Chapter 6, Problem 3M

Summary Introduction

Case summary:

Person B has completed his graduation before six years with an undergraduate degree in finance. His aim is to become an investment banker, though he is satisfied with the present job. Person B was searching for the best college to do MBA program, which he thinks that would assist in achieving his aim. He was looking for University W and College M. The details of Person B's current job and his course details are provided.

Characters in the case:

• Person B
• University W
• College M

Adequate information:

• Person B is not allowed to work anywhere until the completion of MBA program.
• The salaries are not paid for the internship course.

To calculate: The best option for Person B assuming that the payment of salary occurs at the end of every year.

Answer to Problem 3M

The computed total value for each option is greater in the second option that is, pursuing MBA at University W. Hence, the best option for Person B is to pursue MBA at University W.

Explanation of Solution

Given information:

Person B currently works at a money management company, whose salary is $53,000 for a year and it is expected to rise to 3% in a year until the retirement. He is 28 years old and expects to be in employment for 38 years and more. The average rate of tax payable by Person B is 26%.

College R at University W is one of the best programs to do MBA. It is a two years full-time course. The fee is $58,000 annually and the cost of book and other supplies is $2000 in a year. After graduation, he will be employed for $87,000 with a bonus of $10,000. The salary will increase by 4% in a year and the rate of tax will rise to 31%.

School B at College M is less familiar than College R. It provides an accelerated program for one-year with an annual fees of $75,000. The cost of books and other supplies for the program is expected as $4,200. Person B would get an offer of $78,000 for a year after graduation with a bonus of $8,000. The salary would rise to 3.5% for a year and the average rate of tax will be 29%.

Both the schools provide a health insurance plan for the cost of $3,000 for a year, which must be paid at the opening of the year. The boarding and room expenses of Person B in both the companies would be decreased by $4,000 in one year. The rate of discount is 6.5%.

Note: Here, Person B has three choices, one is to remain in the same job, or to pursue MBA at University W, or pursue at College M. As the board and room costs are considered as saved expenses, the reduction in these costs is relevant. Compute the after-tax value under each choice.

If Person B chooses to remain at the present job, then the present after-tax value of him will be the following:

Formula to calculate after-tax value:

$\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)$

Compute the after-tax salary:

$\begin{array}{c}\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)\\ =\$53,000\left(1-0.26\right)\\ =\$39,220\end{array}$

Hence, the after-tax value is $39,220.

Formula to calculate the present value for a growing annuity:

$\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]$

Note: g denotes the growing rate of annuity,

r denotes the rate of discount,

t denotes the number of year.

Compute the present value for a growing annuity:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$39,220\left[\frac{1-{\left[\frac{1+0.03}{1+0.065}\right]}^{38}}{0.065-0.03}\right]\\ =\$39,220\left[\frac{1-0.280885579}{0.035}\right]\\ =\$805,819.074\end{array}$

Hence, the present value is $805,819.074.

If Person B chooses to pursue MBA at University W, then the total value of him will be the following:

Formula to calculate the total direct costs:

$\text{Total direct costs}=\left(\begin{array}{l}\text{Tuition fees}+\text{Books and supplies}+\text{Health insurance}-\\ \text{Reduction in room and board expenses}\end{array}\right)$

Compute the total direct costs:

$\begin{array}{c}\text{Total direct costs}=\left(\begin{array}{l}\text{Tuition fees}+\text{Books and supplies}+\text{Health insurance}-\\ \text{Reduction in room and board expenses}\end{array}\right)\\ =\$58,000+\$2,000+\$3,000-\$4,000\\ =\$59,000\end{array}$

Hence, the total direct cost is $59,000.

Formula of present value of direct costs:

$\text{Present value}=\text{Total direct cost}+\frac{\text{Total direct cost}}{\left(1+\text{discount rate}\right)}$

Compute present value of direct costs:

$\begin{array}{c}\text{Present value}=\text{Total direct cost}+\frac{\text{Total direct cost}}{\left(1+\text{discount rate}\right)}\\ =\$59,000+\frac{\$59,000}{\left(1+0.065\right)}\\ =\$114,399.06\end{array}$

Hence, the present value of the direct costs is $114,399.06.

Formula to calculate the present value of after-tax bonus:

$\text{Present value of after-tax bonus in }2\text{ years}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}$

Compute the present value of after-tax bonus:

$\begin{array}{c}\text{Present value of after-tax bonus in }2\text{ years}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$10,000\left(1-0.31\right)}{{\left(1+0.065\right)}^2}\\ =\frac{\$6,900}{\$1.134225}\\ =\$6,083.45\end{array}$

Hence, the present value of after-tax bonus of Person B is $6,083.45.

Formula to calculate after-tax value:

$\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)$

Compute the after-tax value:

$\begin{array}{c}\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)\\ =\$87,000\left(1-0.31\right)\\ =\$60,030\end{array}$

Hence, the after-tax value if Person B pursues MBA at University W is $60,030.

Note: As Person B’s salary will increase by 4% in a year, compute the present value of after-tax of the increasing salary. Remember that Person B is expected to work for 38 years more in which, two years he will be employed in his course and the balance number of years he has to work is 36 years.

Formula to calculate the present value for a growing annuity:

$\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]$

Note: g denotes the growing rate of annuity,

r denotes the rate of discount,

t denotes the number of years.

Compute the present value for a growing annuity:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$60,030\left[\frac{1-{\left[\frac{1+0.04}{1+0.065}\right]}^{36}}{0.065-0.04}\right]\\ =\$60,030\left[\frac{1-0.425220638}{0.025}\right]\\ =\$1,380,160.20\end{array}$

Hence, the present value is $1,380,160.20.

As the initial payment of salary will be obtained for three years from the present, discount the number of years to 2 to compute the value at present.

Formula to calculate the present value for 2 years:

$\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}$

Compute the present value for 2 years:

$\begin{array}{c}\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$1,380,160.20}{{\left(1+0.065\right)}^2}\\ =\$1,216,831.052\end{array}$

Hence, the present value for 2 years is $1,216,831.052.

Formula to calculate the total value:

$\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for }2\text{ years}-\\ \text{Total direct costs}\end{array}\right)$

Compute the total value:

$\begin{array}{c}\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for }2\text{ years}-\\ \text{Total direct costs}\end{array}\right)\\ =\$6,083.45+\$1,216,831.052-\$114,399.06\\ =\$1,108,515.44\end{array}$

Hence, the total value, if Person B pursues MBA in University W is $1,108,515.44.

If Person B chooses to pursue at College M, then the total value of him will be the following:

Formula to calculate the total direct costs:

$\text{Total direct costs}=\left(\begin{array}{l}\text{Tuition fees}+\text{Books and supplies}+\text{Health insurance}-\\ \text{Reduction in room and board expenses}\end{array}\right)$

Compute the total direct costs:

$\begin{array}{c}\text{Total direct costs}=\left(\begin{array}{l}\text{Tuition fees}+\text{Books and supplies}+\text{Health insurance}-\\ \text{Reduction in room and board expenses}\end{array}\right)\\ =\$75,000+\$4,200+\$3,000-\$4,000\\ =\$78,200\end{array}$

Hence, the total direct cost is $78,200.

Note: This is also the present value costs, as they all are paid at present.

Formula to calculate the present value of after-tax bonus:

$\text{Present value of after-tax bonus in }1\text{ year}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}$

Compute the present value of after-tax bonus:

$\begin{array}{c}\text{Present value of after-tax bonus in }1\text{ year}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$8,000\left(1-0.29\right)}{{\left(1+0.065\right)}^1}\\ =\frac{\$5,680}{\$1.065}\\ =\$5,333.33\end{array}$

Hence, the present value of after-tax bonus of Person B is $5,333.33.

Formula to calculate after-tax value:

$\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)$

Compute the after-tax value:

$\begin{array}{c}\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)\\ =\$78,000\left(1-0.29\right)\\ =\$55,380\end{array}$

Hence, the after-tax value if Person B pursues MBA at College M is $55,380.

Note: As Person B’s salary will increase by 3.5% in a year, compute the present value of after-tax of the increasing salary. Remember that Person B is expected to work for 38 years more in which, one year he will be employed in his course and the balance number of years he has to work is 37 years.

Formula to calculate the present value for a growing annuity:

$\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]$

Note: g denotes the growing rate of annuity.

r denotes the rate of discount.

t denotes the number of years.

Compute the present value for a growing annuity:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$55,380\left[\frac{1-{\left[\frac{1+0.035}{1+0.065}\right]}^{37}}{0.065-0.035}\right]\\ =\$55,380\left[\frac{1-0.34742211}{0.03}\right]\\ =\$1,204,658.78\end{array}$

Hence, the present value is $1,204,658.78.

As the initial payment of salary will be obtained for one year from the present year, discount the number of year to 1 to compute the value at present.

Formula to calculate the present value for 1 year:

$\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}$

Compute the present value for 1 year:

$\begin{array}{c}\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$1,204,658.78}{{\left(1+0.065\right)}^1}\\ =\$1,131,135.005\end{array}$

Hence, the present value for 1 year is $1,131,135.005.

Formula to calculate the total value:

$\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for 1 year}-\\ \text{Total direct costs}\end{array}\right)$

Compute the total value:

$\begin{array}{c}\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for 1 year}-\\ \text{Total direct costs}\end{array}\right)\\ =\$1,204,658.78+\$1,131,135.005-\$78,200\\ =\$2,257,593.79\end{array}$

Hence, the total value, if Person B pursues MBA in College M is $2,257,593.79.