Question

You have an opportunity to buy an office building for $125,000 that produces an annual NOI of $10,000. You can obtain an 80% loan from a bank with a 7% interest rate and amortized for 30 years. Your required investor cash on cash return is 12%. You will have to put 20% of the purchase down. What is the value of the office building?

A. $140,999 B. $118,242 C. $113,895 D. $125,000

Answer 1

Value of building = NOI / Cap rate

Calculation of the CAP rate:-

CAP rate = F + E

Where F= Financing component

E = Equity component

Calculation of the Financing component :-

Annual Mortgage constant = 12 * i / [ 1 - ( 1 / (1+i)n ]

where i = per month interest rate = 7% / 12 = 0..5833%

n = number of months = 30 years * 12 = 360 months

Annual Mortgage constant = 12 * 0.00583 / [ 1 - 1/(1.00583)360 ] = 12* 0.00583 / [ 1 - 0.123206]  

= 12 * 0.006653

Annual Mortgage constant = 0.079836

Financing Component = Annual mortgage constant * Loan to value ratio = 0.079836 * 0.80 = 0.063869

Calculation of the Equity Component :-

Equity component = investor requried rate of return * equity to value ratio = 12% * 20% = 0.024

CAP rate = Financing component + equity component = 0.063869 + 0.024 = 0.087869

CAP Rate = 8.79%

Value of Building = NOI / CAP rate = 10,000 / 0.0879 = $ 113,765.64

Value of building = $ 113,765,64 = $ 113,895 (Approx )

option C is correct