Finance: Share valuation and probabilities.

9.4 You own one share in a company called Invest Co. Inc. Examining the balance sheet, you have determined that the firm has $100,000 cash, equipment worth $900,000, and 100,000 shares outstanding.

Calculate the price/value of each share in the firm, and explain how your wealth is affected if:

A. The firm pays out dividends of $1 per share.

B. The firm buys back 10,000 shares for $10 cash each, and you choose to sell your share back to the company.

C. The firm buys back 10,000 shares for $10 cash each, and you choose not to sell your share back to the company.

D. The firm declares a 2-for-1 stock split.

E. The firm declares a 10% stock dividend.

F. The firm buys new equipment for $100,000, which will be used to earn a return equal to the firm's discount rate.

10.1 A. Calculate the mean and standard deviation of the following securities' returns:

Year
Computroids Inc. Blazers Inc.
1
10% 5%
2
5% 6%

3 3% 7%
4 12% 8%
5 10% 9%

B.
Assuming these observations are drawn from a normally distributed probability space, we know that about 68% of values drawn from a normal distribution are within one standard deviation away from the mean or expected return; about 95% of the values are within two standard deviations; and about 99.7% lie within three standard deviations.

Using your calculations from part A, calculate the 68%, 95%, and 99% confidence intervals for the two stocks. To calculate the 68%, you would calculate the top of the confidence interval range by adding one standard deviation to the expected return, and calculate the bottom of the confidence interval by subtracting one standard deviation from the expected return. For 95%, use two standard deviations, and for 99%, use three.

Your answer should show three ranges from the bottom of the confidence interval to the top of the confidence interval.

C.
For each security, would a return of 14% fall into the 68% confidence interval range? If not, what confidence interval range would it fall into, or would it be outside all three confidence intervals?

[This is the same as asking whether a return of 14% has less than a 68% probability of occurring by chance for that security. If it's not inside the 68% confidence interval, it's unlikely to occur, since it will only occur by chance 32% of the time. Of course, the 99% confidence interval is much more likely to include the observed return, simply by chance. Only 1% of the time will it fall outside the 99% CI. Pretty rare.

10.3 You are starting a new business, and you want to open an office in a local mall. You have been offered two alternative rental arrangements. You can pay the landlord 10% of your sales revenue, or you can pay a fixed fee of $1,000 per month. Describe the circumstances in which each of these arrangements would be your preferred choice.