Question

Dawn, an SOU graduate, has started a new business that makes and sells oak barrels. Dawn makes big barrels that are the traditional size used in the wine and whiskey industries. But Dawn is considering making and selling a new, smaller barrel that may appeal to home winemakers and micro-distilleries. The SOU Small Business Accelerator did a market study, which predicts:

With 0.25 probability, the smaller barrels will be a huge success and will generate $1 million in profits.

With 0.50 probability, the smaller barrels will sell fairly well and will generate $100,000 in profits.

With 0.25 probability, the smaller barrels will not sell and will generate -$200,000 in profits.

Dawn's profits from the smaller barrels can be thought of as a random variable.

a) What is the expected value of Sara’s profits from making the smaller barrels?

b) A second market study predicts that very few home winemakers will be willing to buy these barrels. This study assigns probabilities of: 0.00 to the outcome with $1 million in profits, 0.25 to the outcome with $100,000 in profits; and 0.75 to the outcome with -$200,000 in profits. What is the expected value of Dawn's profits using this second market study?

c) If adding smaller barrels to the product lineup instead does not change the expected value of the firm’s profits, but increases the standard deviation to $100,000, is that a good or bad thing? Why?

Answer #1

a) The expected profit is sum of the probabilities of each event multiplied by the corresponding profit.

So, the expected **profit** is
**$250,000**.

b) For this case, the expected profit will be calculated with the new probabilites.

So, the expected **profit** is
**-$125,000**. In other words, the expected
**loss** is **$125,000**.

c) Normally, an increase in the standard deviation is neither good nor bad, as it just indicates the spread of your data. There will be more chance of making a higher profit, but there will also be the same chance of making a lower profit.

However, the chance of making a loss also increases when the standard deviation is increased. If the aim is to reduce the chance of making a loss, then the increase in standard deviation will not be acceptable.

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