Computation of IRR Assignment Help

Capital Budgeting Decisions - Computation of IRR

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Computation of IRR

(A)     When cash flows are equal for all over the period:

(a)     At first PB/Cumulative PV factor will be calculated. 

Cash Outflow/Annual Cash Inflow 

(b)     After that P.V. Table (cumulative) will be used. In P.V. table, look in the year row (Life of the project), and find out two discount factors closest to PB/CPV factor, one bigger and other smaller than the PB period.

(c)     Interest rates for above two-selected discount factor will be find out.

(d)     After that with the help of above two discount rates, find out present value of cash inflows for the both rates and IRR can be calculated with the help of interpolation technique as follows:.    

          IRR = LDR + (P.V. of inflows at LDR - P.V. of outflows / P.V. of inflows at LDR - P.V. of inflows at HDR )* [HDR - LDR]

 LDR = Lower discount rate, HDR = Higher discount rate 

(B)     When cash flows are unequal for all over the period:

(a)     At first we will determine average annual cash inflow by dividing total cash inflow to be earned from the project with the life of the project.

(b)     After that proxy PB/CPV factor will be calculated by dividing the cash outflow by the average annual cash flow as determined in step (a).

(c)     After that PY Table (cumulative) will be used. In PY table, look in the year row (Life of the project), and find out two discount factors closest to proxy PB/CPV factor, one bigger and other smaller than the proxy PB/CPV factor.

(d)     Interest rates for above two selected discount factor will be found out. It gives rough approximation of the IRR. These rates will be further adjusted on the basis of patterns' of Cash inflow, for example if cash inflow is higher in the initial years, above rates will be adjusted upward otherwise vice: versa.

To find out IRR, adopt Trial and Error approach. This process will be carried on until, out of above two discount rates, one gives greater present value and other smaller present value than the cash outflows. Efforts shall be made to minimize the difference between Present value of outflow & Present values calculated using LDR & HDR to bring accuracy in the calculation of IRR. Remaining procedure would be same as in step (d) of first situation. 

EVALUATION:

This method is conceptually a correct technique to evaluate capital expenditure decisions. As it considers time value of money, it takes in to account the total cash inflows and outflows. It itself provides a rate of return which is indicative of the profitability of the proposal. It is consistent with the over all objective of maximizing shareholders wealth.

On the other hand it also suffers from serious limitations. It generally involves complicated computational problems especially when cash inflows are unequal.

It only considers rate of return, hence in the case of mutually exclusive projects, if a project, which gives higher IRR, will be selected though it is giving smaller NPV than a project, which gives lesser IRR in comparison to former. In such cases, it will not be consistent with the main objective of Financial Management. 

This method also assumes that all intermediate cash inflows are reinvested at the IRR, which is also not realistic. Unlike in the case of the NPV method, the value additive principle does not hold when the IRR method is used- IRRs of projects do not add.

In some cases, multiple IRR can be generated. In case of Non-conventional investments, where outflows are not restricted to the initial period, but are interspersed with cash inflows throughout the life of the project, there can be multiple IRRs. Non-Conventional projects have more than one change in 'signs of cash flows. The number of rates of return depends on the number of times the Sign of the cash flow stream changes. Reversal of sign is a necessary but not a sufficient condition for multiple returns. For example, if cash flows are: 

t0 -1000      t1       4000 t2       -3500 

There could be 2 IRRs i.e. 29.29% & 171.71%.

At both the rate NPV will be Zero, 

(viii) Project IRR & Equity IRR

Project IRR is the rate at which present value of cash inflows generated by a project is equal to present value of cash outflow involved in the project. While calculating Project IRR, impact of source of finance on cash flows is not considered. For example, interest on debt, tax shield on interest expense, flotation cost involved in financing etc.

Equity IRR is the rate at which PV of cash inflows available for equity shareholders is equal to present value of that portion of cash outflow, which is arranged through equity shares. Cash' inflows available for equity shareholders means a cash inflow which is adjusted for impact of financing e.g. interest, preference dividend, repayment of debt/preference share capital, tax shield on interest, flotation costs etc.   

(ix)   Modified Internal Rate of Return (MIRR)

The IRR technique assumes that the intermediate cash inflows are reinvested at a rate equal to the proposal's IRR itself. The reinvestment rate assumption made by IRR creates serious consequences. If this assumption is accepted, different alternative proposals will have different reinvestment rates, which are not realistic. If project's life is longer, this may create more serious consequences. 

MIRR considers this aspect MIRR is that discount rate which equates the present value of terminal value of cash inflows (calculated using terminal value method) with present value of cash outflows. In fact MIRR method is the combination of Terminal Value Method and IRR method. It is also known as Extended Internal Rate of Return. 

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