INTERNAL RATE OF RETURN (IRR)

The internal rate of return (IRR) is that discount rate of a total discounted cash flow that produces a net present value (NPV) of 0. That is, the NPV of all income and benefits exactly equals the NPV of all costs and outgoings. Therefore, IRR can only be calculated for a cash flow that includes both positive and negative cash flows.

EXAMPLE

The cash flow for a complete project (iland value, stamp duty and legal on purchase) is discounted until the NPV = 0:

TABLE 1


 QUARTERS $'000 TOTALS 
 ITEM  0
1 2
3
4
5
LAND VALUE: (178.24)




(178.24)
STAMP DUTY & LEGAL:
(6.42)





(6.42)
CONSULTANTS' FEES

(0.35) (2.10) (3.10) (3.30) (1.05) (9.90)
CONSTRUCTION COSTS: Building 1  (2.00)
(4.00)
(20.00) (30.00) (11.00) (1.00)
(68.00)
Building 2

(1.00) (12.00) (18.00) (25.00) (10.00) (66.00)
Building 3 
(2.00) (10.00) (14.00) (30.00) (10.00) (66.00)
GROUND IMPS etc:



(6.00) (12.00)  
 (18.00)
ADVERTISING: 



(0.20) (0.40) (0.60)
SELLING COSTS:



(4.80) (10.20) (4.80) (19.80)
HOLDING CHARGES:  (1.00)
(1.00)
(1.00)

(3.00)
END MARKET VALUE:




160.00
340.00 500.00
TOTALS:  (187.66) (7.35) (45.10) (69.90)
73.30 300.75
248.70
DISCOUNT FACTORS:  (rounded) 1.000
0.952
0.907
0.864
0.823 0.784
DISCOUNTED CASH FLOWS: (187.66) (7.00) (40.91) (60.38)
60.30
235.65
NET PRESENT VALUE (NPV) = sum of DCFs:  0.00






The internal rate of return (IRR) is that rate of interest which equates the present value of benefits and costs. Therefore, internal rate of return of a discounted cash flow is that discount rate which causes a NPV = 0. In the above table the IRR is 20% per annum.

The IRR is a common and useful measure of the rate or return of all investments and therefore, when used for real estate analysis can be compared with outside investments. For example, government riskfree bond rates. An important advantage of IRR is as the name implies, is that it does not require the input of any external discount rate for example, cost of money. It is calculated solely from the cash flow. From an alternative perspective, the IRR approach reverses the procedure used to calculate the Net Present Value (NPV).

Instead of computing the NPV at a predetermined discount rate, the IRR is found by determining the discount rate which will have a NPV=0.

PROBLEMS WITH THE IRR METHOD
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The IRR method can be a misleading guide when alternative projects differ in scale.

EXAMPLE

The two projects below are strict alternatives to one another.

Project A has an investment cost of 1 000 and is expected to generate a net income of 300 pa in perpetuity.
Project B has an investment cost of 5 000 and is expected to generate a net income of 1 000 pa in perpetuity:

TABLE 2

NET BENEFIT PROFILE OF 2 ALTERNATIVE PROJECTS
YEAR
0
1
2
3
4 ..................
n
PROJECT A:
(1000)
300
300
300
300

300
PROJECT B:  (5000) 1000
1000
1000
1000

1000








IRR PROJECT A:
30%





IRR PROJECT B:  20%













At 10%pa:






NPV PROJECT A =  2 000





NPV PROJECT B =
5 000






Which is the better project?

Using IRR, project A should be recommended. However, the NPV of project A is less than that for project B. Therefore, since the NPV rule is superior in this case, project B should be selected, not project A.

The IRR can mislead where projects have different lengths of life. A project where income and benefits accrue soon after the end of the investment period may yield a higher IRR than one where benefits accrue later but in larger amounts. Use of NPV in this situation overcomes this bias.

A problem of a different kind arises when the decision maker is selecting a portfolio of projects subject to a budget constraint. Under the NPV criterion, the rule is to select that set or package of projects which maximises total NPV subject to the constraint. IRRs are ordinal, not cardinal measures and therefore, cannot be summed. Any attempt to put projects on a common basis, for example by calculating the IRR per dollar of cost is still subject to same scale and length asymmetry problems.

If a project has a time profile of net benefits that crosses zero more than once (eg staged projects), it will usually not be possible to determine a unique rate of return. Large construction projects fall into this category. Similarly, mining projects often have cash outflows in their final years, because of land reclamation and reafforestation costs to meet environmental requirements. If the IRR rate is high (eg greater than 30%) then the method inherently leads to error. This is because it discounts the loss of interest on monies spent in the cash flow at the unrealistically high rate.

However, in most real estate feasibility studies and valuations the IRR is not that large and therefore, the error caused by the "reinvestment problem" is much less than other, for example, forecasting errors. The above "problems" in using IRR are generally, not serious enough to undermine its use in real estate investment analysis and valuations. If used sensibly, it is the best overall measure of the rate of return and is commonly used to value all types of financial investments as well as real estate. However, it is good practice to determine the IRR, NPV and NPV rate of return, using one as a check on the others.
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