A property that produces a level of NOI of $200,000 per year is expected to be sold in year 5 for $2,000,000.If the property was purchased for $2,000,000,what percent of the IRR can be attributed to the operating income only?

Question

Quizplus · Accepted Answer

First, we need to calculate the total IRR by using the formula,
IRR = [(Future Value/Present Value)^(1/n)] - 1

Here, the Future Value is $4,000,000 (the sale price at the end of year 5 including the NOI for that year), Present Value is $2,000,000 (the purchase price at the beginning), and n is 5 (number of years).

IRR = [($4,000,000/$2,000,000)^(1/5)] - 1
= 15.87%

Now, to calculate the portion of IRR that is attributable to the operating income only, we need to calculate the IRR from the operating income stream separately. We can do this by assuming that the property is sold at the end of year 5 for a price that is equal to its market value, i.e., excluding any premium for the operating income. So, the sale price in this case would be $2,000,000.

The NOI for the first four years generates a total of $800,000 ($200,000 per year x 4 years). The remaining operating income at the end of year 5 would be $200,000.

Now, we can calculate the IRR from the operating income stream using the formula,
IRR = [(Future Value/Present Value)^(1/n)] - 1

Here, the Future Value is $2,200,000 ($2,000,000 sale price + $200,000 operating income), Present Value is $2,000,000 (the purchase price at the beginning), and n is 5 (number of years).

IRR = [($2,200,000/$2,000,000)^(1/5)] - 1
= 6.31%

Therefore, the portion of IRR that is attributable to the operating income only is,
(6.31% / 15.87%) x 100%
= 37.9%

Hence, the answer is C.

A Property That Produces a Level of NOI of $200,000