CASE PROBLEM: Arrow Consulting

Will you be able to retire when you want? What will your retirement account be worth when you plan to retire? How much of your salary should you invest now and over time to reach your targeted account value? The Human Resources Department at Arrow Consulting was asked to develop a financial planning model that would help employees address these questions. Kieran Gosby was asked to lead this effort and decided to begin by developing a financial plan for himself. Kieran has a degree in business analytics and, at the age of $40,$ is making $$85,150$ per year. Through contributions to his company's retirement program and the receipt of a small inheritance, Keiren has accumulated a portfolio with a current value of $$55,000.$ Keiren plans to work $20$ more years and hopes to accumulate a portfolio valued at $$1,000,000.$ Can he do it$?$

Kieran began with a few assumptions about his future salary, his new investment contributions, and his portfolio growth rate. He assumed a $5\%$ annual salary growth rate and plans to make new investment contributions at $6\%$ of his salary. After some research on historical stock market performance, Kieran decided that a $10\%$ annual portfolio growth rate was reasonable. Using these assumptions, Kieran developed an Excel worksheet that provides a financial projection for the next five years. In computing the portfolio earnings for a given year, Kieran assumed that his new investment contribution would occur evenly throughout the year, and thus half of the new investment could be included in the computation of the portfolio earning for the year. From the worksheet, we see that, at age $45,$ Kieran is projected to have a portfolio valued at $$124,437.$

Arrow Consulting

Age $40$

Current Salary $$85,150$

Current Portfolio $$55,000$

Annual Investment Rate $6\mathrm{.}00\%$

Salary Growth Rate $5\%$

Portfolio Growth Rate $10\%$

Year Beginning Balance Salary New Investment Earnings Ending Balance Age

$1$ $$55,000$ $$85,150$ $$5,109$ $$5,755$ $$65,86441$

$2$ $$65,864$ $$89,408$ $$5,364$ $$6,855$ $$78,08442$

$3$ $$78,084$ $$93,878$ $$5,633$ $$8,090$ $$91,80643$

$4$ $$91,806$ $$98,572$ $$5,914$ $$9,476$ $$107,19744$

$5$ $$107,197$ $$103,500$ $$6,210$ $$11,030$ $$124,43745$

Kieran$$s plan was to use this worksheet as a template to develop financial plans for the company$$s employees. The data in the spreadsheet would be tailored for each employee, and rows would be added to it to reflect the employee$$s planning horizon. After adding another $15$ rows to the worksheet, Kieran found the amount that he could expect to have in his portfolio after $20$ years. Kieran then took his results to show his boss, Eden Krystkowiak.

Although Eden was pleased with Kieran$$s progress, she voiced several criticisms. One of the criticisms was the assumption of a constant annual salary growth rate. She noted that most employees experience some variation in the annual salary growth rate from year to year. In addition, she pointed out that the constant annual portfolio growth rate was unrealistic and that the actual growth rate would vary considerably from year to year. She further suggested that a simulation model for the portfolio projection might allow Kieren to account for the annual random variability in the salary growth rate and the portfolio growth rate.

After some research, Kieran and Eden decided to assume that the annual salary growth rate would vary from $0\%$ to $5\mathrm{.}1\%$ and that a uniform probability distribution would provide a realistic approximation. Arrow Consulting's accountant suggested that the annual portfolio growth rate could be approximated by a normal probability distribution with a mean $9\mathrm{.}85\%$ and a standard deviation of $4\mathrm{.}9\%.$ With this information, Kieren set off to redesign his spreadsheet so that it could be used by the company$$s employees for financial planning.

Help me set up an excel spreadsheet to get the answers.