Question

Q1 Given the following data for X (number of units sold), a normally distributed random variable.

1. Calculate E[X] or the mean of unit sales and S[X] or the sample standard deviation of unit sales using Excel. Calculate E[X] using "=AVERAGE( )" in Excel.

2. Calculate S[X] using "=STDEV.S( )" in Excel. Round-off each to the nearest unit. Think of this sample of data being collected from one market in the last five years, or think of it as being collected in just one year from five different markets. Here is the data for X:

18,000 units   25,000 units   25,000 units   25,000 units   32,000 units

Q2 Next, create a histogram of the data in Excel with three categories on the horizontal axis.

Q3 Given fixed cost = $1,000,000 , selling price per unit = $120 , variable cost per unit = $70

1. calculate the probability that the firm makes a loss. Recall, unit sales are normally distributed so Z = (BEP - E[Q])/S[Q].

2. Next, suppose the government imposes a $5 per unit tax which will raise the variable cost per unit by $5.

3 Recalculate the probability of making a loss and compare to the pre-tax probability of loss.

4 Does your result make sense?

5 Does this help you understand why many industries lobby for lower business taxes?

Answer 1