# Internal Rate of Return

**Topics:**Net present value, Internal rate of return, Time value of money

**Pages:**6 (992 words)

**Published:**July 4, 2012

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%

Advantage of IRR

It takes into account the time value of money

It considers the profitability of the project for its

entire economic life

It provides for uniform ranking of various

proposals due to the percentage rate of...

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