Chapter 4, Problem 3CC

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 a 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 the Person B's current job and his course structure 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 assumes that the increase in salary payment occurs at the end of every year.

Answer to Problem 3CC

As the computed total value for each option is greater in the second option, that is, 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, and his salary is $53,000 per year and it is expected to rise at 3% a year until the retirement. He is 28 years old, and expects to be in the employment for 38 more years. The average rate of tax payable by the Person B is 26%.

College R at University W is one of the best programs for MBA. It is a two years full-time course. The fee is $58,000 annually and the cost of books and other supplies is $2000 for a year. After graduation, he will be employed for $87,000 and with a bonus of $10,000. The salary will increase at 4% per 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 $75,000. The cost of books and other supplies for the program is expected to be $4,200. Person B would get an offer of $78,000 for a year after the graduation and with a bonus of $8,000. The salary would rise at 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 per year, which must be paid at the beginning of the year. The board and room expenses for any of the two schools that Person B attends will decrease in one year by $4,000. The rate of discount is 5.5%.

Note: Here, Person B has three choices; one is to remain in the same job, or to pursue MBA at University W, or at College M. As the board and room costs are a saved expense, 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 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:

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

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 years.

Compute the present value for a growing annuity:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$39,220\left[\frac{1-{\left[\frac{1+0.03}{1+0.055}\right]}^{38}}{0.055-0.03}\right]\\ =\$39,220\left[\frac{1-0.40199539000165}{0.025}\right]\\ =\$938,149.63\end{array}$

Hence, the present value is $938,149.63.

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

Formula to calculate the total direct costs:

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

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:

$\begin{array}{c}\text{Present value}=\text{Total direct cost}+\frac{\text{Total direct cost}}{\left(1+\text{discount rate}\right)}\\ =\$59,000+\frac{\$59,000}{\left(1+0.055\right)}\\ =\$114,924.17\end{array}$

Hence, the present value of the direct costs is $114,924.17.

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:

$\begin{array}{c}\text{Present value of after-tax bonus in }2\text{ years}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$10,000\left(1-0.31\right)}{{\left(1+0.055\right)}^2}\\ =\frac{\$6,900}{\$1.113025}\\ =\$6,199.32\end{array}$

Hence, the present value of after-tax bonus of Person B is $6,199.32.

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 at 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, in which, the first two years he will be employed in his course and for the remaining 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:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$60,030\left[\frac{1-{\left[\frac{1+0.04}{1+0.055}\right]}^{36}}{0.055-0.04}\right]\\ =\$60,030\left[\frac{1-0.59718881898356}{0.015}\right]\\ =\$1,612,050.35\end{array}$

Hence, the present value is $1,612,050.35.

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:

$\begin{array}{c}\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$1,612,050.35}{{\left(1+0.055\right)}^2}\\ =\$1,448,350.53\end{array}$

Hence, the present value for 2 years is $1,448,350.53.

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:

$\begin{array}{c}\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for }2\text{ years}-\\ \text{Total direct costs}\end{array}\right)\\ =\$6,199.32166842613+\$1,448,350.53120999-\$114,924.170616113\\ =\$1,339,625.68\end{array}$

Hence, the total value, if Person B pursues MBA in the University W is $1,339,625.68.

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

Formula to calculate the total direct costs:

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

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:

$\begin{array}{c}\text{Present value of after-tax bonus in }1\text{ year}=\frac{\text{Bonus amount}\left(1-\text{Increase in tax rate}\right)}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$8,000\left(1-0.29\right)}{{\left(1+0.055\right)}^1}\\ =\frac{\$5,680}{\$1.055}\\ =\$5,383.89\end{array}$

Hence, the present value of after-tax bonus of Person B is $5,383.89.

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 the College M is $55,380.

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 38 more years, in which, the first one year he will be employed in his course and for the remaining 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:

$\begin{array}{c}\text{Present value}=\text{After-tax value}\left[\frac{1-{\left(\frac{1+g}{1+r}\right)}^t}{r-g}\right]\\ =\$55,380\left[\frac{1-{\left[\frac{1+0.035}{1+0.055}\right]}^{37}}{0.055-0.035}\right]\\ =\$55,380\left[\frac{1-0.49255182878472}{0.02}\right]\\ =\$1,405,123.99\end{array}$

Hence, the present value is $1,405,123.99.

As the initial payment of salary will be obtained one year from the present year, discount the number of year 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:

$\begin{array}{c}\text{Present value}=\frac{\text{Present value of the increasing salary}}{{\left(1+\text{Rate of discount}\right)}^t}\\ =\frac{\$1,405,123.99}{{\left(1+0.055\right)}^1}\\ =\$1,331,871.08\end{array}$

Hence, the present value for 1 year is $1,331,871.08.

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:

$\begin{array}{c}\text{Total value}=\left(\begin{array}{l}\text{Present value of after-tax bonus}+\text{Present value for 1 year}-\\ \text{Total direct costs}\end{array}\right)\\ =\$5,383.88625592417+\$1,331,871.07686740-\$78,200\\ =\$1,259,024.96\end{array}$

Hence, the total value, if Person B pursues MBA in the College M is $1,259,024.96.