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Internal rate of return (IRR)

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tanzina_diu:
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_diu:
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 –

1.   Traditional method: PBP, ARR
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.

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