The national coffee store Farbucks needs to decide in August how many holiday-ed

Question

The national coffee store Farbucks needs to decide in August how many holiday-edition insulated coffee mugs to order. These premium mugs sell for $10 and cost $6 each. Farbucks is uncertain of the demand. They believe that there is a 25% chance that they will sell 10,000 mugs (low demand), a 50% chance that they will sell 15,000 (medium demand) and a 25% chance that they will sell 20,000 (high demand). Because the mugs are dated, those that are unsold by January 15 are discounted and sold at 20% of the original price. a) Build a decision tree to determine if they should order 16,000,18,000 or 20,000 mugs. b) Suppose someone can accurately determine which of the three demand states (low with 10,000 mugs, medium with 15,000 mugs and high with 20,000 mugs) will actually occur. How much should Farbucks be willing to pay for this information?

Explanation / Answer

Let's consider the sales value generated for the number of units bought by Farbucks

Consider the below-mentioned decision tree,

Farbucks orders 16000 mugs:

Now if farbucks orders 16000 mugs, then Farbucks have 25% chance of selling 10000 units and it will be left with 6000 units by end of January. the 20% cost of 6000 mugs will be the loss for the company.

So if farbucks sells 10000 mugs, the total earning of Farbugs = 25%*{($10*10000) - 20 % ($6*6000 )}

=$ 23200

there is 25% chance of these earning and balance is 75% chance of selling all the 16000 units as there are 50% chance of selling 15000 units and 25% chance of selling 20000 units.So Farbucks sell all 16000 units in 75% chance.

So if farbucks sells all 12000 units, then earning will be = 75%*($10*16000)

So expected earning of Farbucks if it orders 12000 units = 25%*{($10*10000) - 20 % ($6*6000 )} + 75%*($10*12000) = $ 113,200

Farbucks orders 18000 mugs:

Now if farbucks orders 18000 mugs, then Farbucks have 25% chance of selling 10000 units and it will be left with 8000 units by end of January. the 20% cost of 8000 mugs will be the loss for the company by end of January.

So if farbucks sells 10000 mugs, the total earning of farbucks = 25%*{($10*10000) - 20 % ($6*8000 )}

there is 25% chance of these earning and balance is 75% chance of selling all the 18000 units as there are 50% chance of selling 15000 units and 25% chance of selling 20000 units.So Farbucks sell all 18000 units in 75% chance.

So if farbucks sells all 18000 units, then earning will be = 75%*($10*18000)

So expected earning of Farbucks if it orders 15000 units = 25%*{($10*10000) - 20 % ($6*8000 )} + 75%*($10*18000) = $ 163250

Farbucks orders 20000 mugs:

Now if farbucks orders 20000 mugs, then Farbucks have 25% chance of selling 10000 units and it will be left with 10000 units by end of January. the 20% cost of 10000 mugs will be the loss for the company end of January.

So if farbucks sells 10000 mugs, the total earning of

Farbucks =25%*{($10*10000) - 20 % ($6*10000 )}

there is 25% chance of these earning and balance is 50% chance of selling all the 15000 units.So Farbucks sell all 15000 units in 50% chance and left with 5000 units

So if farbucks sells all 15000 units, then earning will be = 50%*{($10*15000) - 20 % ($6*5000 )}

So if farbucks sells all the 20000 units, then earning will be = 25% ( chance of selling 20000 units) *($10*20000)

So expected earning of Farbucks if it orders 20000 units = 25%*{($10*10000) - 20 % ($6*10000 )} + 50%*{($10*15000) - 20 % ($6*5000 )} +25% ( chance of selling 20000 units) *($10*20000)

= $144000

So Farbucks expected earning is higher if it orders 18000 mugs than 12000 or 20000 mugs.

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