Problem:
After getting your MBA at age 30, you start looking for a job. Here's what's going to happen. Every six months you receive a job offer (with the first offer coming immediately at age 30.0). Assume that once you accept a job offer, you stay with the same job until you turn 70. The annual salary associated with each offer is normally distributed with an average of $100,000 and a standard deviation of $25,000. You have to decide on the spot whether to accept each offer or not. If you decline it, then you earn nothing for the next six months. If you accept it, you receive the offered salary in your first year, with a yearly raise that is uniformly distributed between 3% and 8% above your previous year's salary. Assume a yearly discount rate of 5% for future earnings.
- Discuss the tradeoffs in making this decision.
- Suppose you take a strategy of accepting the first salary offer that is greater than D dollars. Determine a value of D that maximizes the average net present value of your lifetime earnings.
- Compare your choice of D from part b) to your friend's approach, which is to simply accept the very first offer, regardless of the salary (i.e., your friend sets D = 0).
- What is the average difference in NPV of earnings between you and your friend?
- What is the probability that your friend has a greater lifetime NPV than you? (assume that your salary offers and your friend's offers, along with year over year raises, are independent of each other)