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
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
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
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
Project’s promised rate of return given initial
investment and cash flows.
Consistent with wealth maximization
Accept a project if IRR ≥ Cost of Capital
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%
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 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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