Internal rate of return (IRR)

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#### Md. Al-Amin ##### Internal rate of return (IRR)
« on: February 22, 2014, 03:11:39 PM »
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What it is:

Internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero.

Internal rate of return is used to evaluate the attractiveness of a project or investment. If the IRR of a new project exceeds a company’s required rate of return, that project is desirable. If IRR falls below the required rate of return, the project should be rejected.

How it works/Example:

The formula for IRR is:

0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n

where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and
IRR equals the project's internal rate of return.

Let's look at an example to illustrate how to use IRR.

Assume Company XYZ must decide whether to purchase a piece of factory equipment for \$300,000. The equipment would only last three years, but it is expected to generate \$150,000 of additional annual profit during those years. Company XYZ also thinks it can sell the equipment for scrap afterward for about \$10,000. Using IRR, Company XYZ can determine whether the equipment purchase is a better use of its cash than its other investment options, which should return about 10%.

Here is how the IRR equation looks in this scenario:

0 = -\$300,000 + (\$150,000)/(1+.2431) + (\$150,000)/(1+.2431)2 + (\$150,000)/(1+.2431)3 + \$10,000/(1+.2431)4

The investment's IRR is 24.31%, which is the rate that makes the present value of the investment's cash flows equal to zero. From a purely financial standpoint, Company XYZ should purchase the equipment since this generates a 24.31% return for the Company --much higher than the 10% return available from other investments.

A general rule of thumb is that the IRR value cannot be derived analytically. Instead, IRR must be found by using mathematical trial-and-error to derive the appropriate rate. However, most business calculators and spreadsheet programs will automatically perform this function.

[Click here to see How to Calculate IRR Using a Financial Calculator or Microsoft Excel]

IRR can also be used to calculate expected returns on stocks or investments, including the yield to maturity on bonds.  IRR calculates the yield on an investment and is thus different than net present value (NPV) value of an investment.

Why it Matters:

IRR allows managers to rank projects by their overall rates of return rather than their net present values, and the investment with the highest IRR is usually preferred.  Ease of comparison makes IRR attractive, but there are limits to its usefulness. For example, IRR works only for investments that have an initial cash outflow (the purchase of the investment) followed by one or more cash inflows.

Also, IRR does not measure the absolute size of the investment or the return. This means that IRR can favor investments with high rates of return even if the dollar amount of the return is very small. For example, a \$1 investment returning \$3 will have a higher IRR than a \$1 million investment returning \$2 million. Another short-coming is that IRR can’t be used if the investment generates interim cash flows. Finally, IRR does not consider cost of capital and can’t compare projects with different durations.

IRR is best-suited for analyzing venture capital and private equity investments, which typically entail multiple cash investments over the life of the business, and a single cash outflow at the end via IPO or sale.

#### munna99185

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• Test ##### Re: Internal rate of return (IRR)
« Reply #1 on: February 28, 2014, 12:32:13 PM »
Internal Rate of Return (IRR) is 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. 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. IRRs can also be compared against prevailing rates of return in the securities market. If a firm can't find any projects with IRRs greater than the returns that can be generated in the financial markets, it may simply choose to invest its retained earnings into the market.
[Source: http://www.investopedia.com]

Sayed Farrukh Ahmed
Assistant Professor
Daffodil International University

#### tanzina_diu

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• • Posts: 165 ##### Re: Internal rate of return (IRR)
« Reply #2 on: March 01, 2014, 11:18:51 AM »
The discount rate that forces the PV of a project’s future cash inflows, to be equal the PV of its total cost. Equivalently, the rate that forces the NPV to equal zero is internal rate of return.

Procedure to calculate IRR

1.   Given the inflows and cash outflow, choose a discount rate at random and calculate the project NPV.
2.   If the NPV is positive, choose a higher discount rate and calculate the project NPV
3.   If the NPV is negative, choose a lower discount rate and calculate the project NPV
4.   Make adjustment through Interpolation or Trial-and-error method to find out accurate     Internal Rate of Return

IRR > Cost of capital (Requited rate of return) – Accept the project
IRR < Cost of capital (Requited rate of return) - Reject the project
IRR = Cost of capital (Requited rate of return) – Indifferent

   It recognizes Time Value of Money
   It considers all cash flows occurring over the entire life of the project to calculate the rate of return
   The discount rate is easily comparable to the project cost of capital
   It provides a rate of return which is indicative of the profitability of the project
   It is consistent with shareholder’s wealth maximization goal
   It is easily understandable to the business executive

It is not easy to use, understand, and calculate
Complex trial-and-error technique
It provides misleading and inconsistent result when the NPV of a project does not decline with the discount rate
It also fails to indicate a correct choice between mutually exclusive projects under certain situation
It does not hold value additivity principle.
Though it does not use the concept of required rate of return yet, It provides decisions by comparing with that
Sometimes it provides multiple rates that creates confusion
It is determined based on the assumption that all intermediate cash inflows are reinvested at IRR
Tanzina Hossain
Assistant Professor

#### tanzina_diu

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« Reply #3 on: March 01, 2014, 11:19:26 AM »
IRR Method:
A method of ranking investment proposals using the rate of return on an investment calculated by finding the discount rate that equals the PV of future cash inflow to the PV of cash outflow

Economic Rationality of IRR Method

o   The IRR on a project is its expected rate of return
o   If the IRR exceeds the cost of fund used to finance the project, a surplus remains after paying for the capital and these surplus accruals to the firm’s shareholder
o   Taking on a project that is IRR exceeds cost of capital increases share holder’s wealth.
Tanzina Hossain
Assistant Professor

#### tanzina_diu

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« Reply #4 on: March 01, 2014, 11:20:09 AM »
Multiple IRR

There is one other situation in which the IRR approach may not be usable-when projects with nonnormal cash flows are involved. A project with nonnormal cash flow can create multiple IRR (more than one IRR). A project has normal cash flows if it has one or more cash outflows (costs) followed by a series of cash inflows. If, however, a project calls for large cash out flow sometime during or at the end of its life, then the project has nonnormal cash flows. When we try to find out the IRR on the basis of nonnormal cash flows, we must get more than one IRR, which are called Multiple IRR.

For example: Suppose, if we invest Tk. 16,00,000 in a gas field, after one year we get TK 100,00,000 cash inflow but at the next year TK 10000000 cash outflow occurs for an accident. Therefore, the project’s expected net cash flows are as follows:

Expected Net cash flows
Year  0                             End of year 1                  End of year 2
-16 lakh.                               +100 lakh.                         -100 lakh.

Now we can calculate the IRR by using the values in the formulae-

-16 lac          100 lac        -100 lac
(1+IRR)0      (1+IRR)1         (1+IRR)2

If we solve this equation, we will find NPV=0 when IRR = 25% and also when IRR = 400%. Therefore, the IRR of the investment is both 25 and 400 percent and that are multiple IRR.
So, in this situation, it is very difficult to make decision by using IRR method.
Tanzina Hossain
Assistant Professor

#### tanzina_diu

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« Reply #5 on: March 01, 2014, 11:21:06 AM »
Modified Internal Rate of Return (MIRR)

The process by which the assumption of reinvestment of Net Present Value is combined with the internal rate of income, that is modified IRR. This is the discount rate at which the PV of a project cost is equal to the PV of its terminal value, where the terminal value is found as sum of the FV of its cash inflows, compound at the firm’s cost of capital. The MIRR is similar to the IRR but it is theoretically superior as it is free of two weakness of IRR.

•   It correctly assumes reinvestment at the project’s cost of capital
•   It avoids the problem of Multiple IRR
•
The MIRR correctly assumes reinvestment at the project’s cost of capital and avoids the problem of multiple IRR. There are three basic steps of MIRR. They are –
1.   Estimate all cash flows as in IRR
2.   Calculate the future values of all cash inflows over the project’s life
3.   Determine the discount rate that causes the future value of all cash inflows determined in step two to be equal to the firm’s investment at time zero. This discount rate is known as the MIRR.

We can present the Modified IRR by the following equation –

Investment(CO) = Terminal value of inflows/ (1+MIRR)n

CO      TV
MIRR =                    -         =  0
(1+MIRR)n          (1+MIRR)n

PV of cost = PV of TV

TV
PV =
(1+MIRR)n

Here the terminal value indicates the cost which is found after reinvestment of net cash inflow at the rate of cost of capital.

Tanzina Hossain
Assistant Professor

#### tanzina_diu

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« Reply #6 on: March 01, 2014, 11:22:16 AM »
Why NPV is better than IRR?

To take an exact decision for investment, first the firm evaluates the proposed projects accurately. There are two methods of evaluating investment projects. They are –

2.   Discounted cash flow method: NPV, IRR, PI
Generally, we consider discounted cash flow method as the better method comparing this with conventional methods in evaluating the capital expenditures or measuring the appropriateness of investment decisions. Because, pay back period and ARR don’t consider time value of money as well as all the cash flows during the life time of a project. Since, discounted cash flow method considers all those, it is considered as the best method. NPV (Net present value) method IRR (Internal rate of return) method and Profitability Index Methods are the discounted cash flow methods where NPV and IRR are the better than PI due to some weaknesses of PI.

At first we should clear the concept of NPV and IRR. The full appreciation of NPV is Net Present Value. It is a sophisticated capital budgeting technique; found by subtracting a project’s initial investment from the present value of its cash inflows discount at a rate equal to the firm’s cost of capital.

The full appreciation of IRR is Internal Rate of Return. It is also a sophisticated capital budgeting technique; the discount rate that equates the NPV of an investment opportunity with \$0 (because the present value of cash inflows equals the initial investment); it is the compound annual rate of return that the firm will earn if it is invests in the project and receives the given cash inflows.

Capital budgeting techniques are very conventional methods and by comparing them, we can always find NPV is better than IRR.
NPV is better than IRR for following five reasons:
•   Absolute measure of profit
•   Problem in making decision regarding loan
•   Multiple IRR
•   Mutually exclusive project
•   Rate of interest

1. Absolute measure of profit:
NPV is useful to determine how much net value will be raised from the investment of any project. The net amount which increases after investing in the project can be measure through the net present value. So it is easy to determine the increasing amount of shareholders wealth by NPV. But it is impossible in IRR method. Simply through IRR we get the rate of profit where NPV gives us the amount of net present value.

For example, NPV of a company is \$6251 means that actual amount of the present value of the profit of this company is \$6251. IRR of a company is 20% means that this company earns 20% profit, but it isn’t clear that the company earn 20% profit on what.

2. Problems in decision making:
In case of lending and borrowing money for the project, a firm may face problem in decision making. Because IRR and NPV may give different result for a particular project. The result which is acceptable in IRR method may not be acceptable under NPV method. Usually NPV is able to provide accurate result than IRR.
Let see the example:
Cash flow ( Tk )
Project   CF-0   CF-1   CF-2   CF-3   IRR   NPV at 10%
A   +1000   -3600   +4200   -1728   20%   -0.75

Here, the IRR for the project is 20% (where cost of capital is10%). From this view, project is very much profitable. But NPV of the project is negative. So, if we take the project we will face a huge amount of loss.

3.  Multiple rates:

In case of a project with non-conventional cash flow, we can get more than one IRR, that’s why we can’t take decision considering IRR. But if we evaluate the project on the basis of NPV, we get only one result, which helps us to take decision. For example:

Project
Cash flows

C-0
C-1
C-2
C-3
C-4
C-5
C-6
IRR   NPV at 10%
A
-1000
+800
+150
+150
+150
+150
-150   -50%
+15.2%
74.9
If we calculate the IRR for above project we get two results (IRR) one is 50% and another is 15.2%. So it is difficult for a firm to take decision under IRR method. But if we measure the project under NPV method we get only one result and we can take decision easily.

4.   Mutually exclusive Project:

Some time we get a project with higher IRR but Lower NPV compare to another project’s IRR and NPV. Here we can’t take decision on the basis of IRR because NPV presents the actual amount of profit. For example:

Project      Cash flow

CF-o
CF-1
IRR         NPV
at 10%
A       -10,000       +20,000           100%           8,182
B       -20,000       +35,000           75%         11,818

From the above table we see that IRR of project A is greater than IRR of project B. But NPV of project A is less than NPV of project B. Project A is acceptable on the basis of IRR but project B is acceptable on the basis of NPV. Now we should select project B because NPV is in actual amount.

IRR also fails to indicate a correct choice between mutually exclusive projects under certain situation. Then NPV is particularly useful for the selection of mutually exclusive project. It is shown below with an example.

(I) Timing of cash flow
(II) Scale of investment

5. Rate of interest:
The interest rate of a project may differ from year to year. If the firm measures the project under NPV method, then the firm can easily adjust the discount rate with new interest rate. But it is difficult to measure and to take decision under IRR method with the changing interest rate and discount rate.

For example, there is a project and the discount rate is 10% for first three years, 12% for 4th and 5th years. Here NPV is 4532 and IRR is 11%.

Y-1   Y-2   Y-3   Y-4   Y-5   NPV   IRR
Dis. rate   10%   10%   10%   12%   12%   +4532   11%

Now it is very easy to take decision on the basis of NPV and at the same time it is very difficult to take decision on the basis of IRR because IRR 11% will compare with 10% discount rate or 12% discount rate is totally unclear.

From the above statement, we can say that NPV is better than IRR to evaluate the project.

Tanzina Hossain
Assistant Professor