Reference no: EM133153085
Katie has just landed a two-year contract for her dream job at Superior Actuaries (SA). But there's a catch: She must pass two of her actuarial exams in the first two years to stay employed beyond year 2. (Actuaries typically pass 7-10 exams over a career.) She can take one or two exams per year (she must take at least one per year), but taking two in a year is more difficult, and it reduces her pass rate on individual exams because her preparation time is spread thinner. Exams get increasingly more difficult, i.e., Exam 1 is the easiest, Exam 2 is a bit harder, etc. The maximum number of exams she could pass in two years is four (Exam 1, Exam 2, Exam 3, and Exam 4).
Her starting base salary is $100,000. Every time she passes an exam (in either year), she gets an immediate $15,000 bonus, regardless of her future employment status. Additionally, each exam she passes in her first year increases her second-year salary by $10,000 (this salary bump does not apply to any exams passed in year 2). If she passes the required two exams in her first two years, she estimates the present value of her future earnings at SA (year 3 and beyond) to be $1,000,000. If she does not pass at least two exams in her first two years, she is released at the end of year 2 and receives no future earnings from SA. Assume
- If Katie takes two exams in any given year and passes only one, it must be the easier exam.
- Taking an exam more than once does not change her pass rate.
- The discount rate for all values is 0 (i.e., treat all $ values in the problem as present values).
- Exams are taken in order. So, for example, if Katie passes Exam 1 in year 1 and opts to take two exams in year 2, the exams are Exam 2 and Exam 3.
The probability of passing an exam depends on whether Katie is taking one exam per year or two. The table below summarizes the probabilities:
|
Take One Exam in a Year (year 1 or year 2)
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Pass Probability
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Take Two Exams in a Year (year 1 or year 2)
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Prob Pass Easier Exam (Fail Harder Exam)
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Prob Pass Both
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|
Exam 1
|
0.9
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Exam 1 & Exam 2
|
0.60
|
0.25
|
|
Exam 2
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0.75
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Exam 2 & Exam 3
|
0.5
|
0.15
|
|
Exam 3
|
0.7
|
Exam 3 & exam 4
|
0.4
|
0.1
|
Using a decision tree, determine how Katie can maximize her total (long run) earnings at SA. I've drawn part of the tree to help you. This part is when Katie decides to take only one exam (Exam 1) in year 1 of her contract.