Question

Quantitative methods, IUL 2020 Part 3: (Expectation) XY industry wants to build a plant, it has to take the decision of building either a large or small plant. The building cost of a large plant is $2.1 million, and a small one will cost only $1.1 million. The XY industry experience provides a probability estimate of demand to be high, moderate, or low for the next 10 years is given in this table: High Demand Moderate Demand Low Demand Probability = 0.5 Probability = 0.3 Probability = 0.2 The potential ANNUAL profit from each decision alternative is given below: High Demand Moderate Demand Low Demand Large Plant $1,000,000 $600,000 -$200,000 Small Plant $250,000 $450,000 $550,000 1) Construct a 10-year payoff table (don't take into consideration the cost of building) 2) Include the cost of building into the payoff table 3) What is the expected value of a large plant? 4) What is the expected value of a small plant? 5) If a market research firm provides XY industry with perfect information about demands, how much is that information worth to XY industry? (Expected value of perfect information)

Answer 1

1)

Without the cost of the building, the 10 year payoff table can be created as shown below

	High	Moderate	Low
Large plant	10000000	6000000	-2000000
Small plant	2500000	4500000	5500000

2)

With the cost of the building into consideration the payoff table is shown below

	High	Moderate	Low
Large plant	7900000	3900000	-4100000
Small plant	1400000	3400000	4400000

3)

The expected value of a large plant = 7900000*0.5 + 3900000*0.3 + (-4100000)*0.2 = 4300000

4)

The expected value of a small plant = 1400000*0.5 + 3400000*0.3 + 4400000*0.2 = 2600000

6)

If we have perfect information, we will choose the best option. That is for each probability the best option will be chosen. The expected value with perfect information is 7900000*0.5 + 3900000*0.3 + 4400000*0.2 = 6000000

The expected value without perfect information is the maximum EMV between large and small plant. That is 4300000.

The expected value of perfect information is 6000000-4300000 = 1700000