Project Evaluation
The expected value calculations are crucial to project investment decisions. The following example explains the use of probabilities in project evaluation.
Example
Home Appliances Limited is planning to introduce a washing machine with superior features. It has two options. The first option is to build a new plant, anticipating full production in 3 years. The second option is to rebuild a small existing pilot plant for limited production for the coming year. If the results of the limited production show promise at the end of the first year, within a short time it can be converted into a full production plant. If the pilot plant option is taken up and if at the end of the first year it is concluded that it is unattractive to go into full production, the pilot plant can still be operated by itself at a small profit. The expected annual profits for various alternatives are as follows:
Production Facility

Demand

Annual Profit (Rs.crore)


New Plant

High

7

New Plant

Low

3

Pilot Plant

High

1

Pilot Plant

Low

0.5


The market research surveys indicate that there is a 50% chance that demand will be high and a 50% chance that demand will be low when full production plant is built in the first year itself. If the pilot plant is put into production with a correspondingly lowkey advertizing program, the survey indicates that the probabilities are 45% for high demand and 55% for low demand. If with the pilot plant the demand is high, there is a 90% probability of high demand even at full production. If the demand with the pilot plant is found to be low, there is only a 10% probability of high demand at full production. Which plant should be built?
For the sake of simplicity, let us ignore the investments to be made and the time value of money. Let us also study the profits that are likely to be earned over the first two years of investment only.
Evaluation for first two years
In the example at the first decision node we have two options, to build a new plant or rebuild the existing pilot plant. If the pilot plant option is taken up there is a 0.45 probability of high demand in the first year. In which case it is given that the plant should be converted into a full production plant. The subsequent events are a 0.9 probability of high demand and a 0.1 probability of low demand in the second year. And in the first year if the option of pilot plant is taken up the probability of low demand is 0.55. In this case there are two options (i.e. at the decision node 3), to continue operating as a pilot plant or to convert into a full production plant in the second year. If the plant continues to operate as a pilot plant then the subsequent events are a 0.45 probability of high demand and a 0.55 probability of low demand. And if the plant is converted into a full production plant the subsequent events in the second year are a 0.1 probability of high demand and a 0.9 probability of low demand in the second year.
We can draw the following decision tree:
Figure
Evaluating decision tree from right to left
At decision node D2  Option is to convert into a full production plant

prob.

x

payoff

=

Expected payoff

Event: High demand

0.9

x

7

=

6.3

Event: Low demand

0.1

x

()3

=

()0.3



Net expected payoff

=

6


At node D3 
Decision  Continue to operate as pilot plant
Event: High Demand

0.45

x

1

=

0.45

Event: Low Demand

0.55

x

0.5

=

0.275



Net expected payoff

=

0.725


Decision  Convert into a full production plant
Event: High Demand

0.1

x

7

=

0.7

Event: Low Demand

0.9

x

()3

=

()2.7



Net expected payoff

=

()2


At D3 the alternative that gives the highest payoff is chosen, i.e. the decision to continue to operate as a pilot plant.
At node D1 
Decision  Build a new plant
In the second year  For E2 & E3:

High demand 0.5

x

7

=

3.5


Low demand 0.5

x

()3

=

()1.5



Net expected payoff

=

2


The payoff is identical at both E2 and E3.
In the first year  E1:

High demand

0.5

x

(7 + 2)

=

4.5


Low demand

0.5

x

(3 + 2)

=

()0.5



Net expected payoff


=

4


Therefore, the net expected payoff for the option to build a new plant = Rs.4 crore.
Decision  Rebuild the pilot plant.
Event

: High demand

0.45

x

(1 + 6)

=

3.15


: Low demand

0.55

x

(0.5 + 0.725)

=

0.67




Net expected payoff

=

3.82


Therefore, the net expected payoff for the option of rebuilding the pilot plant = Rs 3.82 crore.
At the decision node D1 the option that gives the highest payoff is chosen, i.e. building a new full production plant which gives a payoff of Rs.4 crore.