# Real Estate Valuation

There are three approaches to value real estate: (a) comparable sales approach (which is a relative valuation method), (b) income approach which includes the (i) direct capitalization method and (ii) discounted cash flow method and which is based on the concept of time value of money, and (c) cost approach, which values real estate at its replacement cost.

Just like any other assets, real estate value must correspond to its capacity to generate future cash flows. The easiest approach is to assign a value to the property based on value actually assigned to other properties in the market i.e. the comparable sales approach. However, because no two properties are the same and significant differences exist between properties, this approach is not appropriate for all properties and must be used with caution. A theoretically sound approach is one in which we estimate the actual cash flow potential of the property and then value the property at the present value of the future cash flows i.e. the income approach. When no comparable market transactions are available, and it is hard to forecast future cash flows correctly, the cost approach can be used which values a property at its replacement cost.

## Comparable sales approach

Comparable sales approach is a relative valuation method. Just like we find out price multiple for different stocks i.e. price to earnings ratio (P/E ratio), price to book ratio (P/B ratio), etc., in the comparable sales approach we identify past transactions of comparable properties and use them as benchmark to determine value for our property.

Comparable sales approach involves the following steps:

- Identifying actual market transactions in recent past of comparable properties. The comparable transactions must be similar in terms of location, property size, property nature (residential vs commercial), tenant size (whether one tenant or multiple tenants), typical lease duration (i.e. short-term vs long-term, etc.).
- Finding price multiple for the properties based on some feature of the property which derives the property’s value. It involves dividing the property value by say its covered area, number of apartments, etc.
- The multiples derived from comparable transactions are then multiplied with the same feature of the property to arrive at a value estimate, i.e. value per square feet must be multiplied by the property’s area to find value.

## Income approach

Income approach is an absolute valuation method. There are two variants of the income approach: the simpler direct capitalization approach and the more advanced discounted cash flow method.

Direct capitalization method values a property as a perpetuity i.e. an infinite stream of cash flows. It is similar to the Gordon growth model. Value of a property under the direct capitalization approach can be worked out using the following formula:

$$ V=\frac{NOI}{c\ -\ g} $$

Where NOI is the annual net operating income, c is the cap rate and g is the annual growth rate.

The discounted cash flow approach forecasts net operating income (NOI) for foreseeable future by individually forecasting the revenue and expense line items, finding a reversion value i.e. terminal value at the end of the initial foreseeable period and then discounting all the future cash flows using the required rate of return. The required rate of return is a discount rate which correctly captures the property’s risk.

Following is the formula for discounted cash flow approach:

$$ V=\frac{{NOI}_1}{{(1+r)}^1}+\frac{{NOI}_2}{{(1+r)}^2}+...+\frac{{NOI}_n}{{(1+r)}^n}+\frac{RV}{{(1+r)}^n} $$

Where NOI_{1}, NOI_{2} and NOI_{n} are the net operating income in first, second and nth period, RV is the reversion value (terminal value) and r is the required rate of return. RV can be estimated using either the multiple-approach or direct capitalization approach.

## Cost approach

The cost approach values a property at its replacement cost i.e. the cost that will be incurred in reconstructing the property. The value of a property under this approach equals the market value of the land on which it is constructed plus the cost of construction of a similar property at current prices.

This approach has a major theoretical weakness because it determines value of a totally new property which may have lower repairs and maintenance costs as compared to an old property.

## Example

You own a 50-unit residential 3-bed apartment complex in Toronto with total area of 50,000 square feet. Let’s call it Property Y.

Average occupancy rate is 90% and the average monthly rent is CAD 8,000 expected to grow by 7% each year for foreseeable future i.e. initial 5 years. 6% of the revenue is never collected. Monthly operating costs are 20% of the revenue in first year and are expected to grow in line with the Consumer Price Index (CPI), let’s say 3% per annum. Insurance costs are 3% of the capacity. Other revenue per year amounts to $500,000 which are expected to stay constant for next 5-years. Property taxes are 5% and income tax is 20%.

During last year, three apartment buildings were sold within one square kilometer area: Building A had a total covered area of 25,000 square feet building, had 30 units and was sold for $40 million; Building B had area of 70,000 square feet, 60 units and was valued at $70 million and Building C had area of 60,000 square feet, 42 apartment and was sold at $55 million.

The market value of the land is $30 million, and it took $20 million to construct the building 10 years ago. Assuming inflation over the last 10 years to be 2.5% on average.

During the last 3 years, comparable properties were valued based on a 10% capitalization rate. Assume in a net average growth in NOI is 5% for the purpose of direct capitalization method forever.

Work out a lower and upper bound for the property’s value based on the most popular real estate valuation methods. Required rate of return keeping in view the risk is 11%.

### Comparable sales approach

The comparable sales approach is the simplest method even though it is impossible to find a perfectly comparable property. The following table shows how the comparable sales approach can be applied to the Property Y:

Property | Value | Area (Square ft) | Units | Value per Square ft | Value per unit |
---|---|---|---|---|---|

A | 40,000,000 | 25000 | 30 | 1,600 | 1,333,333 |

B | 70,000,000 | 70000 | 60 | 1,000 | 1,166,667 |

C | 55,000,000 | 60000 | 42 | 917 | 1,309,524 |

Average | 1,172 | 1,269,841 | |||

Property Y area (Square ft) | 50,000 | ||||

Property Y units | 50 | ||||

Property Y value | $58,611,111 | $63,492,063 |

### Direct capitalization method

For the purpose of direct capitalization method, we need to first work out the net operating income (NOI) in Year 1:

Property Y | CAD |
---|---|

Gross annual rent revenue | 4,800,000 |

Vacancy costs (10%) | (480,000) |

Effective rent revenue | 4,320,000 |

Bad debts (6%) | (259,200) |

Effective rent income | 4,060,800 |

Other income | 500,000 |

Total income | 4,560,800 |

Operating expenses (20% of effective rent) | (812,160) |

Insurance costs (3% of the gross revenue) | (144,000) |

Property taxes (5% of total income) | (228,040) |

NOI | 3,376,600 |

Given a cap rate of 10% determined as the average ratio of the NOI to property value of comparable properties and a growth rate of 5%, the value of the property under the direct capitalization approach works out to CAD 67.532 million:

$$ V=\frac{$3,376,600}{10\%-5\%}=$67,532,000 $$

### Discounted cash flow method

In order to apply the discounted cash flow approach, we need to work out future NOI by forecasting each line item in the NOI calculation, find out a terminal value and then discount those future cash flow to time 0 using the required rate of return.

The following table shows forecasted NOI:

Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Gross annual rent revenue (7% yoy growth) | 4,800,000 | 5,136,000 | 5,495,520 | 5,880,206 | 6,291,821 |

Vacancy costs (10%) | (480,000) | (513,600) | (549,552) | (588,021) | (629,182) |

Effective rent revenue | 4,320,000 | 4,622,400 | 4,945,968 | 5,292,186 | 5,662,639 |

Bad debts (6%) | (259,200) | (277,344) | (296,758) | (317,531) | (339,758) |

Effective rent income | 4,060,800 | 4,345,056 | 4,649,210 | 4,974,655 | 5,322,880 |

Other income | 500,000 | 500,000 | 500,000 | 500,000 | 500,000 |

Total income | 4,560,800 | 4,845,056 | 5,149,210 | 5,474,655 | 5,822,880 |

Operating expenses (20% of effective rent) | (812,160) | (836,525) | (861,621) | (887,469) | (914,093) |

Insurance costs (3% of the gross revenue) | (144,000) | (154,080) | (164,866) | (176,406) | (188,755) |

Property taxes (5% of total income) | (228,040) | (242,253) | (257,460) | (273,733) | (291,144) |

NOI | 3,376,600 | 3,612,198 | 3,865,263 | 4,137,047 | 4,428,889 |

Reversion value (RV) i.e. terminal value | 77,505,550 | ||||

Net cash flows | 3,376,600 | 3,612,198 | 3,865,263 | 4,137,047 | 81,934,438 |

Discount factor (at 11%) | 0.9009 | 0.8116 | 0.7312 | 0.6587 | 0.5935 |

PV of NOI | 3,041,982 | 2,931,741 | 2,826,247 | 2,725,201 | 48,624,101 |

PV Of NOI and RV | 60,149,272 |

The reversion value i.e. the terminal value is calculated using the direct capitalization method formula:

$$ V=\frac{{\rm NOI}_5\times(1+g)}{r-g}=\frac{$4,428,889\times(1+5\%)}{11\%-5\%}=$77,505,550 $$

### Cost approach

The value under the cost approach equals the market value of land plus the construction cost of the building in today’s dollars. The market value of land is $30 million, and the current value of the construction cost can be determined by adjusting the historical cost for inflation.

$$ V=L+C=$30\ million\ +$20\ million\times{(1+2.5\%)}^{10}=$55.60\ million $$