Chapter 4, Problem 3MC

Summary Introduction

Case summary:

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

Characters in the case:

• Person B
• University W
• College M
• Company DL
• College R
• College M
• School B

Adequate information:

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

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

Answer to Problem 3MC

Solution:

As the computed total value for each option is greater in the second option, the best option for Person B is to pursue an MBA at University W.

Explanation of Solution

Given information:

Person B currently works at a money management Company DL, whose salary is $65,000 for a year and is expected to rise to 3% in a year, until retirement. He is 28 years old and expects to be in employment for 40 more years. The average rate of tax payable by Person B is 26%.

College R at University W is one of the best programs for an MBA. It is a two-year full-time course. The fee is $70,000 annually and the cost of the book and other supplies is $3,000 for a year. After graduation, he will be employed for $110,000 with a bonus of $20,000. The salary will increase by 4% in a year and the rate of tax will rise by 31%.

School B at College M is less familiar than College R. It provides an accelerated program for one year with an annual fee of $85,000. The cost of books and other supplies for the program is expected to be $4,500. Person B would get an offer of $92,000 for a year after graduation, with a bonus of $18,000. The salary would rise to 3.5% for a year and the average rate of tax will be 29%.

Both the schools provide health insurance plans for the cost of $3,000 for a year, which must be paid at the beginning of the year. The board and room expenses will be $2,000 more for a year in both the schools. The rate of discount is 6.3%.

Note: Here, Person B has three choices; one is to remain in the same job, or to pursue an MBA at University W or at College M. As the board and room costs are not relevant, they will be the same even if Person B stays in his present job or attends the college. Compute the after-tax value under each choice.

If Person B chooses to remain at the present job, then his present after-tax value 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:

$\begin{array}{c}\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)\\ =\$65,000\left(1-0.26\right)\\ =\$48,100\end{array}$

Hence, the after-tax value is $48,100.

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:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$48,100\left[\frac{1-{\left[\frac{1+0.03}{1+0.063}\right]}^{40}}{0.063-0.03}\right]\\ =\$1,044,728.37\end{array}$

Hence, the present value is $1,044,728.37.

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

Formula to calculate the total direct costs:

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

Compute the total direct costs:

$\begin{array}{c}\text{Total direct costs}=\left(\begin{array}{l}\text{Tuition fees}+\text{Books and supplies}+\text{Health insurance}+\\ \text{Room and board expenses}\end{array}\right)\\ =\$70,000+\$3,000+\$3,000+\$2,000\\ =\$78,000\end{array}$

Hence, the total direct cost is $78,000.

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 the present value of direct costs:

$\begin{array}{c}\text{Present value}=\text{Total direct cost}+\frac{\text{Total direct cost}}{\left(1+\text{discount rate}\right)}\\ =\$78,000+\frac{\$78,000}{\left(1+0.063\right)}\\ =\$151,377.23\end{array}$

Hence, the present value of the direct costs is $151,377.23.

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:

$\begin{array}{c}\text{Present value of after-tax bonus in }2\text{ years}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$20,000\left(1-0.31\right)}{{\left(1+0.063\right)}^2}\\ =\$12,212.72\end{array}$

Hence, the present value of the after-tax bonus of Person B is $12,212.72.

Formula to calculate the after-tax value:

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

Compute the after-tax value:

$\begin{array}{c}\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)\\ =\$110,000\left(1-0.31\right)\\ =\$75,900\end{array}$

Hence, the after-tax value if Person B pursues MBA at University W is $75,900.

Note: As Person B’s salary will increase by 4% a year, compute the present value of after-tax of the increasing salary. Remember that Person B is expected to work for 38 more 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:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$75,900\left[\frac{1-{\left[\frac{1+0.04}{1+0.063}\right]}^{38}}{0.063-0.04}\right]\\ =\$1,862,801.41\end{array}$

Hence, the present value is $1,862,801.41.

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

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:

$\begin{array}{c}\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$1,862,801.41}{{\left(1+0.063\right)}^2}\\ =\$1,648,542.05\end{array}$

Hence, the present value for 2 years is $1,648,542.05.

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:

$\begin{array}{c}\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for }2\text{ years}-\\ \text{Total direct costs}\end{array}\right)\\ =\$12,212.72+\$1,648,542.05-\$151,377.23\\ =\$1,509,377.54\end{array}$

Hence, the total value, if Person B pursues an MBA in the University W is $1,509,377.54.

If Person B chooses to pursue an MBA at College M, then his total value will be the following:

Formula to calculate the total direct costs:

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

Compute the total direct costs:

$\begin{array}{c}\text{Total direct costs}=\left(\begin{array}{l}\text{Tuition fees}+\text{Books and supplies}+\text{Health insurance}+\\ \text{Room and board expenses}\end{array}\right)\\ =\$85,000+\$4,500+\$3,000+\$2,000\\ =\$94,500\end{array}$

Hence, the total direct costs are $94,500.

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

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

$\begin{array}{c}\text{Present value of after-tax bonus in }1\text{ year}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$18,000\left(1-0.29\right)}{{\left(1+0.063\right)}^1}\\ =\$12,022.58\end{array}$

Hence, the present value of the after-tax bonus of Person B is $12,022.58.

Formula to calculate the after-tax value:

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

Compute the after-tax value:

$\begin{array}{c}\text{After-tax value}=\text{Salary of Person B}\left(\text{1}-\text{Tax rate}\right)\\ =\$92,000\left(1-0.29\right)\\ =\$65,320\end{array}$

Hence, the after-tax value if Person B pursues an MBA at the College M is $65,320.

Note: As Person B’s salary will increase at a rate of 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 39 more 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:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$65,320\left[\frac{1-{\left[\frac{1+0.035}{1+0.063}\right]}^{39}}{0.063-0.035}\right]\\ =\$1,509,165.86\end{array}$

Hence, the present value is $1,509,165.86.

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

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:

$\begin{array}{c}\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$1,509,165.86}{{\left(1+0.063\right)}^1}\\ =\$1,419,723.29\end{array}$

Hence, the present value for 1 year is $1,419,723.29.

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:

$\begin{array}{c}\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for 1 year}-\\ \text{Total direct costs}\end{array}\right)\\ =\$12,022.58+\$1,419,723.29-\$94,500\\ =\$1,337,245.87\end{array}$

Hence, the total value, if Person B pursues an MBA in College M is $1,337,245.87.