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Presented by:-Ashima Thakur & Baljinder
Capital budgeting techniques under certainty;
and
II. Capital budgeting techniques under
uncertainty.
Risk can be defined as the chance that the actual outcome will differ from the
expected outcome. Uncertainty relates to the situation where a range of differing
outcome is possible, but it is not possible to assign probabilities to this range of
outcomes.
 Conventional Techniques for Risk Analysis:
(a) Payback
(b) Risk-adjusted Discount Rate
(c) Certainty Equivalent
Meaning:
It is the number of years required to recover the original cash outlay invested in a
project.
Methods to compute PBP:
A ) The first method can be applied when the CFAT is uniform. In such a situation
the initial cost of the investment is divided by the constant annual cash flow: For
example, if an investment of Rs.100000 in a machine is expected to generate cash
inflow of Rs.20,000 p.a. for 10 years.
Its PBP will be calculated using following formula:
PBP=Initial Investment/ constant annual cash inflow = 1,00,000 /20,000=5 yrs
b) The second method is used when a project’s CFAT are not equal. In such a
situation PBP is calculated by the process of cumulating CFAT till the time when
cumulative cash flow becomes equal to the original investment outlays.
For example, A firm requires an initial cash outflow of Rs. 20,000 and the annual
cash inflows for 5 years are Rs. 6000, Rs. 8000, Rs. 5000, Rs. 4000 and Rs. 4000
respectively.
Calculate PBP.
Here, When we cumulate the cash flows for the first three years, Rs. 19,000 is
recovered. In the fourth year Rs.4000 cash flow is generated by the project but we
need to recover only Rs.1000 so the time required recovering Rs. 1000 will be
(Rs.1000/Rs.4000)× 12months = 3 months. Thus, the PBP is 3 years and 3 months
(3.25 years).
Decision Rule:
 The PBP can be used as a decision criterion to select investment proposal. If the
PBP is less than the maximum acceptable payback period, accept the project.
If the PBP is greater than the maximum acceptable payback period, reject the
project.
To allow for risk, the businessmen required a premium over and above an alternative
which is risk free. It is proposed that risk premium be incorporated into the capital
budgeting analysis through the discount rate. i.e. If the time preference for the money
is to be recognized by discounting estimated future cash flows, at some risk free rate,
to there present value, then, to allow for the riskiness of the future cash flow a risk
premium rate may be added to risk free discount rate. Such a composite discount
would account for both time preference and risk preference.
RADR= Risk free rate + Risk Premium OR
k = Rf + Rp
 The RADR accounts for risk by varying discount rate depending on the degree of
risk of investment projects. The following figure portrays the relationship between
amount of risk and the required k.
 The following equation can be used:-
 NPV = ΣNCFt / ( 1+k )t - CO
Where k is a risk-adjusted rate.
The risk adjusted approach can be used for both NPV & IRR.
If NPV method is used for evaluation, the NPV would be calculated using risk
adjusted rate.
If NPV is positive, the proposal would qualify for acceptance, if
it is negative, the proposal would be rejected.
In case of IRR, the IRR would be compared with the risk adjusted required
rate of return.
If the ‘r’ exceeds risk adjusted rate, the proposal would be
accepted, otherwise not.
For example, if an investment project has following cash flows, its NPV using RADR will be as
follows:
Risk free rate is 6% and Risk adjusted rate is 10%.
Year CFAT
(RS.)
PV @10 PV( Rs.)
1
2
3
50000
40000
45000
LESS:
0.909
0.826
0.751
ΣPV
Investment
45450
33040
33795
---------
112285
150000
-------
The certainty equivalent coefficient (α) can be determined as a relationship between the
certain cash flows and the uncertain cash flows.
For example, if a company expected a risky cash flow of Rs. 90,000 and a risk free cash
flow of Rs. 65,000 then
(α1 ) will be calculated as follows:-
(α)t =NCFt* /NCFt = risk free cash flows / risky cashflows=65,000 /90,000
The certainty equivalent coefficient (α ) t assumes a value between 0 and 1 and varies
inversely with risk. The higher the risk, the lower the (α)t and the lower the risk, the
higher the (α)t .
The certainty equivalent approach can be expressed in the form of equation as
follows:
NPV=Σαt NCFt / (1+kf)t
where, NCFt = Net cash flow,
α t= the certainty equivalent coefficient,
kf = Risk free rate
(a) Sensitivity Analysis
(b) Scenario Analysis
(c)Simulation Analysis
1) The sensitivity analysis helps in identifying how sensitive are the various
estimated variables of the project. It shows how sensitive is a project’s NPV or IRR
for a given change in particular variables.
Steps:
The following three steps are involved in the use of sensitivity analysis.
1. Identify the variables which can influence the project’s NPV or IRR.
2. Define the underlying relationship between the variables.
3. Analyze the impact of the change in each of the variables on the project’s
NPV or IRR.
The Project’s NPV or IRR can be computed under following three assumptions
in sensitivity analysis.
1. Pessimistic (i.e. the worst),
2. Expected (i.e. the most likely)
3. Optimistic (i.e. the best)
For example, A company has two mutually exclusive projects for
process improvement. The management has developed following
estimates of the annual cash flows for each project having a life of
fifteen years and 12% discount rate.
PROJECT A
Net investments 90000
CFAT Estimates PVAIF12%,
15yrs
PV NPV
pessimistic 10000 6.811 68110 (21890)
Most likely 15000 6.811 102165 12165
optimistic 21000 6.811 143031 53031
SENSTIVITY ANALYSIS:-
PROJECT A
Net investments 90000
CFAT Estimates PVAIF12%,
15yrs
PV NPV
pessimistic 13500 6.811 91948.5 1948.5
Most likely 15000 6.811 102165 12165
optimistic 18000 6.811 122598 32598
The NPV calculations of both the projects suggest that the projects are equally
desirable on the basis of the most likely estimates of cash flows.
However, the Project– A is riskier than Project – B because its NPV can be negative
to the extent of Rs. 21,890 but there is no possibility of incurring any losses with
project B as all the NPVs are positive.
As the two projects are mutually exclusive, the actual selection of the projects
depends on decision maker’s attitude towards the risk. If he is ready to take risk, he
will select Project A, because it has the potential of yielding NPV much higher than
(Rs. 53031) Project B. But if he is risk averse, he will select project B.
The another way to examine the risk of investment is to analyze the impact of
alternative combination of variables , called the scenarios , on the project NPV.
EXAMPLE:- In the expected scenario, it may be possible to increase the sales
volume of 1 lac units to 1,25000 units . If the company reduces the selling price
from Rs. 15 to Rs. 13.50, resorts to aggressive advertisement campaign, their by
increasing unit variable cost to Rs.7.1( 5% increase) & fixed cost is rs.44,000.
Calculate the NPV.
OPTIMISTIC :-1,25,000
PESSIMISTIC:-75,000
NEUTRAL:- 1,00,000
REVENUE = 1250 *!6.50=20625RS.
VARIABLES BASE VALUE PESSISMISTIC OPTIMISTIC
SALES VOLUME 1000 750 1250
SELLING PRICE
/UNIT
RS.15 13.50 16.50
VARIABLE COST /
UNIT
7.1 7.43 6.75
FIXED COST 4400 4840 4400
 Sensitivity analysis and Scenario analysis are quite useful to understand the
uncertainty of the investment projects. But both the methods do not consider the
interactions between variables and also, they do not reflect on the probability of
the change in variables.
Monte simulation considers the interaction among variables & probabilities of
change in variables & its impact on NPV of cash inflows . In this a computer generates
a very large no. of scenarios according to the probability distribution of variables.
Steps:-
1)Identification of the variables , which influences the cash inflows.
Initial investment ,Market size ,Fixed cost & variable cost , market growth rate
2) Specify the formula which relates the variables.
3)Assign the probabilities to each variables
4)Develop a computer program, that randomly selects 1 value from the probability
with each variable & uses these values, to calculate projects NPV.
Presentation on capital budgeting

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Presentation on capital budgeting

  • 2. Capital budgeting techniques under certainty; and II. Capital budgeting techniques under uncertainty.
  • 3. Risk can be defined as the chance that the actual outcome will differ from the expected outcome. Uncertainty relates to the situation where a range of differing outcome is possible, but it is not possible to assign probabilities to this range of outcomes.  Conventional Techniques for Risk Analysis: (a) Payback (b) Risk-adjusted Discount Rate (c) Certainty Equivalent
  • 4. Meaning: It is the number of years required to recover the original cash outlay invested in a project. Methods to compute PBP: A ) The first method can be applied when the CFAT is uniform. In such a situation the initial cost of the investment is divided by the constant annual cash flow: For example, if an investment of Rs.100000 in a machine is expected to generate cash inflow of Rs.20,000 p.a. for 10 years. Its PBP will be calculated using following formula: PBP=Initial Investment/ constant annual cash inflow = 1,00,000 /20,000=5 yrs
  • 5. b) The second method is used when a project’s CFAT are not equal. In such a situation PBP is calculated by the process of cumulating CFAT till the time when cumulative cash flow becomes equal to the original investment outlays. For example, A firm requires an initial cash outflow of Rs. 20,000 and the annual cash inflows for 5 years are Rs. 6000, Rs. 8000, Rs. 5000, Rs. 4000 and Rs. 4000 respectively. Calculate PBP. Here, When we cumulate the cash flows for the first three years, Rs. 19,000 is recovered. In the fourth year Rs.4000 cash flow is generated by the project but we need to recover only Rs.1000 so the time required recovering Rs. 1000 will be (Rs.1000/Rs.4000)× 12months = 3 months. Thus, the PBP is 3 years and 3 months (3.25 years). Decision Rule:  The PBP can be used as a decision criterion to select investment proposal. If the PBP is less than the maximum acceptable payback period, accept the project. If the PBP is greater than the maximum acceptable payback period, reject the project.
  • 6. To allow for risk, the businessmen required a premium over and above an alternative which is risk free. It is proposed that risk premium be incorporated into the capital budgeting analysis through the discount rate. i.e. If the time preference for the money is to be recognized by discounting estimated future cash flows, at some risk free rate, to there present value, then, to allow for the riskiness of the future cash flow a risk premium rate may be added to risk free discount rate. Such a composite discount would account for both time preference and risk preference. RADR= Risk free rate + Risk Premium OR k = Rf + Rp  The RADR accounts for risk by varying discount rate depending on the degree of risk of investment projects. The following figure portrays the relationship between amount of risk and the required k.  The following equation can be used:-  NPV = ΣNCFt / ( 1+k )t - CO Where k is a risk-adjusted rate.
  • 7. The risk adjusted approach can be used for both NPV & IRR. If NPV method is used for evaluation, the NPV would be calculated using risk adjusted rate. If NPV is positive, the proposal would qualify for acceptance, if it is negative, the proposal would be rejected. In case of IRR, the IRR would be compared with the risk adjusted required rate of return. If the ‘r’ exceeds risk adjusted rate, the proposal would be accepted, otherwise not. For example, if an investment project has following cash flows, its NPV using RADR will be as follows: Risk free rate is 6% and Risk adjusted rate is 10%. Year CFAT (RS.) PV @10 PV( Rs.) 1 2 3 50000 40000 45000 LESS: 0.909 0.826 0.751 ΣPV Investment 45450 33040 33795 --------- 112285 150000 -------
  • 8. The certainty equivalent coefficient (α) can be determined as a relationship between the certain cash flows and the uncertain cash flows. For example, if a company expected a risky cash flow of Rs. 90,000 and a risk free cash flow of Rs. 65,000 then (α1 ) will be calculated as follows:- (α)t =NCFt* /NCFt = risk free cash flows / risky cashflows=65,000 /90,000 The certainty equivalent coefficient (α ) t assumes a value between 0 and 1 and varies inversely with risk. The higher the risk, the lower the (α)t and the lower the risk, the higher the (α)t . The certainty equivalent approach can be expressed in the form of equation as follows: NPV=Σαt NCFt / (1+kf)t where, NCFt = Net cash flow, α t= the certainty equivalent coefficient, kf = Risk free rate
  • 9. (a) Sensitivity Analysis (b) Scenario Analysis (c)Simulation Analysis 1) The sensitivity analysis helps in identifying how sensitive are the various estimated variables of the project. It shows how sensitive is a project’s NPV or IRR for a given change in particular variables. Steps: The following three steps are involved in the use of sensitivity analysis. 1. Identify the variables which can influence the project’s NPV or IRR. 2. Define the underlying relationship between the variables. 3. Analyze the impact of the change in each of the variables on the project’s NPV or IRR.
  • 10. The Project’s NPV or IRR can be computed under following three assumptions in sensitivity analysis. 1. Pessimistic (i.e. the worst), 2. Expected (i.e. the most likely) 3. Optimistic (i.e. the best) For example, A company has two mutually exclusive projects for process improvement. The management has developed following estimates of the annual cash flows for each project having a life of fifteen years and 12% discount rate.
  • 11. PROJECT A Net investments 90000 CFAT Estimates PVAIF12%, 15yrs PV NPV pessimistic 10000 6.811 68110 (21890) Most likely 15000 6.811 102165 12165 optimistic 21000 6.811 143031 53031 SENSTIVITY ANALYSIS:- PROJECT A Net investments 90000 CFAT Estimates PVAIF12%, 15yrs PV NPV pessimistic 13500 6.811 91948.5 1948.5 Most likely 15000 6.811 102165 12165 optimistic 18000 6.811 122598 32598
  • 12. The NPV calculations of both the projects suggest that the projects are equally desirable on the basis of the most likely estimates of cash flows. However, the Project– A is riskier than Project – B because its NPV can be negative to the extent of Rs. 21,890 but there is no possibility of incurring any losses with project B as all the NPVs are positive. As the two projects are mutually exclusive, the actual selection of the projects depends on decision maker’s attitude towards the risk. If he is ready to take risk, he will select Project A, because it has the potential of yielding NPV much higher than (Rs. 53031) Project B. But if he is risk averse, he will select project B.
  • 13. The another way to examine the risk of investment is to analyze the impact of alternative combination of variables , called the scenarios , on the project NPV. EXAMPLE:- In the expected scenario, it may be possible to increase the sales volume of 1 lac units to 1,25000 units . If the company reduces the selling price from Rs. 15 to Rs. 13.50, resorts to aggressive advertisement campaign, their by increasing unit variable cost to Rs.7.1( 5% increase) & fixed cost is rs.44,000. Calculate the NPV. OPTIMISTIC :-1,25,000 PESSIMISTIC:-75,000 NEUTRAL:- 1,00,000
  • 14. REVENUE = 1250 *!6.50=20625RS. VARIABLES BASE VALUE PESSISMISTIC OPTIMISTIC SALES VOLUME 1000 750 1250 SELLING PRICE /UNIT RS.15 13.50 16.50 VARIABLE COST / UNIT 7.1 7.43 6.75 FIXED COST 4400 4840 4400
  • 15.  Sensitivity analysis and Scenario analysis are quite useful to understand the uncertainty of the investment projects. But both the methods do not consider the interactions between variables and also, they do not reflect on the probability of the change in variables. Monte simulation considers the interaction among variables & probabilities of change in variables & its impact on NPV of cash inflows . In this a computer generates a very large no. of scenarios according to the probability distribution of variables. Steps:- 1)Identification of the variables , which influences the cash inflows. Initial investment ,Market size ,Fixed cost & variable cost , market growth rate 2) Specify the formula which relates the variables. 3)Assign the probabilities to each variables 4)Develop a computer program, that randomly selects 1 value from the probability with each variable & uses these values, to calculate projects NPV.