Question

Ned Stark wants to buy a building. The annual revenues are $350,000 and annual operating expenses are $125,000. Ned decides that a fair and honorable price to pay would be $4,000,000.

What is the cap rate of this purchase?

2) After Ned’s unexpected and almost immediate demise, his son Robb inherits the building. Ever the crazy optimist, Robb expects that through his superior management skills, revenues will grow 5% a year after Year 1 and expenses will decrease 5% in Year 2 and remain flat after that.

If Robb is successful, assuming cap rates are unchanged, what will the value of this building be at the end of Year 5?

3) After Robb’s unexpected and almost immediate demise, his cousin Jon Snow inherits the building. Jon Snow knows nothing about real estate, but he does sense that the economic climate is changing. One indication of this is the valuation the probate court puts on the building. Although revenues and expenses have not changed, the value is 25% less than the price Ned paid for the building. What is the new cap rate the court has assigned?

4) Jon Snow’s worst fears are realized. Increasingly harsh conditions lead to lower occupancies and higher expenses, due mainly to higher utility expenses. Revenues drop by 5% a year, every year, after Year 1, and expenses increase by 3% a year, every year, after Year 1. At the end of Year 5 Jon Snow quits in frustration and sells the building to Dwight Walker for the same cap rate that applied when he inherited it.   What does Walker pay for the building?

Answer 1

Part (1):

Cap rate= NOI/Price

Where NOI= Net Operating Income= Revenues-Expenses= $350,000-$125,000 = $225,000

Also given price= $4,000,000

Cap rate= 225000/4000000 = 5.625%

Part (2)

Given, growth rate in revenues=5% and Growth rate in expenses= -5%

Therefore, NOI after 5 years= 350000*(1+5%)^5 – 125000*(1-5%)^5

= 446,698.55 – 96,722.62 = $ 349,975.93

Value= NOI/Cap rate.

At the earlier Cap rate, Value of the building= $ 349,975.93/5.625% = $6,221,794.31

Part (3)

Given, Revenues and expenses remain unchanged. Hence NOI= $225,000

New value assessed is less by 25%

Therefore, new value= $4,000,000*(1-25%) = $3,000,000

New cap rate= $225,000/$3,000,000 = 7.5%

Part (4)

Given, growth rate in revenues=-5% and Growth rate in expenses= 3%

Therefore, NOI after 5 years= 350000*(1-5%)^5 – 125000*(1+3%)^5

= 270,823.33- 144,909.26 = $125,914.07

Cap rate at the time of inheritance (as in part 3)= 7.5%

Sale price at the above cap rate= NOI/Cap rate= $125,914.07/7.5% = $1,678,854.25