adjust for risk by varying the discount rate present a sensitivity graph and discuss
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LEARNING OBJECTIVES. Adjust for risk by varying the discount rate Present a sensitivity graph and discuss break-even NPV Undertake scenario analysis Make use of probability analysis to describe the extent of risk facing a project and thus make more enlightened choices - PowerPoint PPT PresentationTRANSCRIPT
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.1
• Adjust for risk by varying the discount rate • Present a sensitivity graph and discuss break-even NPV • Undertake scenario analysis • Make use of probability analysis to describe the extent of risk facing a project and thus make more enlightened choices • Discuss the limitations, explain the appropriate use and make an accurate interpretation of the results of the four risk techniques described in this chapter
LEARNING OBJECTIVES
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.2
What is Risk?
• Certainty
• Risk and uncertainty
• Objective probabilities
• Subjective probabilities
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.3
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.4
• Subjective probabilities
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.5
ADJUSTING FOR RISK THROUGH THE DISCOUNT RATE
Level of risk Risk-free rate (%) Risk premium (%) Risk-adjusted rate (%)
Low 9 +3 12Medium 9 +6 15High 9 +10 19
The project currently being considered has the following cash flows:
Time (years) 0 1 2Cash flow (£) –100 55 70
If the project is judged to be low risk:
55 70NPV = –100 + + = +£4.91
1 + 0.12 2
Accept.
If the project is judged to be medium risk:
55 70NPV = –100 + + = +£0.76
1 + 0.152
Accept.
If the project is judged to be high risk:
55 70NPV = –100 + + = –£4.35
1 + 0.192
Reject.
(1 + 0.12)
(1 + 0.15)
(1 + 0.19)
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.6
Adjusting for risk
Drawbacks of the risk-adjusted discount rate method:
• Risk classification is subjective• Difficulty in selecting risk premiums
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.7
Sensitivity analysis identifies the extent to which NPV changes as key variables are changed
A “what-if” analysis:
Acmart plc• new product line – Marts• likely demand for 1,000,000 a year• price of £1• four-year life of product• initial investment £800,000
Cash flow per unit £Sale price 1.00CostsLabour 0.20Materials 0.40Relevant overhead 0.10
0.70Cash flow per unit 0.30
Required rate of return = 15 per cent
SENSITIVITY ANALYSIS
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.8
Annual cash flow = 30p 1,000,000 = £300,000.
Present value of annual cash flows = 300,000 annuity factor for 4 years @ 15%
£= 300,000 2.855 = 856,500Less initial investment –800,000Net present value + 56,500
NET PRESENT VALUE (1)
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.9
• What if the price achieved is only 95p for sales of 1m units (all other factors remaining constant)? Annual cash flow = 25p 1m = £250,000.
£ 250,000 2.855 713,750 Less initial investment 800,000 Net present value –86,250
• What if the price rose by 1 per cent? Annual cash flow = 31p 1m = £310,000.
£ 310,000 2.855 885,050 Less initial investment 800,000 Net present value +85,050
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.10
• What if the quantity demanded is 5 per cent more than anticipated? Annual cash flow = 30p 1.05m = £315,000.
£ 315,000 2.855 899,325 Less initial investment 800,000 Net present value +99,325
• What if the quantity demanded is 10 per cent less than expected? Annual cash flow = 30p 900,000 = £270,000.
£ 270,000 2.855 770,850 Less initial investment 800,000 Net present value –29,150
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.11
• What if the appropriate discount rate is 20 per cent higher than originally assumed (that is, it is 18 per cent rather than 15 per cent)? 300,000 annuity factor for 4 years @ 18%
£ 300,000 2.6901 807,030 Less initial investment 800,000
+7,030
• What if the discount rate is 10 per cent lower than assumed (that is, it becomes 13.5 per cent)? 300,000 annuity factor for 4 years @ 13.5%.
£ 300,000 2.9441 883,230 Less initial investment 800,000
+83,230
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.12
Sensitivity graph for Marts
–20–100
–15 –10 –5 0 5 10 15 20 25
–50
0
50
100
% deviation of variable from expectation
Saleprice
Salevolume
DiscountrateN
PV
(£0
00)
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.13
Break-even NPV calculations
Advantages of using sensitivity analysis:
• Information for decision making
• To direct search
• To make contingency plans
Drawbacks of sensitivity analysis:
• No formal assignment of probabilities
• Each variable is changed in isolation
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.14
Acmart plc: Project proposal for the production of Marts
SCENARIO ANALYSIS Observing NPV when numerous factors change Worst-case scenarioSales 900,000 unitsPrice 90pInitial investment £850,000Project life 3 yearsDiscount rate 17%Labour costs 22pMaterial costs 45pOverhead 11p
Cash flow per unit £Sale price 0.90Costs
Labour 0.22Material 0.45Overhead 0.11
0.78
Cash flow per unit 0.12
Annual cash flow = 0.12 900,000 = £108,000£
Present value of cash flows 108,000 2.2096 = 238,637Less initial investment –850,000
Net present value –611,363
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.15
Acmart plc: Project proposal for the production of Marts (continued)
SCENARIO ANALYSIS
Best-case scenarioSales 1,200,000 unitsPrice 120pInitial investment £770,000Project life 4 yearsDiscount rate 14%Labour costs 19pMaterial costs 38pOverhead 9p
Cash flow per unit £Sale price 1.20Costs
Labour 0.19Material 0.38Overhead 0.09
0.66
Cash flow per unit 0.54
Annual cash flow = 0.54 1,200,000 = £648,000£
Present value of cash flows 648,000 2.9137 = 1,888,078Less initial investment –770,000
Net present value 1,118,078
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.16
Pentagon plc: Use of probability analysis
PROBABILITY ANALYSIS
Return Probability of return occurring
Project 1 16 1.0
Project 2 20 1.0
Project 3 –16 0.2536 0.5048 0.25
Project 4 –8 0.2516 0.5024 0.25
Project 5 –40 0.100 0.60
100 0.30
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.17
The expected return is the mean or average outcome calculated by weighting each of the possible outcomes by the probability of occurrence and then summing the result.
EXPECTED RETURN
x- = x1 p1 + x 2 p2 + ... x n pn
or
i=nx- = (x i pi)
i=1
where x- = the expected returni = each of the possible outcomes (outcome 1 to n) p = probability of outcome i occurringn = the number of possible outcomes
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.18
Pentagon plc: expected returns
Pentagon plc Expected returns
Project 1 16 1 16Project 2 20 1 20Project 3 –16 0.25 = –4
36 0.50 = 1848 0.25 = 12
26Project 4 –8 0.25 = –2
16 0.50 = 8
24 0.25 = 6
12Project 5 –40 0.1 = –4
0 0.6 = 0100 0.3 = 30
26
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.19
Pentagon plc: Probability distribution for projects 3 and 5
0
–100 –80 –60 –40 –16 0 20 36 48 80 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
£m
Project 3 Project 5
Pro
babi
lity
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.20
The standard deviation is a statistical measure of the dispersion around the expected value. The standard deviation is the square root of the variance
STANDARD DEVIATION
2
nVariance of x = x2 = (x1 – x- )2 p1 + (x2 – x- )2 p2 + ... (xn – x- )2 p
i=nor x
2 = {(x i – x- )2 pi}i=1
Standard deviation
i=n x = x
2 or {(xi – x- )2 pi}i=1
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.21
Pentagon plc: Calculating the standard deviations for the five projects
Outcome Probability Expected Deviation Deviation Deviation(Return) return squared squared
timesprobability
Project xi pi x- xi – x- (xi – x- )2 (xi – x- )2pi
1 16 1.0 16 0 0 0
2 20 1.0 20 0 0 0
3 –16 0.25 26 –42 1,764 44136 0.5 26 10 100 5048 0.25 26 22 484 121
Variance = 612Standard deviation = 24.7
4 –8 0.25 12 –20 400 10016 0.5 12 4 16 824 0.25 12 12 144 36
Variance = 144Standard deviation = 12
5 –40 0.1 26 –66 4,356 4360 0.6 26 –26 676 406
100 0.3 26 74 5,476 1,643
Variance = 2,485Standard deviation = 49.8
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.22
Pentagon plc: Expected return and standard deviation
Expected return x Standard deviation xProject 1 16 0Project 2 20 0Project 3 26 24.7Project 4 12 12
Project 5 26 49.8
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.23
Returns and utility
• Risk averter
• Risk lover
RISK AND UTILITY
Diminishing marginal utility
Investment A Investment BReturn Probability Return Probability
Poor economic conditions 2,000 0.5 0 0.5Good economic conditions 6,000 0.5 8,000 0.5Expected return 4,000 4,000
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.24
Project X will be preferred to Project Y if at least one of the following conditions apply:
1 The expected return of X is at least equal to the expected return of Y, and the variance is less than that of Y.
2 The expected return of X exceeds that of Y and the variance is equal to or less than that of Y.
MEAN-VARIANCE RULE
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.25
Pentagon plc: Expected return and standard deviations
00 12 24.7 49.8
5
10
15
20
25
30
Standard deviation
Project 1
Project 2
Project 4
Project 3
Project 5
Exp
ecte
d re
turn
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.26
EXPECTED NET PRESENT VALUES AND STANDARD DEVIATION
i=n
NPV = (NPVi pi)i=1
where NPV = expected net present valueNPV i = the NPV if outcome i occurs
p i = probability of outcome i occurringn = number of possible outcomes
The standard deviation of the net present value is
i=n
NPV = {(NPV i – NPV )2 p i}i=1
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.27
Purchase price, t0 £500,000Refurbishment, t0 £200,000
£700,000
The Year 1 cash flows are as follows:
HORIZON PLC
Probability Cash flow at end of Year 1
Good customer response 0.6 100,000Poor customer response 0.4 10,000
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.28
Conditional probabilities for the second yearIf the first year elicits a good response then:
Probability Cash flow at endof Year 2
1 Sales increase in second year 0.1 £2mor2 Sales are constant 0.7 £1.6mor3 Sales decrease 0.2 £0.8m
If the first year elicits a poor response then:
Probability Cash flow at endof Year 2
1 Sales fall further 0.5 £0.7mor2 Sales rise slightly 0.5 £1.2m
Note: All figures include net trading income plus sale of pub.
HORIZON PLC
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.29
An event tree showing the probabilities of the possible returns for Horizon plc
Cashflow atTime 0(£000s)
–700
Probabilitypi
Cashflow atTime 1(£000s)
Conditionalprobability
Cashflow atTime 2(£000s)
Jointprobability
Outcome
100
10
2,000
800
1,600
700
1,200
0.1
0.2
0.5
0.5
0.7
0.6 0.1 = 0.06
0.6
0.6
0.4 0.5 = 0.20
0.4 0.5 = 0.201.00
0.6
0.4
a
c
b
d
e
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.30
(1.1)2
2,000
(1.1)2
800
Expected net present value, Horizon plc
Outcome NPV ProbabilityNet present values(£000s)
100a –700 + + = 1044 1,044 0.06 = 631.1
100b –700 + + = 713 = 300
1.1
100c –700 + + = 52 = 6
1.1
10d –700 + + = –112 = –221.1
10e –700 + + = 301 = 601.1
Expected net present value 407or £407,000
(1.1)2
1,600
700(1.1)2
(1.1)2
1,200
713 0.42
52 0.12
–112 0.20
301 0.20
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.31
Exh
ibit
6.1
7 S
tan
dar
d d
evia
tion
for
Hor
izon
plc
Out
com
eP
roba
bili
tyE
xpec
ted
Dev
iati
onD
evia
tion
Dev
iati
on
£000
sN
PV
squa
red
squa
r ed
tim
es
prob
abil
ity
NP
V ip i
NP
VN
PV
i–
NP
V( N
PV i
–
NP
V)2
( NP
V i –
NP
V)2
pi
a1,
044
0.06
407
637
405,
769
24,3
46
b71
3 0.
42
407
306
93,6
3639
,327
c52
0.
12
407
–355
12
6,02
5 15
,123
d–1
12
0.20
40
7–5
19
269,
361
53,8
72
e30
1 0.
20
407
–106
11
,236
2,24
7
Var
ianc
e=
134,
915
Sta
ndar
d de
viat
ion
=13
4,91
5=
367
or£3
67,0
00
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.32
Independent Probabilities
The initial cash out flow = £150,000
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.33
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.34
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.35
Exhibit 6.21 The normal curve
THE RISK OF INSOLVENCY
95.44 per cent99.74 per cent
68.26per cent
–3 –2 –1 +1 +2 +3
Standard deviations
X
Pro
babi
lity
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.36
Exhibit 6.22 Probability of outcome being between expected return and one standard deviation from expected return
–3 –2 –1 +1 +2 +3
Standard deviations
Probability
X
34.13 per cent
Pro
babi
lity
95.44 per cent99.74 per cent
68.26per cent
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.37
Z =
where:
Z is the number of standard deviations from the mean
X is the outcome that you are concerned about
is the mean of the possible outcomes
is the standard deviation of the outcome distribution
THE Z STATISTIC
X –
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.38
Exhibit 6.23 The standard normal distribution
Value of the Probability that X liesZ statistic within Z standard deviations
above (or below) the expected value (%)
0.0 0.000.2 7.930.4 15.540.6 22.570.8 28.811.0 34.131.2 38.491.4 41.921.6 44.521.8 46.412.0 47.722.2 48.612.4 49.182.6 49.532.8 49.743.0 49.87
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.39
Exhibit 6.24 Probability of outcome between and 2 from
Roulette plc
Maximum loss = £5mExpected return = £8mStandard deviation = £6.5m
–3 –2 –1 +1 +2 +3
Outcome
Probability
X
47.72per cent
£–5m £+8m
Pro
babi
lity
6 RISK AND PROJECT APPRAISAL
Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002
OHT 6.40
• Too much faith can be placed in quantified subjective probabilities
• Too complicated for all managers to understand
• Projects may be viewed in isolation
PROBLEMS OF USING PROBABILITY ANALYSIS