Christopher Cross graduated from college five years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he narrowed his choice to either University of British Columbia or Thompson Rivers University. Although internships are encouraged by both schools, to get class credit for internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program.

Christopher currently works at a fund management firm of Wilcox and Smith. His annual salary at the firm is $$65,000$ per year, and his salary is expected to increase at $3\mathrm{.}0$ percent per year until retirement. He is currently $25$ years old and expects to work till he is $65$ years old $(40$ years left to work$).$ His current job includes a fully paid health insurance plan, and his current average tax rate is $30$ percent. Christopher has a savings account with enough money to cover the entire cost of his MBA program.

The Sauder School of Business at University of British Columbia is one of the top MBA programs in the country. The MBA degree requires two years of full$-$time enrollment at the university. The annual tuition is $$87,000,$ payable at the beginning of each school year. Books and other supplies are estimated to cost $$5,000$ per year. Christopher expects that after graduation from UBC, he will receive a job offer for about $$110,000$ per year, with a $$35,000$ signing bonus. The salary at this job will increase $3\mathrm{.}7$ percent per year. Because of the higher salary, his average income tax rate will increase to $37$ percent.

The School of Business and Economics at Thompson Rivers University began its MBA program in $2005.$ TRU is smaller and less well known than UBC. TRU offers an accelerated, one$-$year program, with a tuition cost of $$75,000$ to be paid upon matriculation. Books and other supplies for the program are expected to cost $$5,000.$ Christopher thinks that he will receive an offer of $$95,000$ per year upon graduation, with a $$20,000$ signing bonus. The salary at this job will increase $4\mathrm{.}2$ percent per year. His average tax rate at this level of income will be $35$ percent.

Both schools offer a health insurance plan that will cost $$3,000$ per year, payable at the beginning of the year. Christopher estimates that room and board expenses will cost $$5,000$ more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is $5\mathrm{.}2$ percent.

$2.$ What initial salary would Christopher need to receive to make him indifferent between attending UBC and staying at his current position?