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What is Decision Tree? How it measure risk?


Decision Tree: It is a tool which helps to measure risk in uncertainty. It is tree like diagram which shows decision and its alternatives and probability of occurrence of an outcome of alternatives. It helps to calculate Expected Monetary Value (EMV).


Symbols uses in diagram are as follows:



Advantages of decision tree:
·         It is simple to draw decision tree diagram
·         It is easy to understand by ordinary people.
·         It shows all alternatives and their possible outcomes.
·         It helps to make a decision.

Disadvantages of decision tree:
·         It shows less accurate result if there is lots of nodes in decision tree diagram.
·         It does not show the reality because outcomes of different alternatives are based on expectation.

Expected Monetary Value = Probability*Outcome

Example: Mr. B has Rs.5, 00,000 and he wants to invest it he has two options:
·         Invest in bank to earn 8.2% interest
·         Purchase a machine worth Rs.5, 00,000 whose three years cash flows are as follows – Rs.90, 000, Rs.85000 and Rs.75000 respectively.
                                                                                         
Solution:


EMVCASH DEPOSIT= 1*123000
= Rs.1, 23,000

EMVMACHINE= 1/3{90,000) +1/3(85,000) +1/3(75,000)
=29999+28333+24999
=Rs.83, 331

So, investing in bank is best option than purchasing a machine.

Example: Find the best option to among the following alternatives through decision tree model.

Growth
Decline
Stock
30
20
Debenture
10
5
Fixed Deposit
10
10
Probability
0.7
0.3

Solution:





EMVSTOCK= payoff*probability
=30*0.7+20*0.3
=21+6
=Rs.27

EMVDEBENTURE= payoff*probability
=10*0.7+5*0.3
=Rs.8.5

EMVFIXED DEPOSIT= payoff*probability
=10*1
=Rs.10

So, investing in stock is best option.

Example: Company A manufacturing a cheese and dairy products and also running a restaurant. The company purchased recently a land of Rs. 20, 60,000 which is away from city. Company has four options that is
·         To build a new factory.
·         Start a new restaurant on that land.
·          Third is selling that land on Rs. 32, 00,000 to company Z.
·         Give that land for farming and earn Rs. 1, 00, 000 per year.
Company found that the land is good for cultivation and near that land there is a tourist place. Find out which option is the best for Company A and why?

Proposal
Success
Failure
Amount (Rs.)
Success
Amount (Rs.)
Failure
Sell
---
--
32, 00, 000

Restaurant
0.40
0.60
27, 50, 000
16, 00,000
Building factory
0.60
0.40
38, 00,000
19, 00,000
Farming
0.80
0.20
20, 00,000
11, 00,000

Solution:



Expected Monetary Value on selling = Rs.30, 00,000
Expected Monetary Value on new restaurant = 0.40*27, 50,000 + 0.60*16, 00,000
= 11, 00,000 + 9, 60,000
= 20, 60,000
Expected Monetary Value on building a factory = 0.60*38, 00,000 + 0.40*19, 00,000
= 22, 80,000 + 7, 60,000
= 30, 40,000
Expected Monetary Value on farming = 0.80*20, 00,000 + 0.20*11, 00, 000
= 16, 00, 000 + 2, 20, 000
= 18, 20, 000
The expected monetary value of option third that is building a factory is higher than all available options. So, building a new factory is the best option for company A.



 

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