The NOI for a small income property is expected to be $150,000 at the end of the first year. Financing will be based on a 1.2 DCR (debt coverage ratio) applied to the end of 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?
(b) What is the total present value of the property (mortgage (debt) and equity)?
Please show your calculations!

The profitability of real estate assets that produce income is evaluated using a formula known as net operating income (NOI). NOI is the total revenue from the asset less all running costs that are deemed to be absolutely required. The term "net operating income" (NOI) refers to a before-tax figure that leaves out loan principal and interest payments, capital expenses, depreciation, and amortization on a property's income and cash flow statement. The term "EBIT," which stands for "profits before interest and taxes," is used when this metric is applied to other industries.

To solve the question :

Particulars Formula Value ($)

Loan Payment-------------------NOI/DCR-----------------------150,000/1.20=125,000

PV of NOI----------------------PV (10% ÷ 12,240,-125,000/12)--------1,079,423.11

FV of NOI

for 5 years---------------------FV (10% ÷ 12,60,-125,000/12,0--------954,634.88

Projected NOI for 5 years :

Year NOI Loan Payment Cash flow to equity

(increasing at 3%) ($)

1. 150,000 125,000 150,000-125,000= 25,000

2. 150,000×1.03

= 154,500 125,000 154,500-125,000= 29,500

3. 154,500 ×1.03

= 159,135 125,000 159,135-125,000= 34,135

4 159,135 × 1.03

= 163,909.05 125,000 163,909.05-125,000 = 38,909.05

5 163,909.05 × 1.03

= 168,826.32 125,000 168,826.32-125,000 = 43,826.32

6 168,826.32 × 1.03

= 173,891.11 (Resale value) - -

Particulars Formula Value ($)

Cash flow Future value of

from resale (Resale- Loan balance) 173,891/0.09- 954,634.88 = 977,487.34

PV of cash flow to equity :

Year Cash flow PVF at 12percent PV of cash flow to equity

to equity ($) = 1 / (1.12) ^ n.

1 25,000 0.892857 25,000 × 0.892857 = 22,321.43

2 29,500 0.797194 29,500 × 0.797194 = 23,517.22

3 34,135 0.71178 34,135 × 0.71178 = 24,296.62

4 38,909.05 0.635518 38,909.05 × 0.635518 = 24,727.40

5 43,826.32

+ 977,487.34

= 1,021,313.66 0.567427 1,021,313.66 × 0.567427= 579,520.80

Total - - 674,383.47

Particulars Formula Value

Total Present Value PV of cash flow to equity 674,383.47

+ PV of loan + 1,079,423.11

= 1,753,806.58

Hence, 1,753,806.58 is the Total Present Value.

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