Untitled-29

Capital Budgeting under Risk and Uncertainties^155

Figure 6.16: Decision Tree

Following the above decision strategy, the decision maker, may, depending on the

outcome at chance points, traverse paths as shown in Figure 6.17.

Path Probability Net present value

(Rs.)

D 12 ÆC 21 ÆD 22 0.40 -20,000

D 12 ÆC 22 ÆD 31 ÆD 41 0.15 -620,000

D 12 ÆC 22 ÆD 31 ÆD 42 0.10 -780,000

D 12 ÆC 22 ÆD 31 ÆD 43 0.05 -2,380,000

D 12 ÆC 23 ÆD 41 ÆD 51 0.03 -620,000

D 12 ÆC 23 ÆD 41 ÆD 52 0.11 -780,000

D 12 ÆC 23 ÆD 41 ÆD 53 0.16 -2,380,000

Figure 6.17: Paths, Possibilities, and Net Present Values

Evaluation

Decision trees are useful for analysing a project that has the characteristics:

l Decision on continuing the project are made in well-defined stages.

l The outcomes at each stage fall into few broad classes.

C Rs. in million

11 (Dry)

p = 1/2

C 12 (Wet)

-0.6

p = 1/4 -0.8

C 13 (Soaking) -2.4

C 11 (Dry)

p = 1/2

C 12 (Wet)

-0.6

p = 1/4 -0.8

C 13 (Soaking) -2.4

C 41 (Dry)

p = 1/2

C 42 (Wet)

-0.6

p = 1/3 -0.8

C 43 (Soaking) -2.4

C 51 (Dry)

p = 1/10

C 52 (Wet)

-0.6

p = 11/30 -0.8

C 53 (Soaking) -2.4

C 31 (Dry)

p = 4/5

C 32 (Wet)

-0.6

p = 1/10 -0.8

C 33 (Soaking) -2.4

C 21

Drill

D 22

Do not drill

C 31

Drill

D 32

Do not drill

C 41

Drill

D 42

Do not drill

p = 1/4

p = 1/10

0

p = 1/6

0

p = 16/30

0

C 22 (Open

structure)

p = 3/10

D 32

Conduct

Siesmic

experiments

-0.2

D 11

Drill

D 12

Do nothing^0

p =

1/10

C^21

(No structure)

C^23

(Closed structure)

D 2

0

C 2

564

D 1

544

C 1

500

p = 3/10

D 3

367

D 4

1513

C 2

-16

C 2

-16

C 2

-16

C 4

367

C 5

1513