present value amount (column 4 in the image)

Now lastly, the present value of the annual cash inflows (rentals) has been calculated by using the below formula:

PV = PVF times cash inflow of a particular year  

For example, PV of Year 1 = cash inflow of year 1( i.e. $8,000) times PV factor of year 1 as calculated above (i.e. 0.909) = $7,272.73. A similar calculation has been done for all the remaining 11 years.

STEP 4: Calculation of the total present value of the investment

To calculate the total present value of the investment, sum up the PV amounts (i.e. sum of column 4 in the image).

Therefore, the answer to the question (i.e.the present value of the investment in the building) is $54,509.53