Prof. Prapti Paul

Capital Budgeting contd.

Question on Decision Tree Approach in Capital Budgeting• A firm has an investment proposal, requiring an outlay of Rs.40,000. the investment

proposal is expected to have 2 years economic life with no salvage value. In year 1, there is 0.4 probability that the cash inflow after tax will be Rs.25,000 and 0.6 probability that the cash inflow after tax will be Rs.30,000. the probabilities assigned to cash inflows after tax for the year 2 are as follows:

• Cash inflow in year 1: Rs. 25000 Rs.30000• Cash inflow in year 2: Probability Probability Rs. 12000 0.2 Rs. 25000 0.4 Rs.16000 0.3 Rs.25000 0.5 Rs.22000 0.5 Rs.30000 0.1The firm uses a 10% discount rate for this type of investment.Required:a) Construct a decision tree for the proposed investment projectb) What NPV will the project yield if worst outcome is realized? What is the

probability of occurrence of this NPV?c) What will be the best outcome and the probability of that occurrence?d) Will the project be accepted?

Solution :a) The decision tree:

Cash outlay Rs.40,000

Rs.25000

Rs.30000

Rs.12000

Rs.16000

Rs.25000

Rs.25000

Rs.30000

Rs.20000

Path No. Joint probability yr1*yr2

1 0.08

2 0.12

3 0.20

4 0.24

5 0.30

6 0.06

1.00

• The decision tree shows that there are six possible outcomes each represented by a path. The NPV of each path at 10% discount rate is given below:

Path (Cash Inflow yr1*disc factor yr1)(a)

(Cash inflow yr2*discount factor yr2)(b)

Total cash inflow(c )=(a)+(b)

Cash outflow (d)

NPV(e) = (c )-(d)

1 Rs.25,000*0.909=22725 Rs.12000*0.826=9912 Rs.32637 Rs.40000 Rs.-7363

2 Rs.25000*0.909 =22725 16000*0.826= 13216 35941 40000 -4059

3 Rs.25000*0.909 =22725 22000*0.826=18172 40897 40000 897

4 30000*0.909=27270 20000*0.826=16520 43790 40000 3790

5 30000*0.909=27270 25000*0.826=20650 47920 40000 7920

6 30000*0.909=27270 30000*0.826=24780 52050 40000 12050

• Statement showing the expected NPV:

b) If the worst outcome is realized, the NPV which the project will yield is Rs.7363 (negative). The probability of occurrence of this NPV is 8%.

c) The best outcome will be path 6 when NPV is highest i.e. Rs.12050 (positive). The probability of occurrence of this NPV is 6%

d) Yes, the project will be accepted since the Expected NPV is positive.

Path NPV @10% (A)

Joint Probability (B)

Expected PV(A)*(B)

1 Rs. -7363 .08 Rs.-589.04

2 -4059 .12 -487.08

3 897 .20 179.40

4 3790 .24 909.60

5 7920 .30 2376.00

6 12050 0.06 723.00

1.00 3,111.88