Question

An income property is under evaluation for purchase with a $455,000 loan (FRM with 8% annual rate for 10 years and payments are by year). We plan to hold the property for 3 years and then sell it at the end of year 3. The NOI for year 1 is 72,000 with a growth rate of 2. The end capitalization rate is 12%. We assume after year 3, the NOI still increases at a rate of 2%.

b. With the asking price of 413,000, what is the IRR for this investment?

Answer 1

b. NOI for year 1 = $72,000

NOI for year 2 = NOI for year 1*(1+growth rate) = $72,000*(1+0.02) = $72,000*1.02 = $73,440‬

NOI for year 3 = NOI for year 2*(1+growth rate) = $73,440*(1+0.02) = $73,440*1.02 = $74,909

Sale value at the end of year 3 = [NOI for year 3*(1+growth rate)]/(end capitalization rate - growth rate)

Sale value at the end of year 3 = [$74,909*(1+0.02)]/(0.12-0.02) = ($74,909*1.02)/0.1 = $76,407/0.1 = $764,070‬

IRR is the internal rate of return at which present value of NOI will be equal to asking price.

asking price = NOI year 1/(1+IRR) + NOI year 2/(1+IRR)2 + (NOI year 3 + Sale value at the end of year 3) /(1+IRR)3

Year	Cash flows
0	-$413,000
1	$72,000
2	$73,440
3	$838,979
IRR	37.62%

Calculations