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Modern Techniques To Evaluate Risk And Uncertainty

  Modern Techniques to Evaluate Risk and Uncertainty

Illustration 113

The manager of a fresh juice company has to decide upon the two investment projects. Project I is the investment in the introduction of high quality commodity and the investment J in the introduction of bottles of cold beverages. The two investment projects capitulates the subsequent net cash flows and the initial investment outlay.

                                                Net Cash Flows

Investment Projects

1st Year

2nd Year

3rd Year

Initial Investment Outlay in $

I

25000

35000

20000

60000

J

20000

40000

25000

55000

  1. Compute the net present value NPV of every project with risk free discount rate of 4%
  1. Which of the investment projects the manager must select if the risk premium is 2% on project I and 3 percent on project J.

Solution

  1. The NPV of projects I and J at 4% risk free rate of discount

                        NPVI   =          R1       +          R2       +          R3                   -Co
                                               (1+r)                (1+r) ^2           (1+r) ^3

                                    =          25000  +          35000  +          20000              - 60000
                                                (1+0.04)          (1+0.04) ^2     (1+0.04) ^3

                                    =          25000  +          35000  +          20000              - 60000
                                                1.04                 1.0816             1.1249

                                    =          24038.5           +          32359.47         +          17779.36         - 60000

                                    =          14177.33

                        NPVJ   =          20000  +          40000  +          25000              - 55000
                                                1+0.04             (1+0.04) ^2     (1+0.04) ^3

                                    =          20000  +          40000  +          25000              - 55000
                                                1.04                 1.0816             1.1249

                                    =          19230.77         +          36982.25         +          22224.20         - 55000

                                    =          23437.22

  1. With a risk premium of 2% on project I and 3% on project J, the risk adjusted discount rate is 4 + 2 = 6%. Therefore, the risk adjusted net present value of project I is

NPVI   =          25000  +          35000  +          20000              - 60000
                       (1+0.06)          (1+0.06) ^2     (1+0.06) ^3

           =          25000  +          35000  +          20000              - 60000
                        1.06                 1.1236             1.1910

           =          23584.91   +     31149.88    +    16792.61     - 60000

           =          11527.4

The risk premium for project J is 3%, the risk adjusted discounted rate is 4 + 3 = 7%

                        NPVJ   =          20000  +          40000  +          25000             - 55000
                                               1+0.07            (1+0.07) ^2    (1+0.07) ^3

                                    =          20000  +          40000  +          25000              - 55000
                                                1.07                 1.1449             1.2250

                                    =          18691.59         +          34937.55         +          20408.16         - 55000

                                    =          19037.3

The above outcomes depicts that through project J is more risky than project I. it will be selected by the manager as its risk adjusted net present value is higher as compared to that of project I.

Illustration 114

A manager of a cold beverage company has to decide which of the two advertisement policies to promote sales and profits of the company: (1) Giving publicity on several Medias, (2) Giving publicity in several national newspapers. The marketing division of the company has evaluated the following feasible sales and their probabilities of each publicity policy.

Policy I (Publicity on Television Media)

Policy II (Publicity on Newspaper Media)

Sales Value in Million $

Possibility

Sales Value in Million $

Possibility

40

0.2

40

0.3

50

0.3

60

0.4

60

0.3

80

0.3

70

0.2

   

It is notorious that 75% of sales of the company comprise profits of the company.

  1. Compute the anticipated value of monetary profits for the two alternatives sales promotion policies.
  1. Compute the level of risk for every sales promotion policy
  1. Which sales promotion policy the manager must select?

Solution

Considering 75% of sales constitute profits, we compute below the anticipated value of monetary profits of the alternative promotion policies.

Policy I – Publicity in Television Media

Profits

Probability

 

πi

Pi

πi Pi

       _
πi - π

  _
(πi – π) ^2

 _
     (πi – π) ^2 * Pi

30

0.2

6

-11.25

126.56

25.312

37.5

0.3

11.25

- 3.75

14.06

4.218

45

0.3

13.5

+ 3.75

14.06

4.218

52.5

0.2

10.5

+ 11.25

126.56

25.312

_
π = 41.25

 

160.308

_
π or Σ πi Pi     =          41.25

                                    n                   _
σ                      =          Σ          (πi – π) ^2. Pi  =          √ 160.308
                                    t=1

                        =          12.66

Co-efficient of Variance         =          12.66   =          0.31
                                                           41.25

Profits

Probability

 

πi

Pi

πi Pi

       _
πi - π

  _
(πi – π) ^2

_
     (πi – π) ^2 * Pi

30

0.3

9

-15

225

67.5

45

0.4

18

0

0

0

60

0.3

18

15

225

67.5

 _
 π = 45

 

135

_
π or Σ πi Pi     =          45
                                   
                                     n                  _
σ                      =          Σ          (πi – π) ^2. Pi  =          √ 135
                                    t=1

                        =          11.62

Co-efficient of Variance         =          11.62   =          0.26
                                                              45

Therefore, it will be seen from above that policy I has higher anticipated value of monetary profits however is more risky than policy I on the basis of co-efficient variance.

The manager who is risk unbiased or risk seeker will go in for sales promotion policy I. but if the manager is risk hesitant, it cannot be said he will select as it is based on the utility function of the manager which is not provided in the problem.

Illustration 115

Presume an investor is taking into account to invest in a project which capitulate return of $62500 for the subsequent 5 years whose initial cost is $125000 provided that risk free interest is 10% and his certainty equivalent is 0.4.

Determine the net present value of the investment project.

Solution
           
α = 0.4;            R = 62500;      r = 10% or 0.10

                                                n
                        NPV    =          Σ             αRt               - Co
                                                t=1       (1+r) ^t
                                               
                                                5
                                    =          Σ          0.4(62500)       - 125000
                                                t=1       (1 + 0.10) ^t

                                    =          25000                          - 125000
                                                (1.10) ^t

                                    =          25000  (  1   )   t          - 125000
                                                            (1.10 )

                                    =          25000 * 3.7908           - 125000

                                    =          94770                          - 125000

                                    =          - 30230

Therefore, the net present value is negative and the project must be rejected.

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