Consider John. He is trying to decide whether or not to enter a full$-$time MBA program. Currently, he works for IBM as a systems analyst earning $$80,000$ per year. With an MBA he could transfer to IBM's finance division, starting at $$120,000$ per year. His wage increases as an analyst would just be at cost$-$of$-$living and would be $4\%$ per year. His wage increases in the finance division would be $8\%$ per year. The MBA is a two$-$year program and costs $$15,000$ per year. John's time horizon is $6$ years. $($Assume for simplicity that expenses are due at the start of a year, but earnings flow in at the end of a year.$)$

a$.$ Draw an age$-$earnings profile for John to represent these two alternatives.

b$.$ If the market interest rate is $5\%,$ what decision would you recommend for John based on Net Present Value calculations? Show your work and your calculations.

c$.$ How would your answer to $($b$)$ change if the appropriate interest rate is $10\%?$ If the appropriate interest rate is $2\%?$ Explain. Recalculate the value of each investment at $10\%$ and then $2\%,$ and compare your numbers.

d$.$ What other factors would be important for John to consider as he makes this decision? Explain.