# Question

In your new position as supervisor of product introduction, you have to decide on a pricing strategy for a talking doll specialty product with the following cost structure:

Variable costs per unit ...... $ 60

Fixed costs ........ $240,000

The dolls are manufactured upon receipt of orders, so the inventory levels are insignificant. Your market research assistant is very enthusiastic about probability models and has presented the results of his price analysis in the following form:

a. If you set the selling price at $120 per unit, the probability distribution of revenues is uniform between $360,000 and $720,000. Under this distribution, there is a 0.50 probability of equaling or exceeding revenues of $540,000.

b. If you lower the selling price to $84 per unit, the distribution remains uniform, but it shifts up to the $720,000-$1,080,000 range. Under this distribution, there is a 0.50 probability of equaling or exceeding revenues of $900,000.

REQUIRED

1. This is your first big contract and, above all, you want to show an operating income. You decide to select the strategy that maximizes the probability of breaking even or earning a positive operating income.

a. What is the probability of at least breaking even with a selling price of $120 per unit?

b. What is the probability of at least breaking even with a selling price of $84 per unit?

2. Your assistant suggests that maximum expected operating income might be a better objective to pursue. Which pricing strategy would result in the higher expected operating income?

Variable costs per unit ...... $ 60

Fixed costs ........ $240,000

The dolls are manufactured upon receipt of orders, so the inventory levels are insignificant. Your market research assistant is very enthusiastic about probability models and has presented the results of his price analysis in the following form:

a. If you set the selling price at $120 per unit, the probability distribution of revenues is uniform between $360,000 and $720,000. Under this distribution, there is a 0.50 probability of equaling or exceeding revenues of $540,000.

b. If you lower the selling price to $84 per unit, the distribution remains uniform, but it shifts up to the $720,000-$1,080,000 range. Under this distribution, there is a 0.50 probability of equaling or exceeding revenues of $900,000.

REQUIRED

1. This is your first big contract and, above all, you want to show an operating income. You decide to select the strategy that maximizes the probability of breaking even or earning a positive operating income.

a. What is the probability of at least breaking even with a selling price of $120 per unit?

b. What is the probability of at least breaking even with a selling price of $84 per unit?

2. Your assistant suggests that maximum expected operating income might be a better objective to pursue. Which pricing strategy would result in the higher expected operating income?

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