Capital Budgeting Decision to Drill Oil Well or Not - CA Final SFM

Question: - ABC Oil Ltd is wondering whether to drill for oil in Rajasthan. The prospects are as follows:-

Depth of Well	Total Cost in Millions of Dollar	Cumulative Probability of Finding Oil	PV of Oil ( If Found) Millions of Dollars
2000 Feet	4	.50	10
4000 Feet	5	.60	9
6000 Feet	6	.70	8

Draw a Decision Tree showing the Successive drilling decision to be made by ABC Oil Ltd. How deep should it be prepared to drill?

Solution: - 

  

Calculation of Probability

S1 = .50    {Given}

F1 = .50    {Given}

F1*S2 = Incremental Probability

F1*S2 = (.60-.50)

.50*S2 = .10

S2 = .10/.50

S2 = .20

F2 = 1 - .20

F2 = .80

F1*S2 = Incremental Probability

F1*F2*S3 = (.70 - .60)

.50*.80*S3 = .10

S3 = .10/.40

S3 = .25

 ABC Ltd has to take Decision at three Decision Points Namely D1, D2 and D3.

By Using Rolling Back Technique, we should take decision at D3 First whether we should Drill or not up to 6000 Feet if we had already drilled up to 4000 Feet and similarly we should take decision at D2 and D1.

Statement showing the evaluation of decision at D3

Decision	Event	Probability	PV of Oil (if found) {Millions of Dollar	Expected PV of Oil (if found) {Millions of Dollars}
Drill Up to 6000 Feet	Find Oil	.25	8 – 6 =2	.50
	Not Found Oil	.75	(6)	(4.5)
				(4)
Do Not Drill Up to 6000 Feet				(5)

Since the Expected PV of Oil (if found) on drilling up to 6000 feet is (4) Millions of Dollar is greater than the cost of not drilling up to 6000 feet is (5) Millions of Dollar. Therefore, ABC Oil Ltd should drill up to 6000 Feet.

Statement showing the evaluation of decision at D2

Decision	Event	Probability	PV of Oil (if found) {Millions of Dollar	Expected PV of Oil (if found) {Millions of Dollars}
Drill Up to 4000 Feet	Find Oil	.20	9 – 5 = 4	.80
	Not Found Oil	.80	(4)*	(3.2)
				(2.4)
Do Not Drill Up to 4000 Feet				(4)

Since the Expected PV of Oil (if found) on drilling up to 4000 feet is (2.4) Millions of Dollar is greater than the cost of not drilling up to 4000 feet is (4) Millions of Dollar. Therefore, ABC Oil Ltd should drill up to 4000 Feet.

*Explanation: - When ABC Oil Ltd does not found Oil on Drill Up to 4000 then ABC Oil Ltd should Drill Up to 6000 Feet (Decision taken at D3). Hence we used Expected PV of Oil on Drill Up to 6000 Feet.   

Statement showing the evaluation of decision at D1

Decision	Event	Probability	PV of Oil (if found) {Millions of Dollar	Expected PV of Oil (if found) {Millions of Dollars}
Drill Up to 2000 Feet	Find Oil	.50	10 – 4 = 6	3
	Not Found Oil	.50	(2.4)**	(1.2)
				1.8
Do Not Drill Up to 2000 Feet				0

Since the Expected PV of Oil (if found) on drilling up to 2000 feet is 1.8 Millions of Dollar. Therefore, ABC Oil Ltd should drill up to 2000 Feet.

**Explanation: - When ABC Oil Ltd does not found Oil on Drill Up to 2000 then ABC Oil Ltd should Drill Up to 4000 Feet (Decision taken at D2). Hence we used Expected PV of Oil on Drill Up to 4000 Feet.   

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