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What is Simulation Analysis? How does it calculate?


Simulation Analysis: It uses statistical technique to draw probability and assigned random numbers. It overcomes the limitation of sensitivity analysis it provides probability of occurrence of a certain (cash flows) events which is not provided in sensitivity analysis. It calculates risk and uncertainty in project with the help of Monte Carlo method of simulation.

Probability distribution: It is a chance of occurrence of a certain events. There are two type of distribution discrete and continuous distribution. In Discrete distribution is specified single numbers is given and in continuous distribution a range of numbers are given. For example-

Discrete distribution: 
                                                                                                          
X
Probability
 2
0.20
5
0.30
3
0.50

Continuous distribution:

Class interval
Probability
0-5
30
6-10
40
11-15
30


Random numbers: The number whose occurrence is not known is called random number. For example if we throw a dice it comes 5 and if we thrown again then 2 came there is no fixed outcome
.
Advantages of simulation:
·         In this method less data and time is requires.
·         It helps to forecast in uncertainty.

Disadvantages of simulation:
·         It is not a standardised method.
·         It is difficult to interpret the result.

Example: A firm decided to replace a machine and purchase new one of Rs.5 lakhs and the scrap value of old machine is Rs.2, 00,000. The discount rate is 8% p. a. Find out the NPV with simulation analysis.

Year
Cash flow
Probability
Random numbers
1
450000
0.20
30
2
590000
0.30
55
3
680000
0.20
45
4
750000
0.30
75

Solution:

Calculate NPV with simulation:

Year
Cash Flow
Probability
Cumulative  Probabilities
*Tag numbers
1
300000
0.20
0.20
00-19
2
450000
0.30
0.50
20-49
3
380000
0.20
0.70
50-69
4
470000
0.30
1.0
70-99

*Tag numbers/assigned random numbers are 00 to 99 and assigned according to cumulative probabilities

Calculate the present value of cash flows:

Year
Random numbers (Given in question)
*Cash flow
Present Value
Cash out flows (Rs.5,00,000-2,00,000)
Discount rate 8%
NPV
1
30
450000
416666.66
3,00,000
1.08
116666.66
2
55
380000
269503.54
3,00,000
1.41
-30496.454
3
75
470000
251336.89
3,00,000
1.87
-48663.10
4
45
470000
217592.59
3,00,000
2.16
-82407.41
-44900.3

*Cash flow is generated with the help of random numbers which was given in the question. First of all see random number and then find out in tag numbers column where that number exist in the row like 30 (random number) exist in  2nd year row where cash flow is Rs.450000.


With the help of probabilities NPV is calculated which shows negative result so it is not good for company to purchase new machine by replacing old one.

Example: Company Y wants to invest in shares of Company Q. The share cost of Rs. 60 each and company Y is  interested to buy 100 shares because the financial position of the company is very good and it pays dividend regularly to its shareholders. But company Y doesn’t know how much dividend he gets in future. Find out the expected dividend by using simulation method.

Year
Previous 4 year dividend
Probability
Random numbers
1
8
0.20
43
2
8.9
0.10
92
3
10
0.40
50
4
12
0.30
10

Solution:

Year
Previous 4 year dividend
Probability
Cumulative
 probability
Tag numbers
1
8
0.20
0.20
00-19
2
8.9
0.10
0.30
20-29
3
10
0.40
0.70
30-69
4
12
0.30
1.00
70-99

Random numbers
Dividend
43
10
92
12
50
10
10
8

= Total dividend / No. Of years
= 40 / 4

= Rs.10

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