Assume that Time $0($present$)$ is Year $2015.$ Natasha Kingery is $30$ years old and has a Bachelor of Science degree in computer science. She is currently employed as a Tier $2$ field service representative for a telephony corporation located in Seattle, Washington, and earns $$38,000$ a year that she anticipates will grow at $3\mathrm{.}5\%$ per year. Natasha hopes to retire at age $60$ and has just begun to think about the future.

Natasha has an apartment that she recently inherited from her aunt. She is considering whether she should further her education and would use her inheritance to pay for it$.$ She has investigated a couple of options and is asking for your help as a financial planning intern to determine the financial consequences associated with each option. Natasha has already been accepted to two programs and could start either one soon $($i$.$e$.,$ from Time $1).$

One alternative that Natasha is considering is attaining a certification in network design. This certification would automatically promote her to a Tier $3$ field service representative in her company. The base salary for a Tier $3$ representative is $$4,000$ more than the salary of a Tier $2$ representative, and she anticipates that this salary differential will grow at a rate of $3\mathrm{.}5\%$ a year for as long as she remains employed. The certification program requires the completion of $20$ Web$-$based courses and a score of $80\%$ or better on the final exam. She has learned that the average amount of time necessary to finish the program is one year. The total cost of the program is $$5000,$ due when she enrolls in the program $($i$.$e$.,$ paid at Time $0).$ Because she will do all the work for the certification on her own time, Natasha does not expect to lose any income during the certification process.

Another option is going back to school for an MBA degree. With an MBA degree, Natasha expects to be promoted to a managerial position in her current firm. The managerial position pays $$8,000$ a year more than her current position. She expects that this salary differential will also grow at a rate of $3\mathrm{.}5\%$ per year for as long as she keeps working. The evening program, which will take three years to complete, costs $$20,000$ per year, due at the beginning of each of her three years in school $($i$.$e$.,$ paid at Time $0,$ Time $1,$ and Time $2).$ Because she will attend classes in the evening, Natasha doesn$$t expect to lose any income while she is earning her MBA if she chooses to undertake it$.$

Use $2\%$ interest rate as the discount rate for the remainder of this problem.

$1.$ Draw a timeline for Natasha$$s alternatives: $(1-1)$ the certification program $(1\mathrm{.}5$ Points$)$ and $(1-2)$ MBA degree options, using the following assumptions:

A$.$ Salaries for the year are paid only once, at the end of the year.

B$.$ The salary increase becomes effective immediately upon graduating from the MBA program or being certified. That is$,$ because the increases become effective immediately but salaries are paid at the end of the year, the first salary increase will be paid exactly one year after graduation or certification.

$2.$ Calculate the present value of the salary differential for completing the certification program. Subtract the cost of the program to get the value of undertaking the certification program. Determine the value of undertaking the certification program. Show and clearly write the formula and your calculation process.

$3.$ Calculate the present value of the salary differential for completing the MBA degree. Calculate the present value of the cost of the MBA program. Based on your calculations, determine the value of undertaking the MBA. Show and clearly write the formula and your calculation process.

$4.$ Based on your answers to Questions $2$ and $3,$ what advice would you give to Natasha?