Assume that Carolyn places currently available funds in the savings account. Determine the amount of money Carolyn will have available at retirement once she sells her house if she retires at (1) age 62 and (2) age 65.

Carolyn Bowen, who just turned 55, is employed as an administrative assistant for the Xcon Corporation, where she has worked for the past 20 years. She is in good health, lives alone, and has two grown children. A few months ago her husband died, leaving her with only their home and the proceeds from a $75,000 life insurance policy. After she paid medical and funeral expenses, $60,000 of the life insurance proceeds remained. In addition to the life insurance proceeds, Carolyn has $37,500 in a savings account, which she had accumulated over the past 10 years. Recognizing that she is within 10 years of retirement, Carolyn wishes to invest her limited resources so she will be able to live comfortably once she retires.

Carolyn is quite superstitious. After consulting with a number of psychics and studying her family tree, she is certain she will not live past 80. She plans to retire at either 62 or 65, whichever will allow her to meet her long-run financial goals. After talking with a number of knowledgeable individuals—including, of course, the psychics—Carolyn estimates that to live comfortably in retirement, she will need $45,000 per year before taxes. This amount will be required annually for 18 years if she retires at 62 or for 15 years if she retires at 65. As part of her financial plan, Carolyn intends to sell her home at retirement and rent an apartment. She has estimated that she will net $112,500 if she sells the house when she is 62 and $127,500 if she sells it when she is 65. Carolyn has no financial dependents and is not concerned about leaving a sizable estate to her heirs.

If Carolyn retires at age 62, she will receive from Social Security and an employer-sponsored pension plan a total of $1,359 per month ($16,308 annually); if she waits until age 65 to retire, her total retirement income will be $1,688 per month ($20,256 annually). For convenience, Carolyn has already decided to convert all her assets at the time of retirement into a stream of annual income and she will at that time purchase an annuity by paying a single premium. The annuity will have a life just equal to the number of years remaining until her 80th birthday. If Carolyn retires at age 62 and buys an annuity at that time, for each $1,000 that she puts into the annuity she will receive an annual benefit equal to $79 for the subsequent 18 years. If she waits until age 65 to retire, each $1,000 invested in the annuity will produce an annual benefit of $89.94 for the 15 years.

Carolyn plans to place any funds currently available into a savings account paying 6% compounded annually until retirement. She does not expect to be able to save or invest any additional funds between now and retirement. For every dollar that Carolyn invests today, she will have $1.50 by age 62; if she leaves the money invested until age 65, she will have $1.79 for each dollar invested today.


a.       Assume that Carolyn places currently available funds in the savings account. Determine the amount of money Carolyn will have available at retirement once she sells her house if she retires at (1) age 62 and (2) age 65.

b.      Using the results from item a, determine the level of annual income that will be provided to Carolyn through purchase of an annuity at (1) age 62 and (2) age 65.

c.       With the results found in the preceding questions, determine the total annual retirement income Carolyn will have if she retires at (1) age 62 and (2) age 65.

d.      From your findings, do you think Carolyn will be able to achieve her long-run financial goal by retiring at (1) age 62 or (2) age 65? Explain.

e.       Evaluate Carolyn’s investment plan in terms of her use of a savings account and an annuity rather than other investments. Comment on the risk and return characteristics of her plan. What recommendations might you offer Carolyn? Be specific.






Case Problem 2.1 Dara’s Dilemma: What to Buy?

Dara Simmons, a 40-year-old financial analyst and divorced mother of two teenage children, considers herself a savvy investor. She has increased her investment portfolio considerably over the past five years. Although she has been fairly conservative with her investments, she now feels more confident in her investment knowledge and would like to branch out into some new areas that could bring higher returns. She has between $20,000 and $25,000 to invest.

Attracted to the hot market for technology stocks, Dara was interested in purchasing a tech IPO stock and identified, a company that makes sophisticated computer chips for wireless Internet connections, as a likely prospect. The 1-year-old company had received some favorable press when it got early-stage financing and again when its chip was accepted by a major cell phone manufacturer.


Dara also was considering an investment in 400 shares of Casinos International common stock, currently selling for $54 per share. After a discussion with a friend who is an economist with a major commercial bank, Dara believes that the long-running bull market is due to cool off and that economic activity will slow down. With the aid of her stockbroker, Dara researches Casinos International’s current financial situation and finds that the future success of the company may hinge on the outcome of pending court proceedings on the firm’s application to open a new floating casino on a nearby river. If the permit is granted, it seems likely that the firm’s stock will experience a rapid increase in value, regardless of economic conditions. On the other hand, if the company fails to get the permit, the falling stock price will make it a good candidate for a short sale.

Dara felt that the following alternatives were open to her:

·         Alternative 1: Invest $20,000 in when it goes public.

·         Alternative 2: Buy Casinos International now at $54 per share and follow the company closely.

·         Alternative 3: Sell Casinos short at $54 in anticipation that the company’s fortunes will change for the worse.

·         Alternative 4: Wait to see what happens with the casino permit and then decide whether to buy or short sell the Casinos International stock.


a.       Evaluate each of these alternatives. On the basis of the limited information presented, recommend the one you feel is best.

b.      If Casinos International’s stock price rises to $60, what will happen under alternatives 2 and 3? Evaluate the pros and cons of these outcomes.

c.       If the stock price drops to $45, what will happen under alternatives 2 and 3? Evaluate the pros and cons of these outcomes.


Case Problem 2.2 Ravi Dumar’s High-Flying Margin Account

Ravi Dumar is a stockbroker who lives with his wife, Sasha, and their five children in Milwaukee, Wisconsin. Ravi firmly believes that the only way to make money in the market is to follow an aggressive investment posture—for example, to use margin trading. In fact, Ravi has built himself a substantial margin account over the years. He currently holds $75,000 worth of stock in his margin account, though the debit balance in the account amounts to only $30,000. Recently Ravi uncovered a stock that, on the basis of extensive analysis, he feels is about to take off. The stock, Running Shoes (RS), currently trades at $20 per share. Ravi feels it should soar to at least $50 within a year. RS pays no dividends, the prevailing initial margin requirement is 50%, and margin loans are now carrying an annual interest charge of 10%. Because Ravi feels so strongly about RS, he wants to do some pyramiding by using his margin account to purchase 1,000 shares of the stock.


a.       Discuss the concept of pyramiding as it applies to this investment situation.

b.      What is the present margin position (in percent) of Ravi’s account?

c.       Ravi buys the 1,000 shares of RS through his margin account (bear in mind that this is a $20,000 transaction).

1.      What will the margin position of the account be after the RS transaction if Ravi follows the prevailing initial margin (50%) and uses $10,000 of his money to buy the stock?

2.      What if he uses only $2,500 equity and obtains a margin loan for the balance ($17,500)?

3.      How do you explain the fact that the stock can be purchased with only 12.5% margin when the prevailing initial margin requirement is 50%?

d.      Assume that Ravi buys 1,000 shares of RS stock at $20 per share with a minimum cash investment of $2,500 and that the stock does take off and its price rises to $40 per share in one year.

1.      What is the return on invested capital for this transaction?

2.      What return would Ravi have earned if he had bought the stock without margin—that is, if he had used all his own money?

e.       What do you think of Ravi’s idea to pyramid? What are the risks and rewards of this strategy?