Solve for net present value

Question 1
A doctor spent two weeks doing charity medical work in Mexico. In calculating her taxable income for the year, her accountant deducted as business expenses her round-trip airline ticket, meals, and hotel bill for the two-week stay. She was surprised to learn that the accountant, following IRS rules, could no deduct as cost of the trip the $8,000 of income she lost by being absent from her medical practice for two weeks. She asked the accountant, "Since lost income is not deductible as an expense, should I ignore it when I make my decision next year to go to Mexico for charity work?" Can you give the doctor some advice on decision making?

Question 2
An article in The Wall Street Journal discusses a trend among some large U.S. corporations to base the compensation of outside members of their boards of director partly on the performance of the corporations. "This growing practice more closely aligns the director to the company. (Some) companies link certain stock or stock-option grants for directors to improved financial performance, using a measure such as annual return on equity."
How would such a linkage tend to reduce the agency problem between managers and shareholders as a whole? Why could directors be more efficient than shareholders at improving managerial performance and changing their incentives?

Question 3
Fortune magazine reported that SkyWest, an independent regional airline, negotiated a financial arrangement with Delta and United to provide regional jet service for the two major airlines. For its part of the deal, SkyWest agreed to paint its jets the colors of Delta Connection and United Express and to fly routes specified by the two airlines. In return, Delta and United agreed to pay SkyWest a predetermined profit margin and to cover most of the regional airline's costs. Fortune explained that while the deal limited volatility in earnings since Delta and United covered SkyWest's fuel costs, increased its load factor (the percentage of seats occupied), and managed its ticket prices.
Fortune suggested that Wall Street liked the deal because SkyWest's market valuation instead from $143 million to $1.1 billion after it began its service with the two major airlines. Explain carefully how this arrangement with Delta and United could have caused the value of SkyWest to increase dramatically even though it limited the amount of profit SkyWest could earn.

Mathematical Exercises
Question 12
What is the present value of a firm with a five-year life span that earns the following stream of expected profit? (Treat all profits as being received at year-end.) Use a risk-adjusted discount rate of 12 percent.

Year Expected Profit
1 $10,000
2 20,000
3 50,000
4 75,000
5 50,000

Question 2
Suppose you are the manager of a California winery. How would you expect the following events to affect the price you receive for a bottle of wine?
a. The price of comparable French wines decreases.
b. One hundred new wineries open in California
c. The unemployment rate in the United States decreases.
d. The price of cheese increases.
e. The price of a glass bottle increases significantly due to new government anti-shatter regulations.
f. Researchers discover a new wine-making technology that reduced production costs.
g. The price of wine vinegar, which is made from the leftover grape mash, increases.
h. The average age of consumers increases, and older people drink less wine.