Investment Analysis
Lecture: 10
Course Code: MBF702
Outline
•
RECAP
•
•
Risk Analysis in investment analysis
Techniques for risk analysis
Comparing Methods
Basis of
measurement
Measure
expressed as
Strengths
Limitations
Payback
period
Cash
flow s
Number
of years
Easy to
Understand
Accounting
rate of return
Accrual
income
Percent
Easy to
Understand
Net present
Internal rate
value
of return
Cash flow s
Cash flow s
Profitability
Profitability
Dollar
Percent
Amount
Considers time Considers time
value of money value of money
Allow s
Allow s
Accommodates
Allow s
comparison
comparison
different risk
comparisons
across projects across projects
levels over
of dissimilar
a project's life
projects
Doesn't
Doesn't
Difficult to
Doesn't reflect
consider time
consider time
compare
varying risk
value of money value of money
dissimilar
levels over the
projects
project's life
Doesn't
consider cash
flow s after
payback period
Doesn't give
annual rates
over the life
of a project
Risk in Investment Appraisal
Risk: refers to a situation where the future is unclear and there is more
than one possible outcomes.
4
Techniques for dealing with Risk
• The techniques for dealing with risk include:
a) the expected NPV rule;
b) the risk-adjusted discount rate approach;
c) sensitivity analysis
d) Simulation
e) Scenario Analysis
5
Expected Net Present Value
The expected NPV rule (ENPV):
EV of a project is the mean value which will be obtained if
the project was repeated many times over
EV is not the most likely value of the project.
It is only the weighted average of all the possible outcomes
EV is calculated by multiplying the each possible outcome
by its probability of occurrence and then add them up
6
Example
•
• Shorten Ltd needs to purchase a machine to manufacture a new product.
The choice lies between two machines (A and B). Each machine has an
estimated life of three years with no scrap value.
• Machine A will cost £30,000 and machine B will cost £40,000, payable
immediately in each case. The total variable cost of manufacture of each
unit are £2 if made on machine A, but only £1.00 if made on machine B.
This is because machine B is more sophisticated and requires less labour
to operate it.
• The product will sell for £8 each.
• The demand for the product is uncertain but is estimated at 2,000 units
for each year, 3,000 units for each year or 5,000 units for each year. (Note
that whatever sales level actually occurs, that level will apply to each
year.)
• The sales manager has placed probabilities on the level of demand as
follows:
7
Shorten Ltd: Example
Annual demand Probability of occurrence
2000
0.2
3000
0.6
5000
0.2
a)
b)
Presume that both taxation and fixed costs will be unaffected by any
decision made.
Shorten Ltd’s cost of capital is 6% p.a.
Calculate the NPV for each of the three activity levels for each machine
A and B and state your conclusion.
Calculate the expected NPV for each machine and state your
conclusion.
8
Shorten Ltd: Example
Machine A
2000
Demand
3000
Demand
£
•
•
•
•
•
•
•
•
•
•
•
•
Year 0
1 (£8-£2)/unit
2
3
Discounted :
Year0
1
2
3
(30,000)
12,000
12,000
12,000
£
(30,000)
18,000
18,000
18,000
5000
Demand
£
(30,000)
30,000
30,000
30,000
Factor
(1.00)
(0.94)
(0.89)
(0.84)
£
(30,000)
11,280
10,680
10,080
£2,040
£
(30,000)
16,920
16,020
15,120
£18,060
£
(30,000)
28,200
26,700
25,200
£50,100
Expected value
= (0.2 x 2,040) + (0.6 x 18,060) + (0.2 x 50,100)
= £21,264
9
Solution
Different cash flows of Machine B
2000
3000
Demand
Demand
£
£
Year 0
40,000
40,000
1(£8-£1)/unit 14,000
21,000
2
14,000
21,000
3
14,000
21,000
5000
Demand
£
40,000
35,000
35,000
35,000
10
Solution
Demand:
Discounted : Factor
Year0
(1.00)
1
(0.94)
2
(0.89)
3
(0.84)
2000 3000
5000
£
£
£
(40,000) (40,000) (40,000)
13,160
19,740 32,900
12,460
18,690 31,150
11,760
17,640 29,400
(£2,620) £16,070 £53,450
Expected value
= (0.2 x 2,620) + (0.6 x 16,070) + (0.2 x 53,450)
= £19,808
11
The Risk Adjusted Discount Rate
This approach to investment decision making
process is an attempt to deal with risk in a manner
that takes account of the attitudes of the decision
maker.
12
The Risk Adjusted Discount Rate
Example 4.2
• Before any investments are considered, the decision
maker should begin by determining an appropriate
discount rate for risk-free investments.
• Suppose that the rate on such bonds issued by the
government is currently 7%. This figure should be
used as the base from which discount rates are
calculated for risky investments.
13
The Risk Adjusted Discount Rate
Class of Risk
•
•
•
•
•
•
Example of
type of project
Risk Premium
Discount rate
Very low
Low
Buying a bond
1%
8%
Improvement in
Existing factory
3%
10%
Medium
Increased in existing
Output
5%
12%
High
Launch a new product 8%
15%
Very high
Research on areas
Related to current activity 11%
18%
The use of risk-adjusted discount rate approach to investment appraisal is indeed, a
common sense approach. However, it is subjective, particularly, the choice of the risk
premiums and the assignment of projects to particular risk classes is based on personal
judgement.
14
Sensitivity Analysis
• Sensitivity analysis:
– is a procedure that calculates the changes in the
net present value given a change in one of the
cash flow elements such as product price.
– With sensitivity analysis each of the figures used
in the NPV is examined in turn, to determine how
variations from the estimated figures impact on
the NPV
15
Sensitivity Analysis
– Sensitivity analysis helps managers to gain better
understanding of the nature and degree of risk
associated with a project;
– because it reveals the margin of safety associated
with each key variable relating to a particular
project.
– It is a form of break even analysis. The point at
which NPV is equal to zero is the break-even
point.
16
Sensitivity Analysis
Identifying the key or critical variable i.e. those
with short margin of safety.
17
Sensitivity Analysis – Formulas
•
•
•
•
•
•
•
Selling Price: NPV / Present Value of Sales
Sales Volume: NPV / Present Value of CM
Variable cost: NPV / Present Value of Variable Cost
Fixed Cost: NPV / Present Value of Fixed Cost
Cost / Initial Investment: NPV / Present Value of Investment
Discount Rate: IRR
Project Life: ( Total Life - Discounted Payback Period)/ total life
Sensitivity analysis - Question
Swift Ltd, which has a cost of capital of 12 per cent, is considering
the investment of £7m in an improved moulding machine project
with a life of four years. The garden ornaments produced will retail at
£9.20 each and cost £6 each to make. It is expected that 800,000
ornaments will be sold each year. What are the key variables for the
project?
19
Sensitivity analysis - Solution
NPV of the project can be expressed in terms of the project
variables as follows:
NPV = ( (S -VC) X CPVF.) – I0
Where: S = Selling price per unit
VC = Variable cost per unit
N = No of units sold per year
I0 = initial investment
CPVF. = Cumulative present value factor for four years at 12%
20
Sensitivity analysis - Solution
Inserting the information given in the question and finding the cumulative PV
factor from annuity table, we have:
(9.20 - 6.00) X800,000X 3.037)-7,000,000 = 0
21
Sensitivity analysis (a) Initial investment
a)
Initial investment.
Find the value of I0 that makes the NPV zero
I0 = (9.20 -6.00) x 800,000 x 3.037) = £7,774,720
This is an increase of £774,720 or 11.1 per cent on the planned
initial investment
22
Sensitivity analysis (b) sales price (c)
variable cost
b)
Sales price
S = 6.00 + (7,000,000 / (800,000 x 3.037) ) = £8.88
This is a decrease of 32 pence or 3.5 per cent of planned sales
price.
c)
Variable cost
As a decrease of 32 pence in sales price makes the NPV zero, an
increase of 32 pence or 5.3 per cent in variable cost will have the
same effect.
23
Sensitivity analysis (d) Sales volume
d). Sales volume
N = 700,000 / (9.20 - 6.00) x 3.037) = 720,283
• This is a decrease of 79,717 units or 10 per
cent on the planned sales volume.
24
Sensitivity analysis (e) Discount rate
CPVF = 7,000,000 / (9.20 – 6.00) X 800,000) = 2.734
• Using the annuity tables 2.743 corresponds to the discount rate of
almost exactly 17 per cent. An increase of 5 per cent in absolute
terms or 42 per cent on the current project discount rate.
Sensitivity analysis- Solution summary
Sensitivity analysis of the proposed investment by Swift Ltd
•
•
•
•
Variable
Original est. B/E point
Sales Volume 800,000
720,283
Sales price £9.20
£8.88
Variable cost £6.00
£6.32
Discount rate 12%
17%
•
Initial Inv
£7,000,000
£7,774,720
Difference Dif. as % Sensitivity
(79,717) 10%
Low
(£0.32) 3.5%
High
£0.32. 5.3%
High
5%
42% Very Low
£774,720 11.1%
Low
Advantages and Disadvantages
Advantages
– Useful in directing the attention of managers to the most
sensitive variables of the project
Disadvantages
– Does not formally quantify risk
– Does not clearly provide any clear-cut decision rule
Sensitivity analysis- summary
• Sensitivity analysis is one method of analyzing the risks surrounding
capital expenditure project & enables an assessment to be made of
how responsive the project NPV is to changes in the variables used
to calculate that NPV.
• A sensitivity analysis calculates the consequences of incorrectly
estimating a variable in your NPV analysis.
• It forces you:
• To identify the variables underlying your analysis.
• To focus on how changes to these variables could impact the
expected NPV.
• To consider what additional information should be collected
to resolve uncertainties about the variables.
Scenario Analysis
– A scenario analysis involves changing several variables at once in your
NPV forecast.
Simulation
• Simulation Analysis
– A simulation analysis uses a computer to generate hundreds, or even
thousands, of possible scenarios.
– A probability distribution is assigned to each combination of variables
to create an entire range of potential outcomes.