Calculate expected income at Firm 1 and Firm 2 over a two-year window under the following scenarios:
Scenario 1
In Year 1 tax rates remain the same but there is a non-zero probability that the cost of living will change. The changes that could happen are as follows:
Columbus – stays same (p=.50); increases to 1.25 (p=.50) Chicago – stays same (p=.10); increases to 2.5 (p=.90)
Los Angeles – stays same (p=.05); increases to 3.0 (p=.95)
(all changes in cost-of-living are relative to Columbus in Year 0)
Scenario 2
No tax increase in Year 1 (use tax rates from Year 0) and same cost-of-living differences as in the assignment. Salaries might change. The changes and probability of changes differ by firm as follows:
Firm 1 potential changes to monthly salary
Columbus – stays same (p=.50); increases to 3770 (p=.50) Chicago – stays same (p=.10); increases to 4500 (p=.90)
Los Angeles – stays same (p=.05); increases to 4650 (p=.95)
Firm 2 potential changes to monthly salary
Columbus – stays same (p=.70); increases to 4575 (p=.30) Chicago – stays same (p=.85); increases to 4950 (p=.15)
Los Angeles – stays same (p=.95); increases to 14650 (p=.05)
Calculate expected income at Firm 1 and Firm 2 over a two-year window as we did in class. That is, calculate:
•annual income = monthly income * 12
•After-tax income = annual income * (1-tax rate)
•Cost-of-living-adjusted income = after-tax income/cost-of-living (if relevant) *one city will always be the reference or comparison city
•NPV-adjusted-income = cost-of-living adj. income/ (1+r)^t (where t denotes year in which got income t=0, 1, ….T)
•Expected income for each firm in each city in each year = NPV-adjusted-income * all probabilities
•Expected income for each FIRM in each year = sum, across all cities in each year, expected income for each firm
•Expected income for each FIRM = sum the expected income at a given firm in Year 0 and Year 1
Under each scenario, explain which firm is your better choice (and why)
