DCF Analysis: Unveiling NPV & IRR in Real Estate

Chapter Title: DCF Analysis: Unveiling NPV & IRR in Real Estate

Introduction

This chapter delves into the core principles of Discounted Cash Flow (DCF) analysis, specifically focusing on its application within the real estate investment domain. We will explore two critical metrics derived from DCF: Net Present Value (NPV) and Internal Rate of Return (IRR). These metrics are indispensable tools for evaluating the profitability and feasibility of real estate projects, allowing investors to make informed decisions based on the time value of money.

1. Foundations of Discounted Cash Flow (DCF) Analysis

DCF analysis is a valuation method that estimates the value of an investment based on its expected future cash flows. It operates on the fundamental principle that money received today is worth more than the same amount received in the future, due to its potential earning capacity. This concept is known as the time value of money.

1. Time Value of Money:
   • The time value of money arises due to factors like inflation, opportunity cost, and risk.
   • Inflation erodes the purchasing power of money over time.
   • Opportunity cost represents the potential return from alternative investments.
   • Risk reflects the uncertainty associated with future cash flows.
2. Key Components of a DCF Analysis:
   • Projected Cash Flows: Estimating the magnitude and timing of future cash inflows and outflows.
     • Categories to be addressed in DCF analysis include:
       • Current market rental rates, lease expiration dates, and expected rental rate changes
       • Lease concessions and their effect on market rent
       • Existing base rents and contractual base rent adjustments
       • Lease extensions and renewal options
       • Existing and anticipated expense recovery (escalation) provisions
       • Tenant turnover
       • Vacancy loss and collection allowance
       • Operating expenses and changes over the projection period
       • Net operating income
       • Capital items including leasing commissions and tenant improvement allowances
   • Discount Rate: Determining the appropriate rate to discount future cash flows back to their present value.
     • Reversion and any selling or transaction costs
     • A discount or yield rate (or rates)
   • Terminal Value (Reversion): Estimating the value of the property at the end of the projection period.
     • Reversion and any selling or transaction costs

3. Mathematical Representation:

   The present value (PV) of a future cash flow (CF) received n years from now, discounted at a rate r, is calculated as:

   PV = CF / (1 + r)^n

   Where:

   • PV = Present Value
   • CF = Cash Flow
   • r = Discount Rate
   • n = Number of Years

2. Net Present Value (NPV): A Dollar Reward

NPV is a metric that quantifies the difference between the present value of expected cash inflows and the present value of expected cash outflows associated with an investment. It directly measures the value added to the investor by undertaking the project.

1. NPV Calculation:

   • Calculate the present value of each individual cash flow (both inflows and outflows) using the chosen discount rate.
   • Sum all the present values of inflows.
   • Sum all the present values of outflows (usually the initial investment).
   • Subtract the sum of the present values of outflows from the sum of the present values of inflows.

   Net present value (dollar reward) is the difference between the present value at a desired yield (discount) rate of all positive cash flows and the present value of all negative cash flows, or capital outlays.
   2. NPV Decision Rule:
   * NPV > 0: The investment is considered acceptable because it is expected to generate a return exceeding the required rate of return (discount rate). It increases the investor’s wealth. When the present value of the positive cash flows is greater than the present value of the negative cash flows or capital outlays, the investment exceeds the return requirements of the investor.
   * NPV < 0: The investment is considered unacceptable because it is expected to generate a return lower than the required rate of return. It decreases the investor’s wealth. If the reverse relationship exists (i.e., negative cash flows are greater than positive cash flows), the investment is not considered feasible at the desired yield, or at least not at the discount rate used to calculate present value. However, other investors may find the investment feasible.
   * NPV = 0: The investment is expected to generate a return equal to the required rate of return. It neither increases nor decreases the investor’s wealth. A net present value of zero indicates that the present value of all positive cash flows equals the present value of all negative cash flows or capital outlays at the discount rate.
   3. Mathematical Representation:

   The NPV is calculated using the following formula:

   NPV = Σ [CFt / (1 + r)^t] - Initial Investment

   Where:

   • NPV = Net Present Value
   • CFt = Cash Flow in period t
   • r = Discount Rate
   • t = Time period (year)
   • Σ = Summation operator (summing cash flows over all periods)

2. Example:
   Suppose that a property with an anticipated present value of $1.1 million for all investment returns over a 10-year projection period can be purchased for $1.0 million. If one investor’s NPV goal is $0, this investment exceeds that criterion. It also meets a second investor’s goal for an NPV of $100,000, but it would not qualify if the goal were $150,000.

3. Limitations of NPV:
   Net present value considers the time value of money, and different discount rates can be applied to different investments to account for general risk differences. However, this method cannot handle different required capital outlays. For example, it cannot differentiate between an NPV of $100,000 on a $1,000,000 capital outlay and the same NPV on a $500,000 capital outlay. Therefore, this technique is best used in conjunction with other measures.

   • The hurdle rate analysis is a common example of the use of an NPV analysis. Some investors use a stated yield rate, which is the minimum acceptable rate of return for that investor, to determine the extent to which a potential investment can exceed that minimum. If there is a surplus of NPV above zero to justify further at- tention, the investor can then spend the time and resources to pursue a more precise estimate of potential investment yield if the investment otherwise appears to be worth the exercise.

3. Internal Rate of Return (IRR): The Breakeven Discount Rate

IRR is the discount rate that makes the NPV of all cash flows from a particular project equal to zero. It represents the effective rate of return that an investment is expected to yield.

1. IRR Definition:
   The rate of discount that makes the net present value of an invest- ment equal zero is the internal rate of return. In other words, the IRR is the rate that discounts all returns from an investment, including returns from its termination, to a present value that is equal to the original investment.

   The IRR is the discount rate, r, for which:

   0 = Σ [CFt / (1 + r)^t] - Initial Investment
   Solving this equation for r gives the IRR. It typically requires iterative numerical methods or financial calculators/software.
   2. IRR Decision Rule:
   * IRR > Required Rate of Return: The investment is considered acceptable, as its expected rate of return exceeds the minimum required rate.
   * IRR < Required Rate of Return: The investment is considered unacceptable, as its expected rate of return is lower than the minimum required rate.
   * IRR = Required Rate of Return: The investment is expected to generate a return equal to the required rate.
   3. Practical Application:
   As a simple example of calculating the internal rate of return, consider the in- come data in Table 27.1. The internal rate of return of 11.37% can be calculated using the following HP-12C financial calculator keystrokes:
   1,600,000 (9) 100,000 [9] 5,000 [g] 110,000 [9] 115,000 [9] 2,330,000 [9] [IRR].
   4. Multiple IRR:

More than one internal rate of return is only possible with the presence of nega- tive cash flows. Consider a real estate investment in which the investor puts down $23,000, borrows $100,000, and pays 10% interest only, with the principal to be repaid in a lump sum at the end of 10 years. The investor’s net cash flows can then be tabu- lated as shown in Table 27.2.
* Conditions Leading to Multiple IRRs:
* The search for a single IRR within a plausible range is not always successful. Unusual combinations of cash flows may produce strange results, and more than one IRR—or, in rare cases, no IRR—may be indicated.
In real estate investment analysis, the presence of multiple internal rates of return usually suggests that some other measure of performance (usually net present value analysis) would be more appropriate or that the cash flows or the time frame should be adjusted to permit a more meaningful analysis.

5. Negative Net Present Value at Zero Rate of Return:

The cumulative value of the net cash flows in Table 27.2 is negative. Negative net cash flows total $43,000, while positive net cash flows total $40,000. Therefore, the net present value—i.e., the difference between the present value of expected benefits, or positive cash flows, and the present value of capital outlays, or negative cash flows— with no discounting or at a zero discount rate is -$3,000, as shown in Figure 27.2. This should be a warning sign to an analyst.
Under these conditions, the internal rate of return cannot be positive unless the mixture of positive and negative cash flows over time is such that the net present value increases with increases in the discount rate until the net present value reaches zero. This type of reverse discounting is mathematically valid, but it is contrary to the practical notion of reducing net present value by increasing the discount rate. It is not surprising that, in cases like this, the internal rate of return is difficult to comprehend and of questionable use.

6. Important Statements:

For a given discount rate (Y), the following statements apply:
e If the present value (PV) of future benefits is greater than the capital outlay (CO), the net present value (NPV) is greater than zero and the internal rate of return (IRR) is greater than the discount rate.
e If the present value of future benefits is less than the capital outlay, the net present value is less than zero and the internal rate of return is less than the discount rate.
e If the present value of future benefits is equal to the capital outlay, the net present value equals zero and the internal rate of return is equal to the discount rate.

The formulas are: If PV of future benefits > CO — NPV > 0 and IRR > Y If PV of future benefits < CO — NPV < 0 and IRR < Y If PV of future benefits = CO > NPV = 0 and IRR =Y

7. Negative IRR:
   If the net present value of an investment at a 0% rate of return is negative, a nega- tive internal rate of return may be indicated. The IRR is generally understood to be a positive rate of return, but a negative IRR may be interpreted as a rate of loss. Any prospective rate of loss will normally discourage capital investment.
   The concept of a negative internal rate of return has theoretical, as well as practical, limitations. A glance at the IRR equation reveals that a negative IRR of 100% or more has no meaning because it involves division by zero or powers of a negative number.

8. Little or No Equity:
   Because the internal rate of return is a measure of the return on invested capital, it cannot be used to measure the performance of opportunities that require no invest- ment of capital. Some investments can be “financed out”—i.e., financed with loans that cover 100% or more of the capital required. If the projected net cash flows are all positive, there is no IRR. Obviously, no discount rate can make a series of exclusively positive benefits equal zero.
   The same rationale can be applied to investments calling for very low equity or a very small down payment in relation to expected returns. For example, a profit of $1 on an investment of $1 amounts to a 100% rate of return. A return of $100 on an invest- ment of $1 indicates a 10,000% rate of return. When the investment is very small, slight changes in income can cause astronomical changes in the rates of return and loss. The internal rate of return is an impractical yardstick for these sorts of investments.
   However, the IRR can be a valuable indicator in analyzing investments that are 100% financed at the start and are expected to operate at a loss for a period of time. In these arrangements, the early negative cash flows may represent a significant invest- ment of equity capital, and the prospective IRR may be the best measure of perfor- mance. It may also be useful to compare the prospective IRR before financing with an interest rate that reflects the cost of capital. The difference can be used as a measure of prospective leverage.

4. Reinvestment Concepts

Reinvestment Concepts The internal rate of return on the capital within an investment can be applied to a single property or to an entire investment portfolio. No assumption is made as to how the investor actually employs funds that are received during the investment’s owner- ship. The income from a real estate investment may be reinvested in another project at another rate of return, stored in a vault, or spent, but the IRR is not affected. Regard- less of whether or not an investor in fact reinvests capital withdrawn from the invest- ment at any given rate, a defining characteristic of the internal rate of return is that it is mathematically consistent with reinvestment at the same rate of interest as the IRR. This establishes a framework for distinguishing between the internal rate of return and other measures of investment return that make explicit reinvestment assumptions. Incorporating a reinvestment concept in investment analysis is useful when viewing returns within the context of overall portfolio performance. It is a funda- mental concept of finance that to calculate a rate of return on an investment and to compare two or more alternative investments, all of the funds in an investment must be considered over the entire period of analysis. Income-producing real estate typi- cally generates both a return on and a return of the invested capital over the life of the investment. The rate of return can differ with various reinvestment assumptions.

As described earlier, there are potential problems with the concept of an internal rate of return, but its use does not force any particular reinvestment assumptions, even though it is consistent with reinvestment at the same rate as the IRR.

As discussed above, one problem associated with the internal rate of return is that certain situations (such as negative cash flow) can produce mathematical results that support more than one rate. A different rate of return concept with a specific re- investment premise is sometimes used to avoid multiple IRRs. Although the assump- tion of a specific reinvestment rate other than the IRR does not result in an internal rate of return, reinvestment assumptions are applied in a number of rate of return concepts that make up a family of IRR-related measures.

The IRR with reinvestment is based on the expectation that all income from a proj- ect can be immediately reinvested at a specified rate and left to grow at that rate until the end of the investment projection period. The combined results of the investment’s earnings and reinvestment are then reflected in one overall rate of return. The IRR with reinvestment traces the expected total performance of the original capital sum at work in more than one investment, rather than ignoring what occurs with portions of the capital investment during the ownership period. This measure can also be used to prevent multiple solutions to the internal rate of return equation. The IRR with reinvestment is often called the adjusted or modified IRR (AIRR or MIRR).

As an example, consider the series of equity cash flows with a reinvestment rate for positive cash flows of 6% shown in Table 27.4. The sum of the future values of the posi- tive cash flows is $473,208. Comparing the future value with the present value of the ini- tial investment using a financial calculator will give an equity MIRR of 13.61% with the reinvestment rate of 6%, which is lower than the IRR of 14.8%. Using the IRR of 14.8% as the reinvestment rate in the calculations of MIRR would give an MIRR of 14.8%.

The IRR with a specified borrowing rate is another variation of the internal rate of return that can be used to prevent multiple rates. It is sometimes called the IRR for investment or financial management rate of return (FMRR). The IRR for investment specifies an interest rate for the borrowed funds needed during the period when the investment is producing negative cash flows. As with other rates derived from the internal rate of return, the FMRR recognizes that there are different risks and poten- tial earnings that apply to the funds withdrawn from the original investment. The concept of financial management indicates that lower rates will be paid on borrowed funds and that risk management will permit the investor to eventually earn a higher rate of return on the real estate investment. Again, to derive the FMRR, the entire amount of invested capital is analyzed over the life of the real estate investment, as is the case with other rates that assume reinvestment (AIRR and MIRR).

As an example of the calculation of an FMRR, consider the series of cash flows in Table 27.5, which have an IRR of 21.47%. In this scenario, the cash flow of Year 2 is reduced by $23,810, which is invested at a safe rate of 5% to cover the $25,000 outlay in Year 3. Furthermore, the $100,00 outlay at the end of Year 1 is discounted at the safe rate to be accounted for as part of the initial investment. Finally, the positive cash flows are compounded at an appropriate rate—in this case, 7.5% was used—and the financial management rate of return can then be calculated as 17%.

5. Applicability

The internal rate of return can be as important to the real estate investor as the interest rate is to the mortgage lender. In fact, the two measures are equivalent. The interest rate on a mortgage is the same as the mortgagee’s yield, or the internal rate of return, unless points or other payments such as prepayment penalties are involved. The inter- nal rate of return is not a meaningful measure of all investments and, even when it is meaningful, it is not the only possible criterion. It is, however, a fundamental and pure measure of a particular investment’s financial performance. In general, the internal rate of return is a valuable analytical tool if the decision maker understands its attributes and limitations and has access to complementary or alternative analytical techniques.

6. Other Measures of Performance

Other Measures of Performance
Popular alternative measures of financial performance or profitability include
e Payback period
e Profitability index or benefit/cost ratio
e Time-weighted rate
These yardsticks do not measure performance or profit on the same scale or under the same assumptions as the internal rate of return. Their usefulness depends on the
situation and the user’s preferences. Neither the internal rate of return nor any alter- native measure is superior in all situations.
1. Payback Period
Payback Period As a measure of investment return, the payback period is seldom used alone. It is commonly employed in conjunction with other measures such as the internal rate of return. The payback period (PB) is defined as the length of time required for the stream of net cash flows produced by an investment to equal the original cash outlay. The breakeven point is reached when the investment’s cumulative income is equal to its cumulative cost or loss. The payback period can be calculated from either before- tax or after-tax cash flows, so the type of cash flow selected should be identified. The equation for payback period may be expressed as follows:
_ Capital Outlay
Annual Net Cash Flows
Because real estate appraisers typically account for income as if received annually at the end of the period, full payback is not considered to occur until the end of a year. Therefore, the payback period indicated by the prior equation will be rounded up to a whole number, i.e., to the end of the next year.
This measure of performance is used by investors who simply want to know how long it will take them to recapture the funds they have invested. In theory, an invest- ment with a payback period of three years would be preferable to one with a payback period of five years, all else bein

Conclusion

NPV and IRR are powerful tools for evaluating real estate investments within the DCF framework. While IRR offers a rate-of-return perspective, NPV provides a direct measure of value creation. Understanding the limitations of each metric, particularly regarding reinvestment rate assumptions and the potential for multiple IRRs, is crucial for sound decision-making. Employing these tools in conjunction with other investment analysis techniques enables a more comprehensive assessment of real estate opportunities.