Question

1. A property will generate NOI of $12,000 per year for each of the next 8 years. You purchase this property at a 5% cap rate. If you expect to sell this property in 6 years at a terminal cap rate of 6%, what is you IRR?

Answer 1

We are given the following data:

Net Operating Income NOI = $12,000 per year
Cap rate at property purchase r_i= 5%
Terminal cap rate r_t = 6%
Holding period = 6 years

Property value given the NOI and cap rate r is calculated as

Property value = NOI / r

Therefore, property value at the time of purchase P_i is

P_i = NOI / r_i = $12,000 / 0.05 = $240,000

Similarly, property value at the time of exit, P_t is

P_t = NOI / r_t = $12,000 / 0.06 = $200,000

Cashflows of this investment are as given below:

The cash flow in year 6 includes the NOI of $12,000 and the proceeds from property sale of $200,000.

Now, IRR for this six-month holding period can be calculated using the following equation (since IRR is the discount rate at which NPV becomes 0),

0 = -$240,000 + ($12,000 / (1+IRR)) + ($12,000 / (1+IRR)²) + ($12,000 / (1+IRR)³) + ($12,000 / (1+IRR)⁴) + ($12,000 / (1+IRR)⁵) + ($212,000 / (1+IRR)⁶)

Solving the equation for IRR using Excel, we get the IRR of 2.38%.