Compute the expected payoffs for each alternative shown in the following decisio

Question

Compute the expected payoffs for each alternative shown in the following decision tree. (Enter your answers in millions. Round your answers to 2 decimal places.)

$1.0* $1.3 Do nothing Medium demand (.5 Large demand (.1) Expand $1.3 $1.5 $1.6 $1.8 $0.7 $1.5 $1.0 $1.6 $1.6 $1.5 $1.7 ($0.9) $1.4 $1.0 $1.0 $1.1 $0.9 Do nothing Expand Build Do nothing Other use #1 Other use #2 Small demand (4) Expand Medium demand (.5) Large demand (.1) Do nothing Subcontract Build Do nothing Other use #1 Other use #2 Small demand (.4) Medium demand (.5) Do nothing Other use #1 Other use #2 Net present value in millions $2.4

Explanation / Answer

The expected payoff is sum-product of Probability and Value for each option.

In case of two options with no probability, the maximum of two values in chosen assuming both are possible

Example: In subcontract for Medium demand, the Value = Max(Do nothing, expand) = Max(1.3, 1.3) = 1.3

EV subcontract = 0.4*1 + 0.5*1.3 + 0.1*Max(1.5, 1.6, 1.8) = 0.4*1 + 0.5*1.3 + 0.1*1.8 = 1.23

EV expand = 0.4*Max(0.7, 1.5, 1) + 0.5*1.6 + 0.1*Max(1.6, 1.5, 1.7) = 1.57

EV Build = 0.4*Max(-0.9, 1.4, 1) + 0.5*Max(1, 1.1, 0.9) + 0.1*2.4 = 1.35

Highest is for Expand

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