# Internal Rate of Return

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• Published : July 4, 2012

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Internal Rate of Return

Meaning of Capital Budgeting
 Capital budgeting can be defined as the process

of analyzing, evaluating, and deciding whether
resources should be allocated to a project or
not.
 Capital budgeting addresses the issue of
strategic long-term investment decisions.
 Process of capital budgeting ensure optimal
allocation of resources and helps management
work towards the goal of shareholder wealth
maximization.

Why Capital Budgeting is so Important?

 Involve massive investment of resources
 Are not easily reversible
 Have long-term implications for the firm
 Involve uncertainty and risk for the firm

Capital Budget Techniques
Net PresentValue

Discounted

BenefitCost/Profitability
Index Ratio

IRR

Capital Budget
Techniques

Accounting Rate
of Return
Non Discounted
Payback
Period

Internal Rate of Return
 The rate at which the net present value of cash

flows of a project is zero, I.e., the rate at which
the present value of cash inflows equals initial
investment

 Project’s promised rate of return given initial

investment and cash flows.
 Consistent with wealth maximization
 Accept a project if IRR ≥ Cost of Capital

Question
The management is considering to acquire an
equipment costing \$1,00,000 . It is expected that
the equipment will provide equal annual cash flows
of \$30,000 for a period of 4 years. Should
management accept this investment proposal?

Solution By Present value factor for an annuity of \$1
1.Determine a present value factor for an annuity of \$1 using the following formula:

Present value factor for an annuity of \$1 = Amount to be
invested / Equal annual cash inflows
2. Locate the present value factor (determined in step 1) in the present value of an annuity of \$1 table. First locate the number of years of expected useful life of the investment and then proceed horizontally across the table until you find the present value factor determined in step 1.

3.Identify the internal rate of return by the heading of the column in which the present value factor is located.
4.Accpet the project if the IRR > Cost of Capital

 Present value factor for an annuity of \$1

=\$1,00,000 / \$30,000=3.33
 From the Table check for the present value factor
for an annuity of \$1
 IRR is in between 7% and 8%
IRR=r-(PB-DF

r

)

DFrL-DFrH

r= Either of the two rate of
 PB= Payback Period
 DFr =Discounted factor for the interest rate r.
 DFrL= Discounted factor for the lower interest rate .
 DFrH= Discounted factor for the higher interest rate r.
IRR= 8-(3.333-3.312/3.387-3.312)=7.78%

IRR with Liner Interpolation
 One basis to this method is the NPV come on decreasing as

the rate of return increased.
1.Calculat the NVP at a discounted rate of x%(let take 5%).
Discounted Net Cash Flows at 5%
DCF1 = 30000/(1+5%)1 = 30000/1.05 = 28571.43
DCF2 = 30000/(1+5%)2 = 30000/1.1025 = 27210.88
DCF3 = 30000/(1+5%)3 = 30000/1.15763 = 25915.13
DCF4 = 30000/(1+5%)4 = 30000/1.21551 = 24681.07

NPV = 28571.43 + 27210.88 + 25915.13 +
24681.07 -100000 =6378.51

2.Now as the NPV is positive with a rate of return of 5
%.Take a higher a rate of return i.e y%(10%)
 Discounted Net Cash Flows at 10%

DCF1 = 30000/(1+10%)1 = 30000/1.1 = 27272.73
DCF2 = 30000/(1+10%)2 = 30000/1.21 = 24793.39
DCF3 = 30000/(1+10%)3 = 30000/1.331 = 22539.44
DCF4 = 30000/(1+10%)4 = 30000/1.4641 = 20490.4
NPV Calculation at 10%
NPV = 27272.73 + 24793.39 + 22539.44 + 20490.4 100000= -4904.04

3.IRR with Linear Interpolation
IRR = iL + [(iU-iL)(NPVL)] / [NPVL-NPVU]

iL = 5%;iU = 10%;NPVL = 6378.51;NPVU = -4904.04
IRR = 0.05 + [(0.1-0.05)(6378.51)] / [6378.51--4904.04] = 7.80%