Question

Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an inves\tment banker. He feels that an MBA degree would allow him to achieve his goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its student to work while enrolled in its MBA program. Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $70,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently 28 years old and expects to work for 37 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 28 percent. Ben has a savings account with enough money to cover the entire cost of his MBA program. The Ritter College of Business at Wilton University 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 $65,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $2,000 per year. Ben expected that after graduation from Wilton, he will receive a job offer for about $100,000 per year, with a $10,000 signing bonus. The salary at this job will increase at 4% per year. Because of the higher salary, his average income tax rate will increase to 32 percent. The Bradley School of Business at Mount Perry College began its MBA 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, oneyear program, with a tuition cost of $75,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $3,000. Ben thinks that he will receive an offer of $85,000 per year upon graduation, with a $10,000 signing bonus. The salary at this job will increase at 3.5 percent. His average tax rate at this level of income will be 30 percent. Both schools offer a health insurance plan that will cost $2,500 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $15,000 per year at either school. The appropriate discount rate is 6 percent.

What initial salary would Ben need to receive to make him indifferent between attending Wilton University and staying in his current position?

Answer 1

Step 1). PV of net earnings if MBA is done from Wilton University:

i). PV of MBA costs:

Total annual cost (AC) = tuition fee + book cost + health insurance plan cost + room & boarding = 65,000 + 2,000 + 2,500 + 15,000 = 84,500

Discount rate (r) = 6%; n = 2

PV of MBA cost (using beginning period annuity formula) = (AC/r)*(1+r)*[1 - (1+r)^-n]

= (84,500/6%)*(1+6%)*[1-(1+6%)^-2] = 164,216.98

ii). PV of after-tax earnings after 2 years:

PMT (after-tax annual starting salary) = 100,000*(1-32%) = 68,000; N = 35; annual growth rate (g) = 4%; r = 6%

Using PV of growing ordinary annuity, we have

PV(after 2 years) = PMT/(r-g)*[1 - ((1+g)/(1+r))^N]

= 68,000/(6%-4%)*[1 - ((1+4%)/(1+6%))^35] = 1,654,416.98

Total PV of after-tax earnings = PV(after 2 years) + signing bonus = 1,654,416.98 + 10,000 = 166,416.98

PV of after-tax earnings now (PV(0)) = Total PV/(1+6%)^2 = 1,664,416.98/(1+6%)^2 = 1,481,325.19

iii). PV of net earnings if MBA is done from Wilton University = PV(0) - PV of MBA cost

= 1,481,325.19 - 164,216.98 = 1,317,108.21

Step 2). PV of net earnings if current job is continued:

PMT (current after-tax salary) = 70,000*(1-28%) = 50,400; N = 37; g = 3%; r = 6%

PV of net earnings = PMT/(r-g)*[1 - ((1+g)/(1+r))^N]

= 50,400/(6%-3%)*[1-((1+3%)/(1+6%))^37] = 1,099,276.76

Step 3). For Ben to be indifferent between attending Wilton University and staying in his current job, the starting salary after Wilton University has to be such that the PV of after-tax earnings equals 1,099,276.76 (the PV of earnings from his current job).

Let the starting after-tax salary be X.

PV of salary = 1,099,276.76 + PV of MBA cost - PV of signing bonus

= 1,099,276.76 + 164,216.78 - 10,000/(1+6%)^2

= 1,254,593.28

{X/(r-g)*[1 - ((1+g)/(1+r))^N]}/(1+6%)^2 = 1,254,593.28

X/(r-g)*[1 - ((1+g)/(1+r))^N] = 1,254,593.98*(1+6%)^2

X/(6%-4%)*[1 - ((1+4%)/(1+6%))^35] = 1,409,661

X = 57,940.02

Salary before tax has to be X/(1-32%) = 57,940.02/(1-32%) = 85,205.91

If initial salary is 85,205.91 after attending Wilton University, Ben will be indifferent between doing his MBA from Wilton and staying in his current job.