###### Pricing and Valuation Concepts

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Remember that the direct capitalization method takes a single years’ NOI and the property value into account. When we consider the aspect of property growth at a constant rate in terms of income and value, then:

$$ \text{Cap rate} = (\text{Discount rate} – \text{Growth rate}) $$

Note that the growth rate is implied in the cap rate and has to be explicit when using the DCF valuation method.

Our primary function of calculating the cap rate is as follows:

$$ \text{Cap rate} = \frac {\text{NOI}}{\text{Value}} $$

Where:

\(\text{NOI}\) = Expected income from year one of ownership of the commercial property.

\(\text{Value}\) = An estimation of the worth of the property at the time of purchase.

Hence rearranging the above formula to calculate the property value in the equation:

$$ \text{Value} = \frac {\text{NOI}}{\text{Cap rate}} $$

It is worth noting that the cap rate can be obtained by comparing the rate at which other similar properties are retailing.

Based on our earlier discussion, you’ll remember that this method uses the discount rate to determine the intrinsic value of commercial properties. DCFM does this by discounting the future expected net cash flows, taking the inherent risk into account.

An investor will most likely attach value to a commercial property based on its projected income, considering the risk involved.

Recall:

$$ \text{Cap rate} = (\text{Discount rate} – \text{Growth rate}) $$

Therefore, when we substitute for the discount rate:

$$ \text{Discount rate} = (\text{Cap rate} + \text{Growth rate}) $$

Take note of the following:

- Cap rate is based on NOI as of year one.
- Growth rate focuses on future changes in NOI concerning property value.
- The basic difference between the discount rate and the cap rate lies in the growth in income and value.
- The similarity, in both the discount rate and the cap rate, is that they both start from the same NOI in year one.
- Practically, an investor will likely pay more for an increasing income than one that is constant. Hence, when the price is higher, the cap rate will be lower, explaining the cap rate’s growth concept.
- If the growth rate is constant, then the equation becomes similar to the dividend growth model.

## Question

An investor has the following commercial real estate properties.

$$ \small{\begin{array}{c|c|c|c} \textbf{Commercial Property} & \bf{X} & \bf{Y} & \bf{Z} \\ \hline \text{NOI} & $2,000,000 & $4,000,000 & $12,000,000 \\ \hline \text{Value} & ? & $32,000,000 & $170,000,000 \\ \hline \text{Lease terms (Years)} & 8 & 6 & 2 \end{array}} $$

Using the direct capitalization valuation method, the value of Property X is

closestto:

- $2,000,000.
- $32,000,000.
- $16,000,000.

Solution

The correct answer is C.Property X is closely similar to Property Y , compared to Property Z in terms of the lease period and NOI value. Given this information, we can estimate the value of Property X using cap rate calculated from information derived from Property Y as follows:

$$ {\text{Property Y cap rate }(r_y)} = \frac{\text{NOI}_y}{\text{Value}_y} = \frac{$4,000,000}{$32,000,000} = 12.5\% $$

Value of Property \(X(V_x)\), therefore, is calculated as:

$$ V_x = \frac {NOI_x}{r_y} = \frac {$2,000,000}{12.5\%} = $16,000,000 $$

A is incorrect.The amount relates to the NOI value for Property X.

B is incorrect.The amount relates to Property Y’s value, which aids in calculating the cap rate.

Reading 35: Real Estate Investments

*LOS (i) Calculate a property’s value using the direct capitalization and discounted cash flow methods.*