9. The NOI for a small income property is expected to be $150,000 for the first year. Financing will be based on a 1.2 DCR applied to the first year NOI, will have a 10 percent interest rate, and will be amortized over 20 years with monthly payments. The NOI will increase 3 percent per year after the first year. The investor expects to hold the property for five years. The resale price is estimated by applying a 9 percent terminal capitalization rate to the sixth-year NOI. Investors require a 12 percent rate of return on equity (equity yield rate) for this type of property. a. What is the present value of the equity interest in the property

a. The present value of the equity interest in the property is:

= PV = $1,096,338

Explanation:

a) Data and Calculations:

Debt Coverage Ratio = 1.2

Debt interest = $150,000/1.2 = $125,000

Interest rate = 10%

Therefore, total financing or debt obtained = $125,000/10% = $1,250,000

NOI for the first year = $150,000

NOI for other years = 3% per year after the first year.

Holding period of property = 5 years

Therefore, expected NOIs for the second to fifth year are calculated as follows:

Net operating income (NOI):

First Year  = $150,000      

Second Year = $154,500 ($150,000 * 1.03)

Third Year = $159,135 ($154,500 * 1.03)

Fourth Year = $163,909 ($159,135 * 1.03)    

Fifth Year = $168,826 ($163,909 * 1.03)

Sixth year NOI = $173,891 ($168,826 * 1.03)

Terminal capitalization rate = 9%

Resale price = NOI of the sixth year/Terminal cap rate

= $173,891/9% = $1,932,122

The present value of the equity interest in the property:

From an online financial calculator:

N (# of periods)  5

I/Y (Interest per year)  12

PMT (Periodic Payment)  0

FV (Future Value)  $1,932,122

Results

PV = $1,096,337.91

Total Interest$835,784.09

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in fact, you have to perform the operation inside parentheses first, and then proceed in order: