detailed information about financial mathematics

1. CAPITAL
BUDGETING
Prabhat
40722113

2. INDEX
1.What is Capital Budgeting?
2.Process of CB
3.Components of CB
4.Non-Discounting Techniques
a)Payback Period
b)Average Rate of Return
5.Discounting Techniques
a)Net Present Value
b)Internal Rate Of Return
c)Profitability Index

3. WHAT IS
CAPITAL BUDGETING?
Capital Budgeting 3
Capital budgeting is the process of
determining which real investment
projects should be accepted and given
an allocation of funds from the firm.
To evaluate capital budgeting
processes, their consistency with the
goal of shareholders wealth
maximization is of utmost importance.

4. THE CAPITAL
BUDGETING PROCESS :
 Generate investment proposal consistent with the firms strategic
…objectives.
Estimate after tax incremental operating cash flow for the
…investment projects.
Evaluate project incremental cash flow.
Select projects based on a value-maximizing acceptance
…criterion.
Re evaluate implemented investment projects continually and
…perform post audits for completed projects.
Capital Budgeting 4

5. TECHNIQUES OF
CAPITAL
BUDGETING :
Traditional
Modern

6. TRADITIONAL OR
NON-DISCOUNTING TECHNIQUES :
These techniques don't discount the cash flow to find out
there present worth. There two such techniques available
i.e.,
A. The Payback Period
B. The Accounting Rate Of Return
Capital Budgeting 6

7. THE PAYBACK PERIOD:
Capital Budgeting 7
The payback period is define as the number of years required for the proposal’s cumulative
cash inflow to be equal to its cash outflow.
 In other words the payback period is the length of the time required to recover the initial
cost of the project.
Computation of the payback period :
The payback period can be calculated into two different situation-
a. When Annual Inflows Are Equal: When can inflow generated by the proposal are
equal per time period i.e. the cash inflows are in the form of annuity, the payback period
can be computed by dividing the cash outflow by the amount of annuity .
The Payback Period Is Calculated As Follow:
Payback period = Initial Outflow
Annual Inflow
b. When Annual Inflows Are Unequal: In case the cash inflows from the proposal
are not in annuity form then the cumulative cash inflow are used to compute the payback
period.

8. 8
ACCOUNTING/ AVERAGE RATE OF RETURN:
The ARR is based on the accounting concept of return on investment or rate of return. The
ARR may be defined as the annualized net income earned on the average funds invested in
a project.
In other words, the annual return of a project are expressed as a percentage of the net
investment in the project.
Computation of ARR: Symbolically-
Average Annual Profit(After Tax)
ARR = * 100
Average investment in the project
This clearly shows ARR is a measure based on accounting profits rather than the
cash flow and is very similar to the measures of rate of return on capital employed,
which is generally used to measures the overall profitability of the firm .
The calculation of ARR may be further discussed with reference to equal annual
profits and unequal annual profits.

9. DISCOUNTED CASH FLOW (DCF)
TECHNIQUES :
The main DCF techniques for capital budgeting
includes:
•Net Present Value (NPV)
•Internal Rate Of Return (IRR)
•Profitability Index (PI)
# Each requires estimate of expected cash flow(and
their timing)for the project.
# Includes cash outflow(cost) and inflow ( revenue
or saving) – normally tax effects are also considered
Capital Budgeting 9

10. DISCOUNTED CASH FLOW (DCF)
TECHNIQUES:
Capital Budgeting 10
Each requires an estimate of the project’s risk
so that an opportunity discount rate (opportunity
cost of capital)can be determined.
Some times the above data is difficult to
obtain – this is the main weakness of all DFC
techniques.

11. Capital Budgeting 11
NET PRESENT VALUE (NPV)
Methods: NPV=PVINFLOW – PVOUTFLOW
If NPV > 0, then accept the project ; otherwise reject the
project.
Strengths Weakness
•Resulting number is easy
to interpret: shows how
wealth will change if the
project is accepted.
•Acceptance criteria is
consistent with
shareholder wealth
maximization.
•Relatively straight forward
to calculate
•Requires knowledge of
finance to use.
•An improper NPV
analysis may lead to the
wrong choices of project
when the firm has capital
rationing.

12. INTERNAL RATE OF RETURN (IRR)
IRR is the rate of return that a project generates.
Algebraically, IRR can be determined by setting up
an NPV equation and solving for a discount rate that
makes the NPV=0.
Equivalently, IRR is solved by determining the rate
that equates the PV of cash inflows to the PV of cash
outflows.
Methods : Use your financial calculator or a
spreadsheet; IRR usually cannot be solved manually.
 If IRR > opportunity cost of capital (or hurdle rate);
then accept the project; otherwise reject it.
Capital Budgeting 12

13. Capital Budgeting 13
INTERNAL RATE OF RETURN (IRR)
STRENGTHS WEAKNESSES
•IRR number is easy to
interpret: shows the
return the project
generates.
•Acceptance criteria is
generally consistent with
shareholders wealth
maximization.
•Requires knowledge of
finance to use .
•Difficult to calculate –
need financial calculator.
•It is possible that there
exist no IRR or multiple
IRR’s for a project and
there are several cases
when the IRR analysis
needs to be adjust in
order to make a correct
decision.

14. Capital Budgeting 14
PROFITABILTY INDEX (PI)
PI = PV(cash flow after the initial investments)
Initial Investment
If PI > 1 , then accept the real investment projects;
otherwise reject it.

15. Capital Budgeting 15
PROFITABILITY INDEX (PI)
STRENGTHS WEAKNESSES
•PI number is easy to
interpret: shows how many
$(in PV terms) you get
back per $ invested.
•Acceptance criteria is
generally consistent with
shareholders wealth
maximization.
•Relatively straightforward
to calculate.
•Require knowledge of
finance to use.
•It is possible that PI
cannot be used if the initial
cash flow is an outflow.
•Methods needs to be
adjusted when there are
mutually exclusive
projects.

16. Capital Budgeting 16
The DCF techniques ,NPV, IRR & PI, are all
good techniques for capital budgeting and
allow us to accept or reject investment project
consistent with the goal of shareholders wealth
maximization.
There are times when one techniques output is
better for some decision or when a techniques
has to be modified given certain
circumstances.
CAPITAL BUDGETING