Internal Rate of Return Internal Rate of Return and Profitability Indexand Profitability Index

1-04-20101-04-2010

IRR – What it is?IRR – What it is?

Rate of a return a project earnsRate of a return a project earns The discount rate r which equates The discount rate r which equates

the aggregate present value of the the aggregate present value of the net cash inflows (CFAT) with the net net cash inflows (CFAT) with the net aggregate present value of cash aggregate present value of cash outflows of a projectoutflows of a project

NPV=0 NPV=0

IRR – Accept / Reject DecisionIRR – Accept / Reject Decision

Compare actual IRR with required Compare actual IRR with required rate of return (cut-off rate, hurdle rate of return (cut-off rate, hurdle rate)rate)

IRR > kIRR > k

IRR Computation – Annuity Cash FlowsIRR Computation – Annuity Cash Flows

Determine the payback period for the proposed Determine the payback period for the proposed investmentinvestment

In the table look for the pay back period that is In the table look for the pay back period that is equal to or closest to the life of the projectequal to or closest to the life of the project

In the year row look for PV values closes to PB In the year row look for PV values closes to PB period one bigger than and another smaller period one bigger than and another smaller than it.than it.

Note the interest rate corresponding to the PV Note the interest rate corresponding to the PV valuesvalues

Determine actual IRR by interpolation (Using Determine actual IRR by interpolation (Using equation or indirectly by finding present values equation or indirectly by finding present values of annuity)of annuity)

IRR EquationIRR Equation

IRR = r – ( Payback period – Discount IRR = r – ( Payback period – Discount factor for interest rate r) / (Discount factor for interest rate r) / (Discount factor for lower interest rate – Discount factor for lower interest rate – Discount factor for higher interest ratefactor for higher interest rate

r is either of the two interest rates used in r is either of the two interest rates used in the formulathe formula

If the lowest r is used the following If the lowest r is used the following expression must be added, if higher r is expression must be added, if higher r is used deduct the following expressionused deduct the following expression

IRR Equation - AlternativeIRR Equation - Alternative

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

IRR – Annuity Cash flowsIRR – Annuity Cash flows

Model Problem 1:Model Problem 1: A project costs Rs. 36,000 and is A project costs Rs. 36,000 and is

expected to generate cash inflows of expected to generate cash inflows of Rs. 11,200 annually for 5 years. Rs. 11,200 annually for 5 years. Calculate IRR of the project. Calculate IRR of the project.

IRR – Annuity Cash flowsIRR – Annuity Cash flows Solution:Solution: The pay back period is 3.214 (Rs.36000/ The pay back period is 3.214 (Rs.36000/

Rs.11,200)Rs.11,200) From Table discount factors closest to From Table discount factors closest to

3.214 for 5 years are 3.274 (16 percent 3.214 for 5 years are 3.274 (16 percent rate of interest) and 3.199 (17 percent of rate of interest) and 3.199 (17 percent of interest rate) interest rate)

Using the values in equationsUsing the values in equations IRR = 16+ [(3.274 – 3.214) / (3.274 – IRR = 16+ [(3.274 – 3.214) / (3.274 –

3.199)] = 16.8 per cent3.199)] = 16.8 per cent

IRR – Annuity Cash flowsIRR – Annuity Cash flows

The pay back period is 3.214 The pay back period is 3.214 (Rs.36000/ Rs.11,200)(Rs.36000/ Rs.11,200)

From Table discount factors closest From Table discount factors closest to 3.214 for 5 years are 3.274 (16 to 3.214 for 5 years are 3.274 (16 percent rate of interest) and 3.199 percent rate of interest) and 3.199 (17 percent of interest rate) (17 percent of interest rate)

Using the values in equationsUsing the values in equations IRR = 17 - [(3.214 – 3.199) / (3.274 – IRR = 17 - [(3.214 – 3.199) / (3.274 –

3.199)] = 16.8 per cent3.199)] = 16.8 per cent

IRR – Annuity Cash InflowsIRR – Annuity Cash Inflows PV (CFAT) (0.16) = 11200* 3.274 = PV (CFAT) (0.16) = 11200* 3.274 =

Rs. 36,668.8Rs. 36,668.8 PV(CFAT) (0.170) = 11200*3.199 = PV(CFAT) (0.170) = 11200*3.199 =

Rs. 35.828Rs. 35.828 IRR = 16 + [ ( 36,668.8 – 36,000) / IRR = 16 + [ ( 36,668.8 – 36,000) /

(36,668.8 – 35,828.8) ] * 1 = 16.8 (36,668.8 – 35,828.8) ] * 1 = 16.8 per cent or per cent or

IRR = 17 - [ ( 36, 000 – 35, 828.8) / IRR = 17 - [ ( 36, 000 – 35, 828.8) / (840) ] * 1 = 16.8 per cent or (840) ] * 1 = 16.8 per cent or

IRR – Mixed Stream of cash inflowsIRR – Mixed Stream of cash inflows Calculate the average annual cash inflow Calculate the average annual cash inflow

to get the fake annuityto get the fake annuity Determine the fake pay back period Determine the fake pay back period

dividing the initial outlay by the average dividing the initial outlay by the average annual CFAT determined by step 1annual CFAT determined by step 1

Look for the factor in Table closest to the Look for the factor in Table closest to the fake pay back value in the same manner fake pay back value in the same manner as in the case of annuity. The result is as in the case of annuity. The result is the rough approximation of IRR, based on the rough approximation of IRR, based on the assumption that the mixed stream is the assumption that the mixed stream is an annuityan annuity

IRR – Mixed Stream of cash inflowsIRR – Mixed Stream of cash inflows

Adjust subjectively the IRR obtained by comparing with Adjust subjectively the IRR obtained by comparing with the pattern of the cash flow. (If cash flow is more than the pattern of the cash flow. (If cash flow is more than the calculated annuity raise the percentage few points the calculated annuity raise the percentage few points and vice versa)and vice versa)

Find out the PV (Using table) of mixed cash flows taking Find out the PV (Using table) of mixed cash flows taking IRR as the discount rate as estimated in the previous IRR as the discount rate as estimated in the previous stepstep

Calculate PV using the discount rate. If NPV = 0 that is Calculate PV using the discount rate. If NPV = 0 that is the IRR.the IRR.

If not repeat and stop when two consecutive IRRs If not repeat and stop when two consecutive IRRs causing one NPV positive and another NPV negative are causing one NPV positive and another NPV negative are calculatedcalculated

The actual value can be ascertained by the method of The actual value can be ascertained by the method of interpolation toointerpolation too

Calculate the IRR – Mixed StreamCalculate the IRR – Mixed StreamInitial outlay Rs. 56,125Initial outlay Rs. 56,125

Machine A Machine B

Year CFAT CFAT

1 14000 22000

2 16000 20000

3 18000 18000

4 20000 16000

5 25000 17000

Machine A

Machine B

Year CFATPV Factor

(0.18)Total

PV CFATPV Factor

(0.18)Total

PV

1 14000 0.847 11858 22000 0.847 18172

2 16000 0.718 11488 20000 0.718 13660

3 18000 0.609 10962 18000 0.609 10152

4 20000 0.516 10320 16000 0.516 7472

5 25000 0.437 10925 17000 0.437 6562

55553 56018

Less: In. Inv 56125 56125

-572 -107

SolutionSolution

Machine A

Machine B

Year CFATPV Factor

(0.17) Total

PV CFATPV Factor

(.20)Total

PV

1 14000 0.855 11970 22000 0.833 18326

2 16000 0.731 11696 20000 0.694 13880

3 18000 0.624 11232 18000 0.579 10422

4 20000 0.534 10680 16000 0.484 7712

5 25000 0.456 11400 17000 0.442 6834

56978 57174

Less: In.Inv 56125 56125

853 1049

SolutionSolution

Machine A: Both 17 and 18 percent Machine A: Both 17 and 18 percent are giving positive and negative are giving positive and negative NPVs, interpolation method can be NPVs, interpolation method can be applied to find actual CRRapplied to find actual CRR

Machine B: Both 20 and 21 percent Machine B: Both 20 and 21 percent give negative and positive NPVs give negative and positive NPVs interpolation method can be usedinterpolation method can be used

Evaluation of IRREvaluation of IRR

Positive:Positive: Considers time value of moneyConsiders time value of money Takes total cash inflows into accountTakes total cash inflows into account Easy to understand Easy to understand No use of required rate of return (No No use of required rate of return (No

controversial calculation)controversial calculation) Maximising shareholder wealthMaximising shareholder wealth

Evaluation of IRREvaluation of IRR

Drawback:Drawback: Tedious calculationTedious calculation Produces multiple rates difficult to Produces multiple rates difficult to

handlehandle Mutually exclusive proposals, highest Mutually exclusive proposals, highest

IRR project selected leaving othersIRR project selected leaving others Assumption: All cash inflows are Assumption: All cash inflows are

reinvestedreinvested

Profitability Index Method/ Benefit Cost ratio (B/C Profitability Index Method/ Benefit Cost ratio (B/C Ratio)Ratio)

Measures the present value of Measures the present value of returns per rupee invested returns per rupee invested

PI = Present value cash inflows/ PI = Present value cash inflows/ Present value of cash outflows Present value of cash outflows

Accept/ Reject rule:Accept/ Reject rule: PI > 1 accept the projectPI > 1 accept the project PI = 1 Be indifferentPI = 1 Be indifferent

EvaluationEvaluation

Better in times of capital rationingBetter in times of capital rationing Superior to NPVSuperior to NPV

Calculate PICalculate PI

Machine A Machine B

Rs.56,125 Rs.56,125

3375 11375

5375 9375

7375 7375

9375 5375

11375 3375

5

3000 3000

5