Question 1: Incremental IRR & ERR

Data from the 2016 census shows that the salary benefits from graduate degrees in Engineering are surprisingly low. Statistics Canada found that a Masters Degree in Engineering increased income by 0.7% (for men) and 0.4% (for women), relative to a Bachelors degree. A doctorate in Engineering increased income by 7.8% (for men) and 1.8% (for women) relative to a bachelors degree. In this question, you will determine whether it makes sense for Sam to spend two years to earn a Masters degree, or six years to earn a PhD, given that the average engineering tuition cost in Canada is $7,000 per year.

The Setup

Note: The companion spreadsheet automates this setup for you, in the sense that it takes your information and returns a table with the appropriate cash flows. The information below will be useful if you wish to use equations as part of your solution.

For this question, the setup is a bit different to how we thought of income in Project 2. As in previous projects, Sam mar is 2.45% per year, and they are going to spend three years finishing their bachelors degree in engineering, no matter what. However, they also have the option to spend $7,000 a year for two years to earn a Masters degree, or $7,000 a year for six years to earn a Masters degree, followed by a PhD.

Once Sam finishes their studies, they will start working as an engineer. If Sam completes a bachelors degree, their starting salary is equal to A, where A is your highest baseline salary from Project 1. This time, there is no signing bonus, and Sams salary increases each year at a rate equivalent to 10% every 14 months (about 8.51% per year), which according to Salary Explorer is the average increase in salary for engineers in Canada. Sam will work for a total of 40 years if earning a bachelors degree (from Year 3 to Year 42). For simplicity, we will assume Sam is paid their salary once a year.

If Sam goes for a Masters degree, they will pay $7,000 a year for the two years following the completion of their Bachelors degree. After that, they will receive income equal to (1+m) times what they would have earned, the same year, if they had only had a bachelors degree, where m is the bonus for having a Masters degree (0.7% for men, 0.4% for women). Sam will only work for 38 years if they earn a Masters degree (from Year 5 to Year 42). This means Sams starting salary in this case is equal to (1+m) times the Year 5 salary they would have earned with a bachelors degree: A x (1+8.51%)² x (1+m).

If Sam goes for a doctorate, they will pay $7,000 a year for the six years following the completion of their Bachelors degree (2 years for a Masters, then 4 for a PhD). After that, they will receive income equal to (1+p) times what they would have earned, the same year, if they had a bachelors degree, where p is the bonus for having a doctorate. Sam will only work for 34 years if they earn a doctorate (from Year 9 to Year 42).

1.a

Sam is non-binary. Suppose they receive the same salary benefits from graduate degrees as male Canadian engineers (0.7% higher income for a Masters degree, 7.8% higher income from a doctorate, relative to a bachelors degree).

Use an incremental IRR approach to determine Sams preferred project: stop at a bachelors degree, stop at a Masters degree, or earn a PhD. Show your work.

Note: You may use all numerical/spreadsheet methods, all analytical methods (though the problem may not be tractable), or a mix of numerical and analytical methods. In any case, you need to explain your process, as you are not being marked on your final answer, which may vary by student, but on how you obtained your final answer.

Hint: The companion spreadsheet will automatically create a table of the relevant cash flows for you. Even if you are taking a mostly analytical approach, you may find this useful for visualization.

Preferred Project: ______________________________

[Show your work]

1.b

Sam is non-binary. Suppose they receive the same salary benefits from graduate degrees as female Canadian engineers (0.4% higher income for a Masters degree, 1.8% higher income from a doctorate, relative to a bachelors degree).

Use an incremental IRR approach to determine Sams preferred project: stop at a bachelors degree, stop at a Masters degree, or earn a PhD. Show your work.

Note: You may use all numerical/spreadsheet methods, all analytical methods (though the problem may not be tractable), or a mix of numerical and analytical methods. In any case, you need to explain your process, as you are not being marked on your final answer, which may vary by student, but on how you obtained your final answer.

Hint: The companion spreadsheet will automatically create a table of the relevant cash flows for you. Even if you are taking a mostly analytical approach, you may find this useful for visualization.

Preferred Project: ______________________________

[Show your work]

1.c

As in part b., assume that Sam receives the same salary benefits from a Masters degree as Canadian female engineers. This time, if Sam goes for a Masters degree, they will also receive a $2,500 LOUD Scholarship in Year 2. LOUD Scholarships are given to Canadian LGBTQ+ post-secondary students.

As a result of this scholarship, the incremental cash flow between the Bachelors Degree and Masters Degree project now has two sign changes. Use an incremental approximate ERR method to determine whether Sam should stick to a Bachelors degree or go for a Masters degree.

Hint: Again, the companion spreadsheet will set up the cash flows for each project for you (but not the incremental flows). The incremental approximate ERR approach is the same as the incremental IRR approach, except you use an approximate ERR instead of an IRR.

Preferred Project: ______________________________

[Show your work]

1.d (2-mark bonus question)

Maintain the assumptions and approach (incremental approximate ERR) from 1.c. What is the minimum size of a scholarship in Year 2 that would convince Sam to go for a masters degree instead of stopping with a bachelors degree? Show your work.

Note: In some cases this value could be negative, if Sam would choose to go for a Masters degree even without a scholarship.

Minimum scholarship in Year 2: _______________________________

[Show your work]