10.1 Introduction
Along with stocks and bonds, real estate is one of the biggest asset classes in the world, if not the biggest. However, most real estate is not traded in liquid markets, thus making the real estate market much less efficient to invest in than the stock and bond markets. Valuation of real estate is more similar to real assets and we have to use valuation methods described in chapters 7 and 9.
Investing in real estate is considered more risky than fixed income but less risky than stocks. This is a huge simplification, as investing in real estate comes in different varieties and most often with leverage, increasing the risk level towards or even above that of stocks. A key difference to stocks and bonds is the low market liquidity.
10.2 Types of properties
Real estate comes in many varieties:
In this chapter we will focus on income-producing real estate.
Most commercial real estate space is leased. The most obvious reason is the flexibility for the tenant. If a company buys or builds its own office, business cycles and growth may alter the need for space. Renting instead of buying will give much more flexibility as the company can move more easily to other premises.
Another reason for renting is employment of capital. If a company earns a much higher return on its capital from operations than the return from owning its own office, it should release capital from real estate and invest in its operations. (On the other hand, if there are no borrowing constraints, the company can just borrow to invest more).
10.3 Valuing real estate
First we have to identify the value drivers such as income growth and costs. We will not go into detail about how to forecast rental growth, but we will look more closely into critical inputs such as rental income and operational costs in order to compute the value of a property.
The income in real estate comes from collection of rents. Usually we talk about market rent, which is the prevalent price that a potential tenant has to pay for a specific space at current market levels. The market rent will fluctuate with:
• national/international business cycles
• local business conditions
• industry trends
• supply of new lettable space.
A major drag on property income is vacancy. Most properties experience some vacancy from time to time. Vacancy occurs when tenants leave after the lease expires and no new tenants take up the space. Vacancy can also occur if a newly constructed property hasn’t secured any or a sufficient number of tenants.
Most lease contracts come with a base (minimum) rent that usually has some adjustments attached, such as:
• Step-up lease: A predetermined jump in rent at the end of some specific time.
• Indexed lease: The rent is linked to some index, typically the Consumer Price Index.
• Performance-based: The tenant (lessee) pays a percentage of its turnover/sales to the owner (lessor). Sometimes this kicks in above some minimum turnover/sales. Other contracts are based solely on turnover with no minimum rent.
Costs in real estate can be divided into operational and financial costs. Depending on the level of debt, interest rate costs often represent more than operational costs. While interest rate costs are predominantly determined by conditions in the financial markets, operational costs are more specifically related to the property in question.
Valuation methods
Real estate appraisers use a number for methods to gauge the value of a property. We will discuss a few of them here before digging deeper into the discounted cash flow (DCF) method.
Peer sales
Here we look at sales of very comparable properties (peer comparison). We may use these prices as a benchmark for the market value of a property after adjusting for difference in size, location, age, quality, etc. Because all properties have some unique features, this method, at best, serves as a rough proxy for the value of a property.
Yield/Income approach
A property has a value only because it produces, or is likely to produce, cash flows. And the higher the cash flow, the higher the valuation. Some crude but very widely used valuation methods are:
1 gross income multiplier
2 capitalization rate
3 discounted cash flow (DCF) approach.
1. The gross income multiplier is the value (sales price) of the property divided by gross income:
The multiplier does not tell us anything about the profitability of the investment, but may be used for comparison. If most shopping malls are sold at a multiple of 10, then this could be applied to what should be paid for a similar shopping mall in the same area.
There can be a huge difference between potential and effective gross income for a property. Potential gross income assumes that all space is rented out, and might represent an option to increase the property’s income if business conditions improve and/or management can attract more tenants. Effective gross income is what is actually collected. When comparing multipliers, make sure you use the same definition of gross income.
2. The capitalization rate looks more into the net operating income. Two apparently similar properties might have differences in operating costs. By subtracting operating expenses from gross rent, we get net operating income (NOI). This is then divided by the price. We then get the capitalization rate (“cap rate”):
Or we can use the cap rate to find the value:
Example 10.1
You are considering buying an office building that has 30 million in annual effective gross rent. The annual operating costs have on average been around 32 per cent of the gross income per year. What is the maximum you should pay for the building?
Since several other similar properties have been sold in the same area recently, we can use these transactions as a level for current market prices. We are not interested in the absolute price level, but the capitalization rate (“cap rate”) at which these properties have been sold. We calculate the cap rate for all properties to find the average (see figure 10.1).
Figure 10.1 Data for similar properties.
Using the average cap rate of 6.7 per cent, the market price for the property in question should be:
However, the difference between the highest and lowest cap rates implies a difference of 16 per cent both ways, so an average is just an average and should only be used to check whether the price is “in line” with current market prices. It does not tell us anything about the profitability at this price.
There can be huge differences in the valuation depending on what cap rate is used. If the cap rate is very low, a 1 percentage point difference will have a much larger impact on the price than if the cap rate is higher (see figure 10.2)
Figure 10.2 Relationship between cap rate and value.
3. Discounted cash flow (DCF) approach. Here we look at all future cash flows from the property and discount them back at an appropriate cost of capital. This is a more accurate valuation approach than gross multiple and cap rate, but it is very sensitive to the assumptions about rental growth, operating costs, capital expenditures, and so forth. We have more variables to estimate, and there is always a risk of having too much faith in the estimates. The more complicated the model becomes, the higher the risk of being “exactly wrong” instead of “roughly right”.
Now, let us look at how you find the cash flows from the property.
Cash flow statements
Like other asset class valuations, we have to look at the cash flows. In real estate we have to add and subtract various items to translate gross rental income into net cash flow.
A common pitfall in investment analysis is to ignore or underestimate the importance of capital expenditures. This must be taken into account somewhere in the cash flow projections. Some use net operating income (NOI) and net cash flow interchangeably. However, the former does not necessarily include capital expenditures. In order to get the correct cash flow, one has to add recurring capital expenditures (“cap ex”) to operating expenses (above the NOI-line) and subtract any need for upgrading of roof, lifts, etc. (capital expenditures) from the sales price at the end of the forecasting period (terminal value). Using the approach in figure 10.3 forces you to take cap ex into the equation so you won’t forget to subtract it from the sales price (terminal value).
Figure 10.3 Finding the net cash flow.
Of course, accurate estimation of all items in the cash flow projections is the key to a good analysis. Knowledge about real estate management is therefore helpful.
Example 10.2
Consider an office building that is for sale. It consists of 10,000 square metres of lettable space. The current market rent per square metre is 300 per year, which is in line with current market level. It is to be adjusted in line with the expected inflation rate (“index”) of 2 per cent per year.
The building is leased to a number of tenants that are mostly very creditworthy (high credit ratings, AA or above). All contracts expire in six years. The facility services are paid by the tenants (so-called recoveries). The tenants are charged with 20 per lettable square metre for these. The operational costs are 10 per cent of gross income and there is a management fee of 100,000 per annum. There is some parking space that is rented out for 10 per cent of the rent per square metre, adding to the gross income. There is 10 per cent vacancy in the building and some of the smaller tenants are less creditworthy. We therefore have to make some provision for possible loss of collection, here estimated at 1.5 per cent of effective gross rent. The maintenance and improvement costs are estimated at 30 per square metre lettable area. There is a municipal tax of 1 per square metre. The corporate tax rate is 28 per cent. All inputs are entered in the spreadsheet in figure 10.4.
Figure 10.4 Inputs for property valuation.
Estimate the total income, operating income and cash flow for the period 2013–2018.
We set up a spreadsheet with all inputs and necessary yearly adjustments. We start with the income and expenses (figure 10.5).
Figure 10.5 Income and expenses for office building.
Here we have adjusted the rent in line with the expected index (cell B5). All other income is adjusted with the index as well. We have to subtract expected collection loss (cell B8), also adjusted for index. The same goes for expenses: we adjust them according to index (cell B5).
But we are interested in the net cash flows, not the operating income. We therefore have to add back all non-cash costs and subtract maintenance and capital expenditures that are not accounted for in the operating costs. Now we are ready to adjust the operating income for tax (cells C40:H40 to C44:H44 in figure 10.6) and then add back the depreciation, which is not a cash outflow. We also subtract necessary maintenance and improvement costs to get the net cash flow to the firm.
Figure 10.6 Estimating the cash flow to the firm.
Next, we want to find the value of the property. We remember that the value of any asset is the present value of all future cash flows. Above, we only made projections about the cash flows until the leases expire (six years from now). In order to find the value of the property, we also have to make an assumption about what the property is worth from year 7 onwards. We can think of this as if we sold the property after six years, so we have to make an estimate of how much it can be sold for at the end of year six.
Terminal/Reversion value
It is usual to consider the last year of the estimation period (here year 6) as the year in which the building is sold. This is just an assumption we make in order to find an estimate of the terminal value (TV) in a discounted cash flow analysis.
Terminal value is also known as resale price or reversion value. The shorter the cash flow projection period, the larger the impact the resale price will have on the valuation, so extra care should be taken to make a good estimate of the terminal value. Different methods are typically used.
• Long-term cash flow projection.
• Adjusting “going in” cap rate.
• Yearly change in property value.
Let us look more closely at each of them.
Long-term cash flow projection
We know from earlier that the value of an infinite series is
where
CF |
= |
cash flow next year |
r |
= |
discount rate (cost of capital) |
g |
= |
long-run growth rate. |
In real estate, appraisers often use the denominator (r – g) as the terminal cap rate RTV. We can now use this in equation 10.1 to find the value of the property above.
Example 10.3
Consider the property we just found the cash flows for in the example above. Find the maximum price you would pay for the property. We use the cash flows above, but need to find the cost of capital. Some just use a rule of thumb for the cost of capital, such as the risk-free rate plus some risk premium of 3–5 per cent for unleveraged properties, but here we will use the Capital Asset Pricing Model. The debt to equity ratio is 1 (50 per cent debt to total capital). The unlevered beta for similar properties is 0.5. The beta is used for calculating the cost of capital.
In order to find the value of the property we have to calculate an estimate of the terminal value, discounted back to today’s value, and then add the discounted cash flows from the first six years.
Cash flow in year 6 is estimated to 1,920,460 (cell H46). Long-term growth in rent is expected to follow the inflation rate (“index”) at 2 per cent. Next year’s cash flow (year 7) will therefore be
The missing variable is the cost of capital. How do we find this? We can use the Capital Asset Pricing Model (CAPM), which is described in detail in chapter 8.6.
Remember how we calculate the cost of equity, rE, from CAPM:
re = rf + βL[E(Rm) – rf]
Where
rf = risk-free rate
βL = equity (or leveraged) beta is derived from unleveraged βU. We adjust the unleveraged beta by the debt ratio (50 per cent), assuming debt is risk free (βd = 0):
When the debt to capital ratio is 0.5, there must be an equal amount of debt and equity so the debt to equity ratio must be 1. To find βL after tax (t), we have to use the formula:
Risk premium, [E(Rm) – rf], is assumed to be 5 per cent, so we can now finally insert the values in the CAPM and find the cost of equity:
Now we shall find the cost of capital, r, as the weighted average cost of capital (WACC). Assume the interest on debt, rd, is 6.5 per cent
Now we can find the terminal value (TV), i.e. the value of the property at the end of year 6.
We have to discount all cash flows from years 1–6, including an actual or potential sale of the property at the end of year 6.
Figure 10.7 Net present value of property.
The value of the property is 43.6 million.
Another method for estimating terminal value is by adjusting the cap rate at the time of sale (“terminal cap rate”). Normally, terminal cap rate (“going out”) should be higher than “going in” rate. As the building gets older, its potential income decreases. Expected growth in net operating income (NOI) decreases and capital maintenance and leasehold improvement increase. Changes in interest rate level, economic growth, and risk premium will also affect the “going out” rate. If you think today’s cap rate is unusually high compared to what you expect in the future, you can actually argue for a cap rate that is lower than today’s. This must be considered optimistic, so you should be able to identify what really warrants a lower “going out” rate.
How should you make this adjustment in the cap rate? We can use a heuristic approach or we can collect transaction data for properties that are of similar age/standard and use an average of these cap rates as the estimate for going out rate at the end of the investment horizon (in this case six years).
Example 10.4
Let us assume that the investors in the real estate market in general adjust the “going out” rate upwards by 15 basis points (0.15 per cent) per year after an investment. Applying this approach, what should be the value of the property above in year 6?
First we have to find the “going in” rate. The net operating income (NOI) in year 7 is the NOI in year 6 times the growth rate (2 per cent) = 2,980,984 · (1 + 0.02) = 3,040,604. The cap rate for similar properties is 6.5 per cent. The going out rate will then be:
6.5 per cent + (6 · 0.15 per cent) = 7.4 per cent
Using the cap rate rule, we get the following TV:
The value of the property then drops to 38,000,000 from 43,600,000.
Yearly change in property value
Some investors simply assume that the value of a property follows the general inflation level (i), which implies that the terminal value of the property is worth (1 + i)t times more in year t. We then have the value of the property today (PV) and the value of the property t periods ahead, the terminal value (TV) as PV · (1 + i)t. By discounting the cash flow in the investment period and the terminal value, we can solve the equation:
Assume the inflation level is expected to be the current rent-regulation (index = 2.0 per cent) and the discount rate 6 per cent. What is the value of the property if we assume it follows the inflation level?
We have to find the expression for the terminal value (TV). In this valuation approach, the TV is the same as
Inserting for i and r, we get
Inserting this in equation 10.2, we get
The effect of leverage
In the previous section we looked at the most common methods for valuing a property. We now want to introduce leverage, which splits the capital structure into equity and debt. By replacing some of the equity with debt, we can enhance the return on equity, at least as long as the borrowing rate is less than the expected return on the property (total capital). As an equity investor you will earn the excess return over the interest rate. Furthermore, interest costs are tax deductible, making borrowing attractive. Caveat, investor! Leverage increases risk, as we will see in the following examples.
In the following we will take the property value as given and calculate the profitability of an investment at this price. We shall also look at how leverage will change the expected return, and the risk associated with use of debt.
The best way to illustrate this is by an example.
Example 10.6
Consider a commercial property project whose main data are given in the spreadsheet in figure 10.8.
Depreciation is only related to the building, so we have to separate the purchase price into land and building. Here we assume the value of the building is 80,000,000 and the value of the land 20,000,000. Furthermore, assume the depreciation method is straight line, i.e. an equal amount each year. Rent is adjusted yearly in line with the development in the inflation rate (“index”). All costs are expected to increase by the inflation rate.
Figure 10.8 Data for a commercial property.
Make a five-year investment analysis. Assume that the property will sell at the same nominal price in year 5 as we paid in year 0. The property is financed solely by equity. Find the internal rate of return. Assume all cash flows occur at the end of the year.
We start by finding the cash flow to equity.
Figure 10.9 Estimating net cash flow.
Most cells are calculated straightforwardly; except the cash flow in year 5. Here we have to add the cash flow from the sale to the year-end cash flow. The first part of the formula in cell F30
“F25+F28–IF(F26<0;0;F26)”
is the ordinary cash flow from operation (net operating cash flow). The IF-function is used in order to avoid negative payable tax (you can have negative tax, i.e. the government owes you, but only in accounting terms for future deductions in taxable income). The second part
“(B2–B9)–(B2–(B1–SUM(B28:F28)))*B8”
is the net cash flow from sale. B2 is the sale price from which we have to deduct the capital gain tax. The capital gain is the sale price (B2) minus the book value of the property in year 5, which is the purchase price minus the depreciation during the holding period; (“B1–SUM(B28:F28)”). The tax rate (28 per cent) is in cell B8. If the property is financed by any debt, we have to deduct this (cell B9) in order to get the cash flow to equity. In this case no debt is used.
We can now use the function internal rate of return (IRR) (figure 10.10).
Figure 10.10 Estimating the internal rate of return with no debt.
The internal rate of return is 4.5 per cent after tax.
Let us see what happens if we introduce debt.
Example 10.7
We use the same property as above, but substitute 80,000,000 of equity with debt, implying a debt level of 80 per cent of total capital. Calculate the return on capital as measured by the internal rate of return.
We find the cash flow after interest and taxes (figure 10.11).
The equity part of the purchase price was 20,000,000, which gives us the internal rate of return after tax shown in figure 10.12.
Use of debt increases the return as long as the (unleveraged) return on the property is higher than interest paid on the debt (here 5 per cent). We should expect return on property to be greater than the cost of debt financing since the equity investor risks more than the lender. The lender has the priority to the cash flow and can also take possession of the property if the borrower fails to fulfil its obligations (defaults).
Let us see what happens if the interest rate jumps to 8 per cent, all other parameters unchanged. Then interest costs become larger than the return on the asset. This is called negative leverage and any use of debt reduces the return on equity. The internal rate of return drops to minus 3.1 per cent (figure 10.13).
Why would anyone want to use debt in the case of negative leverage? There could be several reasons, but the two most common are expectations of higher rents or a jump in the resale price (the latter could be related to the former). Leverage will then magnify the return on equity if property values rise. Let us look at two examples.
Figure 10.11 Estimating the cash flows with 80 per cent debt financing.
Figure 10.12 Estimating the internal rate of return with 80 per cent debt financing and interest rate of 5 per cent.
Figure 10.13 Estimating the internal rate of return with 80 per cent debt financing and interest rate of 8 per cent.
Assume an investor expects that the real estate market will improve and prices increase by 30 per cent over the next five years. This implies a terminal value of 100,000,000 · (1 + 0.30) = 130,000,000. Let us look at the difference in internal rate of return in two different cases, one without leverage and another one with five times leverage (80 per cent debt to capital ratio).
We use the previous spreadsheet but enter a new sales price. A 30 per cent increase in the value of property implies a sale price of 130,000,000. Keeping all other variables unchanged, the unleveraged investor can expect an internal rate of return of 8.2 per cent (figure 10.14).
Figure 10.14 Estimating the internal rate of return with 30 per cent increase in property price and no debt financing.
Leverage will magnify the return depending on the leverage level. If we again assume a leverage of five times (80 per cent debt to total capital), the internal rate of return jumps to 22.5 per cent.
Figure 10.15 Estimating the internal rate of return with 30 per cent increase in property price and 80 per cent debt financing.
Of course, leverage works both ways. If the property price falls to 80,000.000, the internal rate of return falls to minus 9.8 per cent or minus 18.2 per cent depending on whether the investor can use the tax deductibility of the capital loss from selling at 80,000,000 (figure 10.16).
Figure 10.16 Estimating the internal rate of return with 20 per cent decrease in property price and 80 per cent debt financing.
If the investor cannot use the loss against other tax gains, we must construct a formula that takes this into account. We therefore add another IF-condition (bold in formula) in cell F30:
If there is a capital loss and the investor cannot deduct the capital loss, this will not be added to the cash flow.
When we have negative internal rates of return, it makes more sense to look at absolute return (“cash on cash”). A loss of 50 per cent will translate into a negative internal rate of “only” minus 7 per cent if it is recognized 10 years from now. If it is recognized after one year, the internal rate of return will be minus 50 per cent. This might encourage money managers that are rewarded for a high internal rate of return to postpone any losses (and push forward any gains).
If the property purchase is leveraged, the investment above will return 10,321,453 of cash (sum of all cash flows undiscounted) during the five years (including divestment) from an investment of 20,000,000.
10.4 Summing it all up
In most of the examples we have used the internal rate of return method. This is quite common in real estate investments analysis. There are some drawbacks to the internal rate of return, as we have discussed earlier in the book. The internal rate of return does not tell us whether the investment is profitable. It only tells us at which discount rate the net present value of the investment becomes zero, i.e. just profitable. If the estimated internal rate of return is less than our required rate of return for an investment of similar risk, then we should forgo the investment.
So how do we find the required rate of return? In real estate investing many investors just use some heuristic rules when estimating the cost of capital. They typically add some risk premium to the risk-free rate (government bond). Others use a weighted yield of corporate bonds with the same maturity as the investment in question analysis and add some risk premium for real estate ownership. Others use the approach from the Capital Asset Pricing Model.
An investment analysis in real estate thus sums up to the following steps.
1 Estimate the net operating income (net cash flows).
2 Select an investment horizon, most typically when the majority of lease contracts expire.
3 Determine a proper required rate of return for the investment horizon.
4 Estimate the terminal value (reversion value) at the end of the investment horizon.
You then calculate the net present value to see if the project returns a positive number.
All investment analysis is only as good as the estimates that are entered into the model. You should therefore always do some sensitivity/scenario analysis or simulations to see the possible outcomes (risks) associated with the investments. And you should do a careful examination of the realism of the estimated inputs (revenues, operating costs).
Problems
10-1. Consider a project for developing a hotel.
First-year occupancy is expected to be 50 per cent, second year 55 per cent and then 60 per cent for all future years. There is a plan for selling the hotel, including furniture etc., in five years for 80,000,000 (plus inflation). Tax on capital gain can be netted against asset category with 20 per cent depreciation (see chapter 9) with the entire sales price. Use 365 days per year. Assume 3 per cent yearly inflation for the next five years. Also assume there are other revenues for tax deduction purposes. Use a nominal cost of capital of 10 per cent to find the net present value of the project. Be careful to include all tax effects (such as depreciation and capital gain). Also find the project’s internal rate of return.
10-2. A property has a net operating income of 500,000 at the start of the year. The property has secured a long-term lease and its rent is adjusted with the change in inflation, which is expected to be 3 per cent per year. In year 5 the property is to be sold at an expected going out yield of 8 per cent. What is the expected value of the property? Use a cost of capital of 12 per cent.
10-3. You are offered a property for 8,500,000. The building represents 80 per cent of the value for tax purposes. Rent at the start of the first year is 700,000, and the rent will be adjusted according to the inflation rate, which is expected to be 3 per cent per year. You can finance the property with 35 per cent equity and 65 per cent debt which carries a fixed interest rate of 6 per cent for the next five years. The loan is amortized over 25 years with monthly payments. The building is linearly depreciated over 50 years, and it will require a reinvestment rate of 5 per cent. In year 5 the property is expected to be sold for the same nominal value as the purchase price. There will be selling costs of 2 per cent. The tax rate is 28 per cent. Disregard any depreciation recapture. Use a cost of capital of 12 per cent. Based on the assumptions above, should you buy the property? At which cost of capital is the investment worthwhile? What will be the present value if the “going out” rate is 6 per cent?
10-4. A portfolio of 200 apartments is for sale. The monthly rent per apartment is 1,250. The rent is adjusted annually in line with the inflation rate, expected to be 3 per cent a year. Vacancy rate is estimated at 3 per cent and credit loss at 1 per cent a year. Insurance costs are 120 per unit, and repair & maintenance is 400 per unit per year. Utilities and miscellaneous cost are expected to be 1.5 per cent and 0.5 per cent respectively. For the sake of simplicity, disregard taxes. In year 5 you want to sell the portfolio at an expected 9 per cent “going out” rate (terminal rate). Using a cost of capital of 11 per cent to find the (maximum) price, should you buy the portfolio?
10-5. Build 2 Last Properties Ltd considers buying an office property. Next year’s cash flow is expected to be 2,000,000. Rent is expected to increase by 4 per cent per year for the foreseeable future. Build 2 Last Properties has a 10-year investment horizon for the investment. Based on surveys of sales of other office buildings that are now 10 years older than the building in question, the going out cap rate should be around 10 per cent. If Build 2 Last Properties applies a cost of capital of 12 per cent, what is the estimated value of the property? Calculate the “going in” rate at this price.
10-6. You are reviewing a small portfolio of retail outlets. The price is 15,000,000 and the potential gross rent is 2,000,000. The rent is projected to increase with an estimated sales growth of 4 per cent per year. Collection losses and vacancy are expected to be 10 per cent of gross potential income. Operating expenses will be 30 per cent of potential gross income. The portfolio can be financed with 70 per cent debt at 8 per cent interest rate amortized over 40 years. The market value of the portfolio is expected to increase in line with an expected inflation rate of 3 per cent a year. If the portfolio is sold after year 5, what will the internal rate of return before tax be? Find out whether the portfolio is a good investment at a cost of capital of 14 per cent.
10-7. You are trying to find a reasonable price for a property based on comparable transactions. Using the gross income multiplier, find the value of a property when there have been the following comparable property transactions recently in the same area. You have to compute the blank fields in the bottom row to answer the question.
10-8. You are trying to find a reasonable price for a property based on comparable transactions. This time you want to use the capitalization rate. Find a reasonable price for the potential property below. You have to compute the blank fields in the two bottom rows to answer the question.
