Lecture 4 Investment Appraisal III: Risk analysis

1
Lecture 4 Investment Appraisal III Risk
analysis

• Objectives
• Discuss the relationship between risk and return
• Evaluate investment projects in the conditions of
  uncertainty
• Discuss the techniques used to evaluate
  investment projects under conditions of
  uncertainty
• Discuss risk analysis in practice

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Risk in Investment Appraisal

• Risk refers to a situation where the future is
  unclear and there is more than one possible
  outcomes.

3
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

4
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

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Example 4.1

• 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

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Shorten Ltd Example 4.1

• Annual demand Probability of occurrence
• 2000 0.2
• 3000 0.6
• 5000 0.2
• Presume that both taxation and fixed costs will
  be unaffected by any decision made.
• Shorten Ltds 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.

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Shorten Ltd Example 4.1

• Machine A
• 2000 3000
  5000
• Demand Demand
  Demand
• 
  
  
• Year 0 (30,000)
  (30,000) (30,000)
• 1 (8-2)/unit
  12,000 18,000 30,000
• 2 12,000
  18,000 30,000
• 3
  12,000 18,000 30,000
• Discounted Factor
• 
  
  
• Year0 (1.00) (30,000)
  (30,000) (30,000)
• 1 (0.94) 11,280
  16,920
  28,200 2
  (0.89)
  10,680 16,020
  26,700
• 3 (0.84)
  10,080 15,120
  25,200
• 
  2,040 18,060
  50,100
• Expected value
• (0.2 x 2,040) (0.6 x 18,060) (0.2 x 50,100)
• 21,264

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Solution 4.1

• Different cash flows of Machine B
• 2000 3000 5000
• demand demand demand
  
• 
  
• Year 0 40,000 40,000 40,000
• 1(8-1)/unit 14,000 21,000 35,000
• 2 14,000 21,000 35,000
• 3 14,000 21,000 35,000

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Solution 4.1

• 2000 3000 5000
• Discounted Factor  
• Year0 (1.00) (40,000) (40,000)
  (40,000) 
• 1 (0.94) 13,160 19,740 32,900 
• 2 (0.89) 12,460 18,690 31,150 
• 3 (0.84) 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

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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.

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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.

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The Risk Adjusted Discount Rate

• Class of Risk Example of Risk Premium
  Discount rate
• type of project
• Very low Buying a bond 1 8
• Low 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.

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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

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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.

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Sensitivity Analysis

• Identifying the key or critical variable i.e.
  those
• with short margin of safety.

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Sensitivity analysis

• Example 4.3
• 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?

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Solution 4.3

• 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

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Sensitivity analysis

• 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

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Sensitivity analysis

• 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

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Sensitivity analysis

• 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.
• 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.

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Exercise 4.1

1. Try to calculate the 32 pence or 5.3 by using
   the general equation above

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Sensitivity analysis

• 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.

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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.

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Sensitivity analysis- summary

• Sensitivity analysis of the proposed investment
  by Swift Ltd
• Variable Original est. B/E point
  Difference Dif. as Sensitivity
• Sales Volume 800,000 720,283
  (79,717) 10 Low
• Sales price 9.20 8.88
  (0.32) 3.5 High
• Variable cost 6.00 6.32
  0.32. 5.3 High
• Discount rate 12 17 5
  42 Very Low
• Initial Inv 7,000,000 7,774,720
  774,720 11.1 Low

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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