Question

Assume today is March 16, 2016. 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% per year. Natasha hopes to retire at age 65 and has just begun to think about the future.

Natasha has $75,000 that she recently inherited from her aunt. She invested this money in 30-year Treasury Bonds. 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 both of these programs, and could start either one soon.

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 $10,000 more than what she currently earns and she anticipates that this salary differential will grow at a rate of 3% a year as long as she keeps working. The certification program requires the completion of 20 Web-based courses and a score of 80% or better on an test at the end of the course work. 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. 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.

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 $20,000 a year more than her current position. She expects that this salary differential will also grow at a rate of 3% per year for as long as she keeps working. The evening program, which will take three years to complete, costs $25,000 per year, due at the beginning of each of her three years in school. 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 the MBA.

**Use a discount rate of 3.71%**

**I have already completed #1,2,3,4. I really need
help understanding how to approach #5**

1. Create a timeline in Excel for her current situation, as well as the certification program and MBA degree options, using the following assumptions: (1) salaries for the year are paid only once, at the end if the year and (2) 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 NPV of undertaking the certification
program.

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 NPV of undertaking the MBA.

4. Based on your answers to Questions 2 and 3, what advice would you give to Natasha? What if the two programs are mutually exclusive? That is, if Natasha undertakes one of the programs there is no further benefit to undertaking the other program. Would your advice be different?

5. In addition, do a sensitivity analysis of your conclusions. Specifically:

(a) The growth rate of the salary differential is assumed to be the same for both certification and an MBA. Find the growth rate (for either choice) that makes her indifferent between the two choices.

(b) At what age would Natasha be indifferent between the two choices?

(c) At what discount rate would Natasha be indifferent between the two choices?

Answer #1

To provide a base for subpart 5, it is important to understand the base from subpart 2 to subpart 4.

**Subpart 2).**
**The present** **value of salary differential
for completing the certification.**

The discount rate is given to be 3.71%. A critical assumption would be that she will work until her retirement age at 65 years.

The salary will grow at a rate of 3 % as long as she remains employed, so we are going to compound the salary differential of 10,000 from the time she completes her certification to her age of retirement. We will use 34 as the number of the periods until the age of retirement because it takes 1 year to complete the program.

The Future value of Annuity is given as follows:

FV of annuity = P
[(1+r)^{n}−1]/r

where

P = Principal = $ 10,000

R = rate = 3%

n = number of periods = 34 years

A = 10,000 ((1 + 0.03)^34 -1)/0.03)

A = 577,301.77

We will discount the future value of annuity $ 577,301.77 to present value at year 0, i.e., when the initial investment amount is paid at year 0. The initial investment is the amount she pays for the program.

Discounting Amount

PV = $ 282,876.75

The net present value of undertaking certification

Net Present Value = PV - Cost of program

Net Present Value = $ 282,876.75 - $ 5,000

Net Present Value = $ 277,876.75

**Subpart 3) Present value for
salary differential for completing MBA**

The salary will grow at a rate of 3 % as long as she remains employed, so we are going to compound the salary differential of 10,000 from the time she completes her certification to her age of retirement. We will use 32 as the number of the periods until the age of retirement because it takes 3 years to complete the program.

The Future value of Annuity is given as follows:

FV of annuity = P
[(1+r)^{n}−1]/r

where

P = Principal = $ 20,000

R = rate = 3%

n = number of periods = 32 years

A = 10,000 ((1 + 0.03)^32 -1)/0.03)

A = 1,050,055.17

We will discount the future value of annuity $ 1,050,055.17 to present value at year 0, i.e., when the initial investment amount is paid at year 0. The initial investment is the amount she pays for the program.

Discounting Amount

PV = $ 498,342.38

PV of Cost of MBA program = $ 72,349.03 (discounting $ 25,000 for 3 years)

The net present value of undertaking certification

Net Present Value = PV – PV of Cost of MBA program

Net Present Value = $ 498,342.38 - $ 72,349.03

Net Present Value = $ 425,993.35

**Now coming to Subpart
5(a)**

We have seen that the growth in salary is a factor that determines the Net Present Value of both scenarios. Hence, If

(a) The growth of salary in case of certification is higher than growth of salary due to MBA (3%), then Natasha would be indifferent between the two options. (OR)

(b) The growth of salary in case of MBA is lower than growth of salary due to certification (3%), then Natasha would be indifferent between the two options.

Now in order to find out the required growth rate, we must equate the two NPV’s

(A) To find out required growth rate for certification

Required NPV = NPV of MBA opportunity

Required NPV = $ 425,993.35

PV - Cost of certificate program = $ 425,993.35

Required PV = $ 425,993.35 + $ 5000

Required PV = $ 430,993.35

For any calculation which involves the number of periods greater than 5, the rate ‘r’ can be found only by trial and error. However, the solver add-in in Excel easily allows us to find the required growth rate.

Growth Rate required = 5.58%

Now we can cross verify the answer by recalculating FV using the steps given in Subpart 2.

Similarly B) To find out growth rate for MBA course

Required NPV = NPV of Certification opportunity

Required NPV = $ 277,876.75

PV – PV of Cost of MBA program = $ 277,876.75

Required PV = $ 277,876.75 + $ 72,349.03

Required PV = $ 350,225.78

For any calculation which involves the number of periods greater than 5, the rate ‘r’ can be found only by trial and error. However, the solver add-in in Excel easily allows us to find the required growth rate.

Growth Rate required = 0.41%

Now we can cross verify the answer by recalculating FV using the steps given in Subpart 3.

**Subpart 5(b)**

This question asks that keeping the growth differentials and cost constant, we need to solve for Natasha’s age such that we get the same NPV in both the scenarios

Using the GRG Non-Linear in Solver add-in and keeping the NPV difference as close to zero as possible, we arrive at an age of 51 as the indifference age.

The NPV in both the case is approximately $ 111,000 with a difference of $ 442 (ignorable)

**Subpart 5(c)**

Using the same technique to solve for discount rate keeping growth rate and age constant with similar assumptions.

We arrive at a discounting rate of 10.95% to arrive at an indifferent NPV of $ 99,370.

All the answers can be cross verified using the traditional techniques.

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