Questions:
1.Jane is trying to decide which of three career paths to pursue. The first one requires one year of training at a cost of $10,000. The second requires two years of training at a cost of $7,000 per year. The third requires four years of training at a cost of $4,000 per year. If she opts for career path one she can work for five years after training is completed earning an incremental wage rate of $2,000 in year 1, $3,000 in year 2, $3500 in year 3, $4,000 in years 4 and $5,000 in year 5. If she elects career path two she will earn an incremental $9,000 the first year after training is completed and $8,000 the second year after training is completed and $4,000 the third year after training is completed. She will only have incremental earnings for three years after training if she elects career path 2. If she opts for career path three she will have incremental earnings of $6,000 per year for each of the five years after training is completed. After this time she will have no incremental earnings.
a.Assuming the first year of training is not to be discounted. Calculate the present value of the costs and the present value of the benefits of each career path assuming an interest rate of 3% and then again at an interest rate of 10%. Which of the career paths should she pursue under each interest rate?
2.Mary expects to retire in five years. She is considering one of three possible career changes. Each has different costs and benefits associated with it. Below is the distribution of costs and benefits over the next five years of each possible career path.
Y0 Y1 Y2 Y3 Y4
Path 1 -5,000 +2,000 +2,500 +1,000 +500
Path 2 -2,000 +3,000 -2,000 +3,000 +0
Path 3 +1,000 -4,000 +2,000 +1,000 +1,000
a.Calculate the present discounted value of each career path at a discount rate of 5% and at a discount rate of 15%.
b.Which career path has the highest net present value at each discount rate?
c. Which career path has the highest benefit/cost at each discount rate.
d.In general, how does the age at which one undertakes a career change impact on the likely return to the chosen career?
3.Kalvin Crook is contemplating a life of crime. If he commits a crime and does not get caught, he stands to gain $80. If he commits a crime and does get caught, he stands to lose $120. He is contemplating a four event crime spree. The probability of getting caught on each day is not a function of whether or not he got caught on the previous day (i.e. the events are independent). Below is a list of the probability of getting caught on each day of crime:
Prday1 Prday2 Prday3 Prday4
Get Caught .2 .3 .2 .4
Go Free .8 .7 .8 .6
a.Calculate Kalvin's expected haul over the four event crime spree.
b.Calculate the probability that Kalvin will never get caught over the four days.
c.Calculate the probability that Kalvin will get caught exactly half the time.
d.Given that Kalvin will get caught exactly two out of four times, calculate his expected haul.
4.Jessica has the following utility of income function: U = 1700Y - .011Y2. Jessica currently has $65,000 and faces a 4% chance of losing $50,000.
a.Calculate Jessica's utility level if she has $65,000.
b.Calculate Jessica's expected income and her expected utility level.
c.Calculate the amount Jessica would be willing to pay to insure against a 4% chance of losing $50,000.
d.Calculate how much Jessica would be willing to pay to insure against a 20% chance of losing $10,000.