Internal rate of return
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The document discusses the Internal Rate of Return (IRR) as a discounted cash flow technique for evaluating investment projects, detailing its calculation methods for both even and uneven cash flows. It explains the acceptance rules based on IRR compared to the cost of capital, alongside the merits and demerits of using IRR and other methods such as the Profitability Index and Discounted Payback Period. Additionally, it highlights the Terminal Value method for assessing projects where cash inflows are reinvested at certain rates until project termination.
Internal rate of return
- 1. Dr. Mohamed Kutty Kakkakunnan Associate Professor P.G. Dept. of Commerce NAM College Kallikkandy Kannur – Kerala – India [email protected]
- 2. INTERNAL RATE OF RETURN Another DCF technique considering the entire cash flows Also known as Yield on Investment, Marginal Efficiency of Capital, Rate of Return Over Cost, Time Adjusted Rate of Internal Return It is the rate that equates the investment outlay with the present value of cash inflows received, after one period Defined as “the rate which equates present of the net cash inflows with the aggregate present value of cash outflows of a project” It is the discount rate which makes NPV = 0 The major difference between NPV and IRR is that in NPV method the rate of return (denoted by k) is known but in IRR, the rate or return (denoted by r) is not known, it is to be ascertained. When the IRR (r) is used for discounting cash inflows NPV becomes zero Considered as the best measure of evaluation of long-term project
- 3. Calculation of IRR Two situations i. Even cash flows an ii. Uneven cash flows Even (annuity) Cash flows Same amount is received as earnings 1. Determine payback period(investment ÷ inflows) 2. Take Cumulative Present Value Table (Annuity Table) and ascertain the factor that is equal to or closest to the life of the project, for the years (life time) concerned 3. Determine the rate (%) for the value. It is the IRR 4. To be more precious, in the year row, find two annuity values or discount factors closest to the true factor one bigger and the other smaller than it
- 4. 5. Then apply the formula Eg., (IRR) Two projects A B Cost (Rs.) 90000 100000 Estimated savings 15000 20000 Economic life (years) 10 8 Answer – Determine the PBP Project A 90000/15000 = 6 Now Look the table Closest table value to 6 is 6.145 at 10% and 5.650 at 12% To find out the accurate IRR apply the above formula 10+.6 = 10.6 %
- 5. IRR in Mixed stream (Uneven cash flows) Trial and error method 1. Take an assumed interest rate 2. Determine the present value of inflows of each year. Use the PV Table (Inflow X PV Factor) 3. Find the total of Present values of inflows 4. Compare it with the outflows 5. If both are the same and the difference is zero, the IRR (r) of the project will be the assumed interest taken in the first step 6. If the PV of inflows > outflows, (NPV is positive) take a higher ‘r’ than that of the first step and vice versa 7. Repeat the steps from two to five 8. Continue the process till NPV = 0 9. Sometimes the IRR may lie in between two rates (say 12% and 14%), then the exact rate is to be determined by interpolation
- 6. Formula for interpolation of exact IRR
- 7. Acceptance Rule Accept the project if IRR is more than the cost of capital or the cut-off rate or opportunity cost of capital, hurdle rate required rate of return (r>k). Reject the project if IRR is less than the cost of capital or the cut-off rate or opportunity cost of capital, hurdle rate required rate of return (r<k). May accept or reject the project where r=k Ranking of projects. Ranked in the descending order of IRR • When IRR > K, NPV will be positive • When IRR < K, NPV will be negative • When IRR = K, NPV will be zero
- 8. Merits of IRR method A popular method of appraising projects. Since, it is in a percentage form, comparison of IRR with cost of capital or cut off rate is very easy. • Recognizes the time value of money • Considers profitability of the project during the entire period of time • Consistent with the shareholder wealth maximization objective. When IRR is greater than cost of capital, shareholders wealth is maximized Demerits • Multiple rates. There are different methods for computing IRR. Each method may give different IRR • In certain mutually exclusive projects, it may give wrong conclusions • As in the case of NPV, value additivity is not possible
- 9. Profitability Index (PI) or Benefit Cost (B/C) Ratio • More or less equal to the NPV method • It measures the Present Value of Returns per Rupee invested, while NPV is based on the difference between the Present Values of inflows and outflows • Major limitation of NPV is that, being an absolute measure, it is not suitable for evaluating projects with different cash outlays and cash flows • PI is a relative measure, can be used for comparing different projects with different cash flows • Defined as “ the ratio which is obtained by dividing the present value of cash inflows by the present value of cash outlays”
- 10. Acceptance Rule • Accept the project, when PI>1 • Reject the project, when PI<1 • May accept or reject the project, when PI=1 When PI = +ve NPV is also +ve PI= - ve NPV is also – ve PI=0 NPV is also 0 Merits • Considers time value • Consistent with wealth maximization objective • Relative measure of profitability, can be used to compare projects with different costs, inflows and life-time Demerit: Require calculation of cash flows, ascertain required rate of return. All create problems
- 11. Discounted Payback Period • Traditional payback period does not consider the time value of money – the major drawback • To avoid this drawback, discounted payback period is calculated • In this method, for calculating the PBP, cash flows are discounted at the desired /required rate of return / cost of capital • Then PBP is calculated
- 12. Terminal Value Method Under this method it is assumed that each cash inflow is reinvested in another asset at a certain rate of return, from the moment it is received until the termination of the project This method is based on the rationale that a firm reinvests its earnings in the business itself In this method the net cash inflows and outflows are compounded forward, rather than discounting them backward as in NPV method Project will be accepted if the present value of the total of the compounded reinvested cash inflows is greater than the present value of the outlays Mutually exclusive projects – project with higher present value of the total of the compounded cash flows is accepted
- 13. In this method, firstly, cash inflows are multiplied by the compounding factor (given in the COMPOUND TABLE showing the compound sum of one Rupee), assuming that the amount of cash inflow is reinvested and it will earn compound interest till the terminal year. At the end (Terminal year), there will be no reinvestment and thus, compound factor is taken as 1 As second step, sum of these compound values are calculated Then, (third step), the sum so obtained is further discounted at the cost of capital (cut off rate given) for the years of life time, to find out the present value
- 14. Fourthly, the amount so obtained in the third step (Present Value of the compounded reinvested cash flows PVTS is compared with the Present value outflow of cash, PV0) Decision criterion Accept PVTS>PV0 Reject PVTS<PV0 Indifferent PVTS=PVO For ranking different mutually exclusive projects- Calculate Net Terminal Values(NTV) NTV= PVTS-PV0 Rank the projects according to the NTV
- 15. Merits 1. Assumes that the net cash inflow is reinvested once they are received and avoid any influence of cost of capital on cash flow streams 2. This method of evaluation is very easy, especially mutually exclusive projects 3. Easy to understand, especially to those businessmen and executives who have no adequate knowledge in accounting and economics Demerits The major demerits is that for calculation, future rate of interest need be forecasted or estimated, which is difficult