# Bill the Spender

**Topics:**Investment, Net present value, Time value of money

**Pages:**5 (1231 words)

**Published:**March 7, 2013

Each student must turn in any two of the four cases.

The due date for each case is different. For whichever cases you select, submit your answers on paper (an Excel printout is fine) by the due date. Also be prepared to explain your answer to the case for the class on the evening of the due date (after the lecture). Bring your Excel file to class on a flash drive or laptop.

Case 1 – Time Value of Money

Due Date: 2/13/2013

There are two people: Joe Spender and Bill Saver. Both have just turned 24 years old. Neither has any savings.

Both have just finished college and are starting their first job, making $41,000 each. For simplicity, assume their salaries remain the same throughout their careers. Also assume that there are no taxes.

Both will retire at age 68, at the end of the year, and both will earn 6.25% annually (at the end of each year) on their investments (i.e., savings).

Joe saves nothing every year. That is, he spends all of his income.

Bill saves and invests 3/8 of his income every year. Income is defined as salary + earnings on investments. Assume that he invests at the end of each year (no interest is earned in the first year working).

By the time they retire, which person will have spent more?

At what age are they spending the same amount annually (round your answer)?

At what age will they have spent the same amount cumulatively (round your answer)?

How much does each have in the account at retirement?

Case 2 – Portfolio Theory

Due Date 3/6/2013

You are a financial advisor. The following clients come to you for advice:

Josephine

Josephine has just landed her first job out of graduate school. She is working for one of the Big Four, earning $50,000 per year. She expects her salary to increase by 3% each year. Josephine has a goal of retiring after 36 years and then traveling the world in retirement for 20 years. Once she retires she will move all of her assets into Treasury Bonds earning 2%. Josephine would pay for her post retirement lifestyle by drawing $90,000 each year from her 401K. She will contribute 15% of her salary to the 401K each year. Her 401K offers her the choice of low-risk bonds yielding 4% a year indefinitely and a stock portfolio that is considerably more risky, but expected to yield 8% per year on average.

Design a long-term portfolio, with appropriate weighting between bonds and stocks, for Josephine that will achieve her goal of allowing her to draw $90,000 a year from her 401K each year for 20 years beginning 36 years from now. You should construct a portfolio that would produce an “expected outcome” that gives her just what she needs (i.e., $90,000 a year for 20 years with nothing left at the end) with the minimum degree of risk possible. For simplicity, assume that whatever portfolio you develop for her would be the same portfolio for the 36 pre-retirement years.

What is the minimum rate of return that she would require? You can use a trial-and-error approach or use Excel’s Goal-Seek function. What proportion of her portfolio should be in low-risk bonds and what proportion should be in stocks?

Jim

Jim has a tax deferred annuity (401k) currently valued at $250,000. At the moment, his 401k is invested in just two stocks: He is 10% invested in Microsoft (MSFT), and 90% invested in McDonald’s (MCD).

Jim has calculated the beta of both stocks (relative to the S&P 500), the standard deviation of both stocks, and the correlation of the returns of the two stocks. He has also checked the risk-free rate and he has estimated the return on the S&P 500. His estimates are below.

Stock Beta Standard Deviation MSFT 1.4 69% MCD 1.0 40%

Correlation (MSFT, MCD) = 0.0450

Risk-free rate = 2%

Expected...

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