Internal Rate of Return and Profitability Index1-04-2010

IRR What it is?Rate of a return a project earnsThe discount rate r which equates the aggregate present value of the net cash inflows (CFAT) with the net aggregate present value of cash outflows of a projectNPV=0

IRR Accept / Reject DecisionCompare actual IRR with required rate of return (cut-off rate, hurdle rate)IRR > k

IRR Computation Annuity Cash FlowsDetermine the payback period for the proposed investmentIn the table look for the pay back period that is equal to or closest to the life of the projectIn the year row look for PV values closes to PB period one bigger than and another smaller than it.Note the interest rate corresponding to the PV valuesDetermine actual IRR by interpolation (Using equation or indirectly by finding present values of annuity)

IRR EquationIRR = r ( Payback period Discount factor for interest rate r) / (Discount factor for lower interest rate Discount factor for higher interest rater is either of the two interest rates used in the formulaIf the lowest r is used the following expression must be added, if higher r is used deduct the following expression

IRR Equation - AlternativeIRR = r [(Present value of cash outlay Present value of cash inflows) / (Difference in the calculated present values of the inflows)] * Difference in interest rates

IRR Annuity Cash flowsModel Problem 1:A project costs Rs. 36,000 and is expected to generate cash inflows of Rs. 11,200 annually for 5 years. Calculate IRR of the project.

IRR Annuity Cash flowsSolution:The pay back period is 3.214 (Rs.36000/ Rs.11,200)From Table discount factors closest to 3.214 for 5 years are 3.274 (16 percent rate of interest) and 3.199 (17 percent of interest rate) Using the values in equationsIRR = 16+ [(3.274 3.214) / (3.274 3.199)] = 16.8 per cent

IRR Annuity Cash flowsThe pay back period is 3.214 (Rs.36000/ Rs.11,200)From Table discount factors closest to 3.214 for 5 years are 3.274 (16 percent rate of interest) and 3.199 (17 percent of interest rate) Using the values in equationsIRR = 17 - [(3.214 3.199) / (3.274 3.199)] = 16.8 per cent

IRR Annuity Cash InflowsPV (CFAT) (0.16) = 11200* 3.274 = Rs. 36,668.8PV(CFAT) (0.170) = 11200*3.199 = Rs. 35.828IRR = 16 + [ ( 36,668.8 36,000) / (36,668.8 35,828.8) ] * 1 = 16.8 per cent or IRR = 17 - [ ( 36, 000 35, 828.8) / (840) ] * 1 = 16.8 per cent or

IRR Mixed Stream of cash inflowsCalculate the average annual cash inflow to get the fake annuityDetermine the fake pay back period dividing the initial outlay by the average annual CFAT determined by step 1Look for the factor in Table closest to the fake pay back value in the same manner as in the case of annuity. The result is the rough approximation of IRR, based on the assumption that the mixed stream is an annuity

IRR Mixed Stream of cash inflowsAdjust subjectively the IRR obtained by comparing with the pattern of the cash flow. (If cash flow is more than the calculated annuity raise the percentage few points and vice versa)Find out the PV (Using table) of mixed cash flows taking IRR as the discount rate as estimated in the previous stepCalculate PV using the discount rate. If NPV = 0 that is the IRR.If not repeat and stop when two consecutive IRRs causing one NPV positive and another NPV negative are calculatedThe actual value can be ascertained by the method of interpolation too

Calculate the IRR Mixed StreamInitial outlay Rs. 56,125

Solution

SolutionMachine A: Both 17 and 18 percent are giving positive and negative NPVs, interpolation method can be applied to find actual CRRMachine B: Both 20 and 21 percent give negative and positive NPVs interpolation method can be used

Evaluation of IRRPositive:Considers time value of moneyTakes total cash inflows into accountEasy to understand No use of required rate of return (No controversial calculation)Maximising shareholder wealth

Evaluation of IRRDrawback:Tedious calculationProduces multiple rates difficult to handleMutually exclusive proposals, highest IRR project selected leaving othersAssumption: All cash inflows are reinvested

Profitability Index Method/ Benefit Cost ratio (B/C Ratio)Measures the present value of returns per rupee invested PI = Present value cash inflows/ Present value of cash outflows Accept/ Reject rule:PI > 1 accept the projectPI = 1 Be indifferent

EvaluationBetter in times of capital rationingSuperior to NPV

Calculate PI

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