My sister is a public school teacher. She is currently 30 years old and has a Master's degree. According to her union contract, if she earns her Ph.D., she will make $12,000 more per year (Union contracts also include cost of living increases, so this increase will be protected from inflation). She plans to retire on her 65th birthday, and will earn 80% of her salary in her pension. She has found a Ph.D. program at a nearby university that she can start next year. Importantly, the courses for this course are mostly online, so she can complete them in the evenings and over the summer, so she does not need to stop working. The program costs $10,000 per year and takes 4 years to complete. My sister enjoys learning, so suppose the psychological "costs" of education are small to her.

(a) What is the net present value of this investment? In your calculation, assume that she starts school next year, she already has the money to pay the costs for the degree so doesn't require student loans, she will finish her PhD and receive the higher earnings on her 35th birthday, she expects to live until her 80th birthday (consistent with U.S. life expectancy at birth for women), and that the rate of return on alternative investments would be 7% per year. Hint: Use a spreadsheet software instead of using the formulas for the present value of annuities.

(b) In part (a), I had you assume the rate of return on alternative investments was 7%. What would this rate need to be for my sister to be indifferent between doing the PhD and taking the alternative investment?