Question

4. Paul is now 30 years old. He has a job that pays him $60,000/year. He plans to work until he is 60 years old. The wage increases at the rate of 2% p.a. The job is quite stable and he believes that the proper discount rate is 3% p.a. He currently has no investment and no debt.

   He is considering going back to school to get a master's degree. The program will take two full-time years (i.e., he will need to take two years off from work) and costs $70,000 up front. Assume that after he graduates, the wage growth rate and the interest rate are the same as above. What is the minimum starting level of salary that he will have to get in order for the degree to be worth it?

Answer 1

Th minimum starting salary can be calculated by equating the present values of 1) continuing with the same job 2) getting the master's degree

1)

Present value of continuing with the same job can be calculated using the formula for present value of a growing annuity

Where P = first payment = $60,000

r = discount rate = 3%

g = growth rate = 2%

n = number of periods

Here, n = number of working years = 60-30 = 30 years

PV = 6,000,000*0.2537430107 = $1,522,458.06 -------------------(1)

2)

Present value of getting the master's degree can be calculated by finding the present value of the growing annuity (new salary) after 2 years, discounting it back to the present and then reducing the degree cost from that

Let X be the new salary

Present value of the growing annuity after 2 years is given by the formula

Where P = first payment = $X

r = discount rate = 3%

g = growth rate = 2%

n = number of periods

Here, n = number of working years = 60-30-2 = 28 years

PV = X * 0.2390387928/0.01 = 23.903879X

This is PV₂, PV after 2 years

Present value of this discounted to the present

PV = PV₂ /(1+r)²

PV = 23.903879X / (1+3%)²

PV = 23.903879X / 1.0609 = 22.531699X

Net present value of getting the master's degree = PV - degree cost = 22.531699X - 70,000 ---------(2)

Equating (1) and (2)

22.531699X - 70,000 = $1,522,458.06

22.531699X = $1,522,458.06 + $70,000 = $1,592,458.06

X = $1,592,458.06 / 22.531699 = $70,676.34

Hence, the minimum starting level of salary should be $70,676.34