Expected Monetary Value - Essay Example

Small-sized station,

Annual returns if the market is: Good: $50,000

      Fair: $20,000

     Poor: -$10,000

            EMV = (1/3) * (50000+20000-10000) = $20,000

Medium-sized station,

Annual returns if the market is: Good: $80,000

      Fair: $30,000

     Poor: -$20,000

            EMV = (1/3) * (80000+30000-20000) = $30,000

Large-sized station,

Annual returns if the market is: Good: $100,000

      Fair: $30,000

     Poor: -$40,000

            EMV = (1/3) * (100000+30000-40000) = $30,000

Very-Large size station,

Annual returns if the market is: Good: $300,000

      Fair: $25,000

     Poor: -$160,000

            EMV = (1/3) * (300000+25000-160000) = $55,000

In the case of Clay Whybark’s choices, all the different states of nature have differing probabilities; therefore the calculation for the best choice from the perspective of EMV will not be very straightforward. The different EMVs are calculated as follows:

Large stock:

            Big demand (30 percent probability):                        $22,000

            Average demand (50 percent probability):    $12,000

            Small demand (20 percent probability):        -$2,000

            EMV = (0.3*22000) + (0.5*12000) + (0.2*(-2000)) = $12,200

Average Stock:

            Big demand (30 percent probability):                        $14,000

            Average demand (50 percent probability):    $10,000

            Small demand (20 percent probability):        $6,000

            EMV = (0.3*14000) + (0.5*10000) + (0.2*6000) = $10,400

Small Stock:

            Big demand (30 percent probability):                        $9,000

            Average demand (50 percent probability):    $8,000

            Small demand (20 percent probability):        $4,000

            EMV = (0.3*9000) + (0.5*8000) + (0.2*4000) = $7,500

Therefore, as shown, a Large stock would provide Clay Whybark with the highest EMV value.

A3. (b)

The Expected Value of Perfect Information (EVPI), as indicated by the term itself, is the abstract monetary value of having certain knowledge of the best decision among two, or more, choices.

In the current case, first, we calculate the monetary value of making the best decision in accordance with the prevailing state of nature,

EV|PI = (0.3*22000) + (0.5*12000) + (0.2*6000) = $13,800

Then,

            EVPI = EV|PI – EMVmax = 13800 – 12200 = $1,600