###### Cointegration

Consider a time series of the inflation rate \((\text{y}_{\text{t}})\) regressed on a time... **Read More**

The direct capitalization method estimates the value of a property by capitalizing the first-year NOI at a market-derived cap rate. The discounted cash flow method projects income after the first year and discounts the income at a yield rate (discount rate). The relationship between the cap rate and the interest rate remains the same if the value and income of the property are expected to change over time.

$$ \text{Cap rate} = \text{Discount rate} – \text{the growth rate} $$

Hence

$$ \text{Discount rate} = \text{Cap rate} + \text{growth rate} $$

When the NOI is growing, the cap rate is lower, and the price is higher.

$$ \text{The value of property} =\frac {NOI}{ (r – g) } $$

Where

\(r\) = the discount rate

\(g\) = the growth rate for income.

The above equation is similar to the dividend growth model applied to stocks. NOI is projected for a specified holding period, and a terminal value is estimated at the end of this holding period.

Greenwood Realtors LTD expects its East Point property NOI to be € 300,000 in the first year, and the NOI is expected to increase by 3% each year. The property value is expected to increase by 2% each year. Investors expect an IRR of 14%; therefore, the discount rate will be 14%. What is the value of the property at the beginning of the first year?

$$ \begin{align*} \text{The value of property} & =\frac {NOI}{ (r – g)} \\

& = \frac {€ 300,000}{ (0.14 – 0.03)} \\

& = € 2,727,272.72

\end{align*} $$

When using a DCF methodology to value property, the most vital input is the estimated sale price (estimated terminal value) at the end of a typical holding period. It is difficult to estimate the terminal value of a property in practice because the property’s value today is not always known. In theory, the terminal value is based on the present value of income to be received by the next investor. The terminal cap rate is the cap rate used to estimate the resale price. The cap rate will be lower if the discount rate is low and the growth rate is expected to be high.

The terminal cap rate is not necessarily the same as the going-in cap rate when the property is appraised. In many instances, the cap rate will be higher than the going-in rate because it is applied to uncertain income. This could also be because the property is older and has a lower growth rate.

Ivan Bjorn works for a real estate investment company that is looking to purchase a 5-year-old office building. The building has five floors with a total leasable area of 20,000 square meters that is 100%leased to 2 tenants. All tenants have five-year leases, which they will both renew at the end of the five years. Your manager has asked you to prepare a discounted cash flow to determine if the property’s purchase would meet the company’s return requirement. The following information was provided.

$$ \begin{array}{c|c|c|c}

\textbf{Assumptions} & & & \\ \hline

{\text{Annual Net Rent per } m^2} & $120 & \text{Initial Cap Rate} & 5.0\% \\ \hline

\text{Leasable Area} & 20,000 & \text{Terminal Cap Rate} & 8.0\% \\ \hline

{\text{Lease 1 } (m^2)} & 10328 & \text{NOI in Year 5(millions)} & $ 4.2 \\ \hline

{\text{Lease 2 } (m^2)} & 9672 & &

\end{array} $$

It is believed that net property income will increase by 3.0% annually.

Below-the-line expenses are 3.5% of NOI.

First-year \(NOI =\frac { $120}{ m^2 \times 20,000 m^2} = $ 2.4 \text{ million}.\)

Purchase price \(= \frac {\text{Year 1 NOI}}{{\text{Cap rate}}} =\frac {$ 2.4 \text{ million}}{ 5\%} =$ 48 \text{ million}.\)

Terminal value at end of year 5 \(=\frac {$ 4.2 \text{ million}}{8.0\%}=$ 52.5 \text{ million}\)

$$ \textbf{Exhibit 1: Cash flow Forecast (}\bf{$} \textbf{ thousands)} \\

\begin{array}{c|c|c|c|c|c|c}

& \textbf{Year 0} & \textbf{Year 1} & \textbf{Year 2} & \textbf{Year 3} & \textbf{Year 4} & \textbf{Year 5} \\ \hline

\text{Lease 1} & & 1,239.36 & 1,276.54 & 1,314.84 & 1,354.85 & 1,395.5 \\ \hline

\text{Lease 2} & & 1,160.64 & 1,195.46 & 1,231.32 & 1,268.26 & 1,306.31 \\ \hline

\text{Net} & & 2,400 & 2,472 & 2,546.16 & 2,623.11 & 2,701.81 \\

\text{Property} & & & & & & \\

\text{NOI} & & & & & & \\ \hline

\text{Capital} & & (84) & (86.52) & (89.11) & (91.81) & (94.56) \\

\text{Spending} & & & & & & \\

\text{and} & & & & & & \\

\text{Leasing} & & & & & & \\

\text{expense} \\ \hline

\text{Property} & & 2,316 & 2,385.5 & 2,457.05 & 2,531.3 & 2,607.25 \\

\text{Cash} & & & & & & \\

\text{Flow} & & & & & &

\end{array} $$

$$ \textbf{Exhibit 2: Discounted Cash Flow Analysis (} \bf{\$} \textbf{ thousands)} \\

\begin{array}{c|c|c|c|c|c|c}

& \textbf{Year 0} & \textbf{Year 1} & \textbf{Year 2} & \textbf{Year 3} & \textbf{Year 4} & \textbf{Year 5} \\ \hline

\text{Initial} & -48,000 & & & & & \\

\text{Outlay} & & & & & & \\ \hline

\text{Annual} & & 2,316 & 2,385.5 & 2,457.05 & 2,531.3 & 2,607.25 \\

\text{Property} & & & & & & \\

\text{cash} & & & & & & \\

\text{flow} & & & & & & \\ \hline

\text{Terminal} & & & & & & 52,500 \\

\text{Value} & & & & & & \\ \hline

\text{Total} & (48,000) & 2,316 & 2,385.5 & 2,457.05 & 2,531.3 & 55,107.25 \\

\text{Cash} & & & & & & \\

\text{flow} & & & & & & \\ \hline

\text{Discount} & 8.0\% & 1/1.08^1 & 1/1.08^2 & 1/1.08^3 & 1/1.08^4 & 1/1.08^5 \\

\text{rate} & & & & & & \\ \hline

\text{Present} & & 0.9259 & 0.8573 & 0.7938 & 0.7350 & 0.6806 \\

\text{value} & & & & & & \\

\text{factor} & & & & & & \\ \hline

\text{Present} & & 2144.44 & 2045.18 & 1950.49 & 1860.58 & 37505.07 \\

\text{value of} & & & & & & \\

\text{property} & & & & & & \\

\text{cash} & & & & & & \\

\text{flows} & & & & & & \\

\end{array} $$

$$ \textbf{NPV and Return Analysis} \\

\begin{array}{c|c}

\text{Sum of present value of cash inflows} & 45,505.76 \\ \hline

\text{Cash Outlay} & (48,000) \\ \hline

\text{NPV} & -2,494.24

\end{array} $$

From the above analysis, it is clear that the purchase of the office building would not result in returns in excess as hoped by the company.

## Question

Assume the NOI for a property is expected to be level at £450,000 per year for a long period into perpetuity. Investors want a 10% return from the property, and the property growth rate increases by 3% per year. The value of the property is closest to:

- £ 450,000
- £ 6,428,571.43
- £ 4,500,000
## Solution

The correct answer is B.$$ \begin{align*} \text{The value of property} & =\frac {NOI}{ (r – g)} \\

&= \frac { £450,000 }{ (0.1 -0.03)} \\

&= £ 6,428,571.43

\end{align*} $$

Reading 36: Investment in Real Estate Through Private Vehicles

*LOS 36 (d) Calculate the value of a property using the direct capitalization and discounted cash flow valuation methods.*