Dr. NICHOLAS WATSON

Internal Rate Of Return - IRR

 

The Internal Rate of Return is the interest rate that makes the Net Present Value zero.

 

The discount rate often used in capital budgeting that makes the net present value of all cash flows from a particular project equal to zero. Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake the project. As such, IRR can be used to rank several prospective projects a firm is considering. Assuming all other factors are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.

 

IRR is sometimes referred to as "economic rate of return (ERR)."

 

You can think of IRR as the rate of growth a project is expected to generate. While the actual rate of return that a given project ends up generating will often differ from its estimated IRR rate, a project with a substantially higher IRR value than other available options would still provide a much better chance of strong growth.

 

Decision Rule

 

A project should only be accepted if its IRR is NOT less than the target internal rate of return. When comparing two or more mutually exclusive projects, the project having highest value of IRR should be accepted.

 

IRR Calculation

 

The calculation of IRR is a bit complex than other capital budgeting techniques. We know that at IRR, Net Present Value (NPV) is zero, thus:

 

NPV = 0; or

 

PV of future cash flows − Initial Investment = 0; or

 

 CF1 +         CF2 +         CF3 + ...  − Initial Investment = 0

( 1 + r )1 + ( 1 + r )2  + ( 1 + r )3

 

Where,

   r is the internal rate of return;
   CF1 is the period one net cash inflow;
   CF2 is the period two net cash inflow,
   CF3 is the period three net cash inflow, and so on ...

 

But the problem is, we cannot isolate the variable r (=internal rate of return) on one side of the above equation. However, there are alternative procedures which can be followed to find IRR. The simplest of them is described below:

 

• Guess the value of r and calculate the NPV of the project at that value.

• If NPV is close to zero then IRR is equal to r.

• If NPV is greater than 0 then increase r and jump to step 5.

• If NPV is smaller than 0 then decrease r and jump to step 5.

• Recalculate NPV using the new value of r and go back to step 2.

 

Example

 

Find the IRR of an investment having initial cash outflow of $213,000. The cash inflows during the first, second, third and fourth years are expected to be $65,200, $96,000, $73,100 and $55,400 respectively.

 

Solution

Assume that r is 10%.
NPV at 10% discount rate = $18,372
Since NPV is greater than zero we have to increase discount rate, thus
NPV at 13% discount rate = $4,521
But it is still greater than zero we have to further increase the discount rate, thus
NPV at 14% discount rate = $204
NPV at 15% discount rate = ($3,975)
Since NPV is fairly close to zero at 14% value of r, therefore
IRR ≈ 14%

 

Watch These Two Videos Below for IRR Calculations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NOW GO HERE TO LOOK AT FURTHER EXAMPLES

 

 

 

Average Return on Book Value

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Some companies judge investments based on their book rate of return.

To compute this, we calculate the average forecasted accounting profits and divided it by the average book value of the investment. This ratio is then compared to some industry average.

 

Consider the following project:

 

An initial investment of $9000 is made to purchase some assets; these are depreciated using straight line depreciation over 3 years to $3000; at the end of 3 years, the project terminates and the assets are sold at book value. The flows in each of the 3 periods are as follows:

 

Year                                                              1                                   2                                                3

 

Revenue                                                   12000                            10000                                         8000

Out of pocket costs                                     6000                              5000                                         4000

Depreciation                                              2000                               2000                                         2000

Profits before tax                                       4000                               3000                                         2000

Tax at 25%                                                1000                                 750                                           500

Net Income after tax                                  3000                                2250                                         1500

Cash flows                                                 5000                                 4250                                        3500 + 3000

Book Value of assets at beginning of year   9000                                7000                                         5000

Book Value of assets at year end                 7000                                5000                                        3000

Average Book Value                              (9000+7000)/2                  (7000+5000)/2                       (5000+3000)/2
                                                                  = 8000                              =6000                                       =4000
 

The average book value equals  8000 + 6000 + 4000 = 6000

                                                                3

 

 

The average net income equals 3000 +2250 + 1500 = 2250

                                                                3

 

 

The average return on book value is 2250/6000 = 37.5%.

 

The NPV (at 20%) is $1879.63.

 

Problems with the accounting rate of return method:

 

It depends heavily on how accountants determine costs. As we know, depreciation is not really an out of pocket cost, but it is treated as a cost by accountants; similarly, some items may be capitalized and others expensed according to non-economic rules. Hence the resulting profit number may be very different from the cash flows.

 

• Distant cash flows are given too much weight, because a simple average of book return over all years, is taken.

• Determination of the cut-off rate is ad hoc and difficult.

 

Can the accounting rate of return be justified?

 

Accounting rate of return numbers have to be computed anyway, and the data is easily available and is comprehensible.

The different projects encountered by the firm may be relatively similar in terms of their structure (e.g. depreciation), and accounting treatment. In such a case, if an industry or a firm benchmark is used, the resulting decisions are likely to be correct.

Watch Summary Calculations Below

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Profitability Index

 

The profitability index is defined as PI = -PV/C0.  It is an index that attempts to identify the relationship between the costs and benefits of a proposed project through the use of a ratio calculated as:

 

 

 

A ratio of 1.0 is logically the lowest acceptable measure on the index. Any value lower than 1.0 would indicate that the project's PV is less than the initial investment. As values on the profitability index increase, so does the financial attractiveness of the proposed project.

 

Watch this summary

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Decision Rule

 

Accept a project if the profitability index is greater than 1, stay indifferent if the profitability index is zero and don't accept a project if the profitability index is below 1.

 

Profitability index is sometimes called benefit-cost ratio too and is useful in capital rationing since it helps in ranking projects based on their per dollar return.

 

Example

Company C is undertaking a project at a cost of $50 million which is expected to generate future net cash flows with a present value of $65 million. Calculate the profitability index.

 

Solution

Profitability Index = PV of Future Net Cash Flows / Initial Investment Required
Profitability Index = $65M / $50M = 1.3
Net Present Value = PV of Net Future Cash Flows − Initial Investment Rquired
Net Present Value = $65M-$50M = $15M.

The information about NPV and initial investment can be used to calculate profitability index as follows:

Profitability Index = 1 + (Net Present Value / Initial Investment Required)
Profitability Index = 1 + $15M/$50M = 1.3

 

 

 

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