Download risk analysis 2020 (1)

ASSESSING RISK
RELATED TO CB
We assess the future expected cash flows from
projects that we expect to invest.
Future cash flows are uncertain, and we use
forecasts of uncertain cash flows in capital
budgeting decisions
Thus,
risk is inherent in Capital Budgeting
Decisions
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Traditional Methods of Risk Analysis
◦Payback Period
◦Risk Adjusted Discount Rate
◦Certainty Equivalent Cash Flow
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Payback Period
◦Managers tend to choose projects with
the least pay back period with the
intention of avoiding risk of being
unable to recover the invested funds.
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Risk Adjusted Discount Rate
The discount rate is decided taking into
consideration the risk of each project. In
deciding the discount rate two factors are
considered
◦ Time preference
◦ Risk Preference
The adjustment for time preference comes with
the risk free interest rate.
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Risk adjustment is effected through the β
coefficient of the project which is used in
measuring risk.
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β coefficient
In the Capital Asset Pricing Model (CAPM) the premium for risk is
determined by multiplying the β coefficient by the difference
between the return for the Market portfolio and the risk free rate.
β(Rm -Rf)
β =Cov(rs, rm)/σ2m
by changing the value of the β coefficient relevant to each
project the proportion for risk preference can be calculated.
A higher β value will be selected for high risk projects and a low β
value will be selected for low risk projects.
Higher β values will give a higher discount rate and lower β values
will give a lower discount rate
example
ER= RF + β(Rm -Rf)
Market return is 15 % , risk free rate is
6%, and β is .8
what will be the expected rate of
return?
what would it be if β =1.2 ? Or β = .73
?
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The Ramakrishna Ltd., in considering the purchase of a new
investment.
Two alternative investments are available (X and Y) each costing
Rs. 150000. Cash inflows
are expected to be as follows:
◦ The company has a target return on capital of 10%. Risk
premium rate are 2% and 8% respectively for investment
X and Y.
◦ Which investment should be preferred?
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year
X
Y
1
60,000
65,000
2
45,000
55,000
3
35,000
40,000
4
30,000
40,000
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solution
year
DF X
12%
CF X
DCFX
CFY
1
60,000
65,000
2
45,000
55,000
3
35,000
40,000
4
30,000
40,000
DFY
18%
DCFY
Investment X
Net present value = 133415 – 150000
= – Rs. 16585
Investment Y
Net present value = 156485 – 150000
= Rs. 6485
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Certainty Equivalent Cash Flow
This is another method of analyzing risk of projects. What we
do here is reduce the estimated cash flows to some
conservative level . For this purpose we use
a “Risk
Adjustment Factor” or “ Certainty Equivalent Coefficient”
which is called “α”
α = Certainty Equivalent CF/ Risky CF
This will take a value between 0-1 . Depending on the
riskiness of the cash flow this α value will change.
In order to convert the cash flows to the
certainty
equivalent values we can multiply the estimated risky cash
flows by the α coefficient.
In converting these to the PV we must use a risk free rate to
discount the cash flows
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Example
Following are details of a project
year
CF
α
1
50,000
0.7
2
60,000
0.6
3
40,000
0.8
4
30,000
0.5
Initial investment is Rs 90,000and the risk free rate is 12%
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year
CF
α
CE CF
1
50,000
0.7
35,000
2
60,000
0.6
36,000
3
40,000
0.8
32,000
4
30,000
0.5
15,000
We can discount the certainty Equivalent CF’s
by the
risk free discount rate.
NPV=-90,000 +92,260.80=2260.80
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exercise
◦ There are two projects A and B. Each involves an investment of Rs. 50,000. The
expected cash inflows and the certainly co-efficient are as under:
year
CF A
CE A
CF B
CE B
1
35,000
.8
25000
.9
2
30,000
.7
35000
.8
3
25,000
.9
20000
.7
Risk-free cutoff rate is 10%. Suggest which
of the two projects. Should be preferred
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solution
First calculate the adjusted cf’s and then
discount them by the risk free rate
◦ Project A
◦ Net present value = Rs. 56,316 – 50,000= Rs.
6,316
Project B
Net present value = 54,095 – 50,000= Rs. 4,095
As the net present value of project A in more
than that of project B. Project A should be
preferred:
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Non Traditional Methods
Statistical Techniques
◦Scenario Analysis
◦Sensitivity Analysis
◦
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Statistical Techniques
◦ We concentrate on two factors
Uncertainty
Probability
Future is uncertain . The Environment changes .
It is difficult to forecast cashflows under
uncertainty.
First we try and forecast the possible economic
conditions with their probability .
Then we would forecast the possible cashflows
under each economic condition.
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Example
year
Economic
Condition
Probability
NCF
1.0
-10,000
growth
0.2
7,000
normal
0.6
5,000
recession
0.2
3,000
growth
0.2
10,000
normal
0.7
8,000
recession
0.1
3,000
growth
0.1
9,000
normal
0.6
7,000
recession
0.3
4,000
0
1
2
3
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If the relevant discount rate is 12% , find the NCF for this project
year
EC
CF
P
ACF
1
growth
7,000
0.2
1400
normal
5,000
0.6
3000
recession
3,000
0.2
600
growth
10,000
0.2
2000
normal
8,000
0.7
5600
recession
3,000
0.1
300
growth
9,000
0.1
900
normal
7,000
0.6
4200
recession
4,000
0.3
1200
2
3
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AACF
5000
7900
6300
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year
DF
0
-10,000
1
4464
2
6297
3
4487
NPV
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DCF
5248
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Variance and Standard Deviation
By looking at variance of the real cash flows from the estimated cash flows would
give us a better picture about the risk of a project.
We can calculate the variance and the standard deviation of the cash flows.
given are the cash flows for two projects P and Q
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event
CF P
Prob. P
CF Q
Prob.Q
1
8,000
.10
5,000
.10
2
7,000
.20
10,000
.30
3
10,000
.40
8,000
.20
4
6,000
.20
7,000
.10
5
9,000
.10
12,000
.30
Calculate the variance and the standard deviation and
comment about the risk of these projects.
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event
CF P
Prob
CF*P
(Ecf-Ecf)^2*P
1
8,000
.10
800
(8000-8300)^2*.1
2
7,000
.20
1400
(7000-8300)^2*.2
3
10,000
.40
4000
(100008300)^2*.4
4
6,000
.20
1200
(6000-8300)^2*.2
5
9,000
.10
900
(9000-8300)^2*.1
(EcfEcf)^2*prob
1615.55
21
event
CF Q
Prob
CFQ*P
1
5,000
.10
500
(5000-9400)^2
*.10
2
10,000
.30
3000
(100009400)^2*.3
3
8,000
.20
1600
(80009400)^2*.2
4
7,000
.10
700
(70009400)^2*.1
5
12,000
.30
3600
(120009400)^2*.3
9400
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conclusion
◦ As the SD of Q is higher than the SD of P project Q is riskier than project P
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Coefficient of Variation
P 1615.55/8300*100= 19.46
Q 2245/9400*100=23.88
the investment decision depends on the
investors risk preference. If an investor is risk
averse s/he will select the project with lower risk
. If an investor prefers risk he will choose the
project that gives a higher return at higher risk
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X 1957.2 Y 1544.8 CV X31.31%,Y29.52%
As the co-efficient of variation of project ‘X’ is more than
that of ‘Y’ project X is more riskier.
Hence, project Y should be selected.
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exercise
From the following information, ascertain which project should be selected
on the basis of standard deviation.
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CF X
Prob.X
CF Y
Prob Y
3200
.2
32000
.1
5500
.3
5500
.4
7400
.3
7400
.4
8900
.2
8900
.1
Evaluate the projects on standard deviation and coefficient
of variation
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Scenario Analysis
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◦ When cash inflows are sensitive under different
circumstances more than one forecast of the future
cash inflows may be made. These inflows may be
regarded as ‘Optimistic’, ‘most likely’ and ‘pessimistic’.
Further cash inflows may be discounted to find out the
net present values under these three different situations.
If the net present values under the three situations differ
widely it implies that there is a great risk in the project
and the investor’s decision to accept or reject a project
will depend upon his risk bearing abilities.
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◦Mr. Silva is considering two mutually
exclusive projects ‘X’ and ‘Y’. You are
required to advise him about the
acceptability of the projects from the
following information.
◦discount rate of 15%.
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Cost of the
investment
Forecast cash
inflows per annum
for 5 years
Optimistic
Most likely
Pessimistic
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X
Y
1,00,000
1,00,000
60,000
35,000
20000
55,000
30,000
20000
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X
ACF
15%
PV
NPV
Optimistic
60,000
3.3522
2,01,132
1,01,132
Most likely
35,000
3.3522
1,17,327
17,327
Pessimistic
20,000
3.3522
67,105
(32,895)
Y
ACF
15%
PV
NPV
Optimistic
55000
3.3522
1,84,371
84,371
Most likely
30000
3.3522
1,00,566
566
Pessimistic
20000
3.3522
67,105
(32,895)
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The acceptability of the project will
depend upon Mr. Silva’s attitude
towards risk.
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Scenario Analysis
There can be three basic levels that are considered in scenario Analysis.
◦ Expected level or the Base level
◦ Upper bound or the Optimistic level
◦ Lower bound or the Pessimistic level
Upper bound Analysis
We expect the best
◦ Highest prices adopted in the case of Income
◦ Lowest prices adopted in the case of expenditure
◦ Expectation for a higher sales volume
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Lower Bound Analysis
We expect the worst in all aspects
◦ Lowest prices adopted in the case of Income
◦ Highest prices adopted in the case of expenditure
◦ Expectation for a lower sales volume
We first take the base level and then adjust it to suit the
upper bound level and the lower bound level
Example: a company is planning to spend Rs 200,000 for
capital expenditure, of which the life time is 5 years.
Cost of capital is estimated to be 12%
Following are relevant estimates for the firm
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Base level
Upper bound
Lower bound
Sales units
6000
6500
5500
Unit price
80
85
75
Variable cost
60
62
58
Fixed cost
50,000
55,000
45,000
Tax is 34% at all levels. Let us re arrange according to the
basic principles.
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Base level
Upper bound
Lower bound
Sales units
6000
6500
5500
Unit price
80
85
75
Variable cost
60
58
62
Fixed cost
50,000
45,000
55,000
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BL
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OP L
PML
sales
6000*80
480,000
6500*85
552500
5500*75
412,500
vc
6000*60
(360,000 )
6500*58
(377,000)
5500*72
(341,000)
contributio
n
120000
175500
71500
fc
(50,000)
(45,000)
(55,000)
70,000
130,500
16,500
depn
(40,000)
(40,000)
(40,000)
PBIT
30,000
90,500
(23,500)
34%
(10,200)
(30,770)
(7,990)
PAT
19,800
59,730
(15,510)
+depn
40,000
40,000
40,000
ACF
59,800
99,730
24,490
PVIFA
3.6048
3.6048
3.6048
PVOA
215,567
359,507
88,280
(200,000)
(200,000)
(200,000)
15,567
159,507
(11,718)
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IRR
15.1%
40.9%
-14.4%
Scenario analysis provides a basic idea about the cash
flows NPV and IRR which will help identifying risky
Areas, but it will not give a clear indication as to
which projects to be selected.
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Sensitivity Analysis
A sensitivity analysis is a technique used to determine how
different values of an independent variable impact a particular
dependent variable under a given set of assumptions.
Most important point here is to identify most important variable
that would make an influence on the NPV.
Once Identified we would change only that , and calculate NPV
keeping other variables at the base level . By looking at the
relationship between the NPV and this critical variable the
management may be able to take measures to control the risk
imposed by that variable
let us take the same example
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Base level
Upper bound
Lower bound
Sales units
6000
6500
5500
Unit price
80
85
75
Variable cost
60
62
58
Fixed cost
50,000
55,000
45,000
Tax is 34% at all levels. Let us re arrange according to the
basic principles.
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BL
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OP L
PML
sales
6000*80
480,000
6500*80
520,000
5500*80
440,000
vc
6000*60
(360,000 )
6500*60
(390,000)
5500*60
(330,000)
contributio
n
120,000
130,000
110,000
fc
(50,000)
(50,000)
(50,000)
70,000
80,000
60,000
depn
(40,000)
(40,000)
(40,000)
PBIT
30,000
40,000
20,000
34%
(10,200)
(13,600)
(6,800)
PAT
19,800
26,400
13,200
+depn
40,000
40,000
40,000
ACF
59,800
66,400
53,200
PVIFA
3.6048
3.6048
3.6048
PVOA
215,567
239,353
191,775
(200,000)
(200,000)
(200,000)
15,567
39,349
(8,225)
39
50
40
30
NPV
20
npv
Линейная (npv)
10
0
430
440
450
460
470
480
490
500
510
520
530
-10
-20
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sales
40
Slope of this line indicates the sensitivity of NPV to sales.
◦ Higher slope indicates high sensitivity of sales on NPV
◦ Lower slope indicates low sensitivity of sales on NPV
Sensitivity analysis using different variables and
comparing the slopes we can have an understanding
about the variables with high sensitivity and low
sensitivity. The High sensitivity variables may be
controlled in order to manage the risk
let us take another variable ; fc
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BL
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OP L
PML
sales
6000*80
480,000
6000*80
480,000
6000*80
480,000
vc
6000*60
(360,000 )
6000*60
(360,000)
6000*60
(360,000)
contributio
n
120,000
120,000
120,000
fc
(50,000)
(45,000)
(55,000)
70,000
75,000
65,000
depn
(40,000)
(40,000)
(40,000)
PBIT
30,000
35,000
25,000
34%
(10,200)
(11,900)
(8,500)
PAT
19,800
23,100
16,500
+depn
40,000
40,000
40,000
ACF
59,800
63,100
56,500
PVIFA
3.6048
3.6048
3.6048
PVOA
215,567
227,463
203,671
(200,000)
(200,000)
(200,000)
15,567
27,463
3671
42
30
25
NPV
20
15
npv
Линейная (npv)
10
5
0
0
10
20
30
40
50
60
FC
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The slope of this line will give us the sensitivity of NPV on FC
We can see that the slope of this line is smaller to the slope of the line
using sales
This implies that NPV is more sensitive to change of sales than for a change
of FC
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