Question

A prospective MBA student earns $45,000 per year in her current job and expects that amount to increase by 12% per year. She is considering leaving her job to attend business school for two years at a cost of $40,000 per year. She has been told that her starting salary after business school is likely to be $125,000 and that amount will increase by 16% per year. Consider a time horizon of 10 years, use a discount rate of 12%, and ignore all considerations not explicitly mentioned here.

Assume all cash flows occur at the start of each year (i.e., immediate, one year from now, two years from now,..., nine years from now). Also assume that the choice can be implemented immediately so that for the MBA alternative the current year is the first year of business school.

What is the net present value of the more attractive choice?

Please round your answer to the nearest dollar.

Answer 1

CHOICE 1

Considering that the prospective MBA student decided against leaving the job, in order to attend the business school.

So she continued with the job. NPV, in this case, is calculated using the below details,

Present Salary = $45,000

Increase = 12% per year

Cash Flows are below,

C₀ = $45,000

C₁ = $50,400

C₂ = $56,448

C₃ = $ 63,221.76

C₄  = $ 70,808.37

C₅ = $ 79305.38

C₆ = $88822.02

C₇ = $ 99480.66

C₈ = $ 111418.34

C₉ = $ 124788.54

Discount Rate = 12%

Time Horizon = 10 Years

Using the below formula, we calculate NPV

NPV = C₀ + C₁ /(1+d) + C₂/(1+d)² +... + C₉/(1+d)⁹

NPV = 45000 + {(45000*1.12)/(1+0.12)} + {(45000*1.12²)/(1+0.12)² + ... + {(45000*1.12⁹) / (1+0.12)⁹}

NPV = $ 450,000

CHOICE 2

Considering that the prospective student left the job at the beginning of next year and took admission in the business school.

Now the NPV of the this choice would be calculated based on the following details,

Cash Flows for the 10 years are

C₀ = $45,000 (Salary Received)

C₁ = -$40,000 (Fee paid to the business school for the 1st year)

C₂ = -$40,000 (Fee paid to the business school for the 2nd year)

C₃ = $125,000 (Salary at New Job)

C₄ = (125,000 *1.16) = $ 145,000 (16% increase every year)

Further 16% increase every year gives,

C₅ = $ 168,200

C₆ = $195,112

C₇ = $ 226,329.92

C₈ = $ 262542.71

C₉ = $ 304549.54

Discount Rate = 12%

So, using the below formula, we calculate the NPV

NPV = C₀ + C₁ /(1+d) + C₂/(1+d)² +... + C₉/(1+d)⁹

NPV = 45000 + {-40000 / (1+0.12)} + {-40000 / (1+0.12)^2} + {125,000 / (1+0.12)^3} + { 145,000 / (1+0.12)^4} + ... + {304549.54 / (1+0.12)^9}

= $ 671051.99

Rounded to nearest integer, NPV = $ 671,052

So, the more attractive choice for the student is CHOICE 2. NPV for the choice is $ 671,052