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 investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to Wilton University. Although internships are encouraged by the school, to get class credit for the internship, no salary can be paid. Other than internships, the school will not allow its students 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 $65,000 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 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 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 $70,000, payable at the beginning of each school year. In addition, books and other supplies are estimated to cost $3,000 per year, payable at the beginning of each year. Ben expects that after graduation from Wilton, he will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary, his average income tax rate will increase to 31 percent.

The school offers a health insurance plan that will cost $3,000 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,000 more per year than his current expenses, payable at the beginning of each year. The appropriate discount rate is 4.7 percent.

Question: Assuming all salaries are paid at the end of each year, what is the best option for Ben — remaining at his current job or pursuing an MBA —from a strictly financial standpoint?

Answer 1

To determine the best option for Ben, we must calculate the Present Values of all the income and expenses for both the options.

Option1:   Keeping his current work for 40 years

There factors to calculate the present values (PV) of this option are:

(a) His annual salary at the firm is $65,000 per year

(b) His salary is expected to increase at 3 % per year until retirement

(c) His current average tax rate is 26 % and discount rate is 6.5%

Here

Salary After tax = c = $65,000 * (1 - 0.26) = $48,100

Discount Rate = R = 6.5% = 0.065

Growth Rate = G = 3% = 0.03

Time Period = T = 40

So Present Value (PV) of Growing Annuity,

PV = C (1 – ( (1+g)/(1+r))^t / r – g )

PV = $48100 (1 – ((1 + 03)/(1 + 065))⁴⁰ / 0.065 – 0.03)

PV = $48100 (1 – ((1.03)/(1.065))⁴⁰ / 0.035)

PV = $48100 (1 – 0.261 / 0.035)

PV = $44 400 (0.739 / 0.035)

PV = $44 400 (21.114)

PV = $1,015,583.4

So the present value of his future income = $1,015,583.4

2.    Getting the MBA at Wilton University

In this case, we must compute 4 parts:

A.   Present Value of salary for 38 years (40 – 2 years)

B.   Present Value of signing bonus

C. Present Value of costs for 2 years at the college

D. Present Value of 2 years’ salary when he continue to work

A.   Present Value of salary for 38 years

The factors to consider are:

(a) He will receive a job offer for about $110,000 per year, with a $20,000 signing bonus

(b) The salary at this job will increase at 4 % per year

(c) Average income tax rate will be 31 %

Salary after tax = C = $110,000 * (1- 0.31)

                            = $75,900

Discount Rate = R = 6.5%

Growth Rate = G = 4%

Time Period = T = 38

So Present Value (PV) of Growing Annuity,

PV = C (1 – ( (1+g)/(1+r))^t / r – g )

PV = $75 900 (1 – ( (1+0.04)/(1+0.065))³⁸ / 0.065 - 0.04)

PV = $75 900 (1 – ((1.04)/(1.065))³⁸ / 0.025)

PV = $75 900 (1 – (0.9765)³⁸ / 0.025)

PV = $1,806,116.4

So the present value of his future income = $1,806,116.4

B.    Present Value of signing bonus

Here

Signing bonus value = FV = $ 20,000

Discount Rate = R = 65%

Time Period = T = 38

PV = FV / (1+r)^t

PV = $20 000 / (1.065)³⁸

PV = $20 000 / 1.1342

PV = $17,633.57

So the present value of Signing bonus is = $17,633.57                  

C.    Present Value of costs for 2 years at the college

The factors to consider are:

(a) Tuition Fee = $70,000

(b) Books and other supplies cost = $3000 per year

(c) Health insurance plan cost $3,000 per year

(d) Room and board expenses = $2,000.

Total Cost = c = $70000 + $3000 + $3000 + $2000 = $78000

Discount Rate = R = 6.5%

Time Period = T = 2

Present Value (PV) of Annuity:

PV = c ( 1 – (1/(1+r)^t / r )

PV = $78000 ( 1 – (1/(1.065)² / 0.065)

PV = $ 142008.86

Present Value of cost = $ 142008.86

D.   PV of 2 years’ salary when he continue to work

The factors to consider are:

(a) His annual salary at the firm is $650,000 per year

(b) His salary expected to increase at 3 % per year until retirement

(c) His current average tax rate is 26 % and discount rate is 6.5 percent.

Salary after tax = $650,000 * (1 – 0.26) = $481000

Present Value (PV) of Growing Annuity.

PV = C (1 – ( (1+g)/(1+r))^t / r – g )

PVGA = $481000 (1 – ((1+3%)/(1+6.5%))2 / 6.5% - 3%)

PVGA = $481000 (1.8486)

PVGA = $889,176.6

Net income = A + B – C + D

                       = $1,806,116.4 + $17,633.57 - $ 142008.86 + $889,176.6

                        = $2,570,917.71

Now as    $2,570,917.71 > $1,015,583.4

So the best option for Ben Bates is to enrolled in its MBA program at Wilton University.