MGS3100 Page 1

MGS3100: Business Analysis

Example: Decision Tree for Sequential Decisions The South Mountain Power Company is investigating the possibility of constructing a new plant to generate electricity. Undertaking this project would require the construction of either a large or a small-sized power plant. The company of course, has the option of not building the new plant at all. The demand in the future is not exactly known but can be either favorable or unfavorable. If the demand were favorable (high), a large facility would give the company a net profit (in net present value) of $200,000. If the demand were unfavorable (low), a $180,000 net loss would occur. A small plant would result in a net profit of $100,000 in a high demand, but a net loss of $20,000 would be encountered if the demand were low. Since the demand is quite uncertain for the company, they initially treat each outcome of the demand equally likely. That is, the probability of high demand is 0.50, the same as the probability of low demand. Suppose that the company has an option to improve their estimates of the future demand condition by conducting its own marketing research or consumer survey (by obtaining more information, the future demand uncertainty may be reduced). The cost of doing this will be about $10,000. Now the company has to make two decisions, first, they need to decide if they need to conduct the consumer survey or not. Then if they choose not to do the study, they must decide to build a large plant, a small plant or no plant. If they elect to do the study, then the result from the survey can be either positive or negative. No matter what result the survey gives, the company must then choose one of the three alternatives: build a large plant, a small plant or no plant. Suppose the company knows that there is a 45% chance of getting positive survey result and a 55% chance of negative survey result. (These numbers are called marginal probabilities.) In addition, we assume that the company knows the following information: if the survey turns out to be positive, there is 78% chance that the demand will be high (the chance of low demand is 22%). But if the survey result is negative, then there is only 27% chance the demand will be high (the chance of low demand is 73%). These numbers about the chances of high and low demand after the survey result becomes available are called posterior probabilities (the original probability estimates of 0.50 for high demand and 0.50 for low demand are called the prior probabilities). How to get these posterior probabilities as well as the marginal probabilities is a topic that will be covered shortly (see page 4). For now, we just assume these numbers are given. Of course, the decision problem facing the company is how to choose its best courses of actions or make a sequence of best decisions. Question 1: How many decisions and what are they? Answer: Two decisions: (1) conduct the survey or don't conduct the survey; (2) To build a large plant, a small plant, or no plant at all. Note decision (1) must be made before (2). Solution Procedure: 1. Construct the Decision Tree (see page 2) 2. Solve the Decision Tree (see page 3)

MGS3100 Page 2

Decision Tree

Payoffs

190,000.00$

(190,000.00)$

90,000.00$

(30,000.00)$

(10,000.00)$

190,000.00$

(190,000.00)$ 90,000.00$

(30,000.00)$

(10,000.00)$

200,000.00$

(180,000.00)$ 100,000.00$

(20,000.00)$

$0.00

Conduct survey

Do not conduct

Result positive(0.45)

Result negative (0.55)

Large

Small

No plant

Small

Large

No plant

Small plant

Large plant

No plant

Demand high (0.78)

Demand low (0.22)

Demand high (0.78)

Demand high (0.27)

Demand high (0.5)

Demand high (0.5)

Demand low (0.22)

Demand high (0.27)

Demand low (0.73)

Demand low (0.5)

Demand low (0.73)

Demand low (0.5)

MGS3100 Page 3

Solved Tree

Payoffs

190,000.00$

(190,000.00)$

90,000.00$

(30,000.00)$

(10,000.00)$

190,000.00$

(190,000.00)$ 90,000.00$

(30,000.00)$

(10,000.00)$

200,000.00$

(180,000.00)$ 100,000.00$

(20,000.00)$

$0.00

Conduct survey

Do not conduct

Result positive(0.45)

Result negative (0.55)

Large

Small

No plant

Small

Large

No plant

Small plant

Large plant

No plant

Demand high (0.78)

Demand low (0.22)

Demand high (0.78)

Demand high (0.27)

Demand high (0.5)

Demand high (0.5)

Demand low (0.22)

Demand high (0.27)

Demand low (0.73)

Demand low (0.5)

Demand low (0.73)

Demand low (0.5)

$106,400

$63,600

-$87,400

$2,400

$40,000

$10,000

$40,000

$2,400

$106,400

$49,200

$49,200

Question 2: What are the best decisions for the company? Answer: The best sequence of decisions is as follows: First, the company should conduct the survey. If the result is positive, then the company should build a large plant. If the result is negative, then a small plant should be built. Question 3: What is the Expected Value of Sample Information (EVSI)? Answer: EVSI = ER w/ SI - ER w/o SI = $49,200 - $40,000 = $9,200 Since the expected return with sample information ($49,200) has already taken into consideration the cost of sample information ($10,000), this is the net EVSI. The true EVSI or the maximum the company should pay for this marketing survey is $9,200 + $10,000 = $19,200.

MGS3100 Page 4

Calculate Posterior Probabilities Using Bayes Theorem

A B C D E F G1 Posterior Probability - South Mountain Power Company23 Prior probability4 Dmd High Dmd Low5 0.5 0.567 Likelihood8 Dmd High Dmd Low9 Positive 0.7 0.2

10 Negative 0.3 0.81112 Joint probability13 Dmd High Dmd Low Marginal14 Positive 0.35 0.1 0.4515 Negative 0.15 0.4 0.5516 11718 Posterior probability19 Dmd High Dmd Low Chksum20 Positive 0.78 0.22 121 Negative 0.27 0.73 122

A B C D1 Posterior Probability - 23 Prior probability4 Dm d High Dm d Low5 0.5 0.567 Likelihood8 Dm d High Dm d Low9 Positiv e 0.7 0.210 Negativ e 0.3 0.81112 Joint probability13 Dm d High Dm d Low M arginal14 Positiv e =B$5*B9 =C$5*C9 =SUM (B14:C14)15 Negativ e =B$5*B10 =C$5*C10 =SUM (B15:C15)16 =SUM (D14:D15)1718 Posterior probability19 Dm d High Dm d Low Chksum20 Positiv e =B$14/$D14 =C$14/$D14 =SUM (B20:C20)21 Negativ e =B$15/$D15 =C$15/$D15 =SUM (B21:C21)22