a. Formulate a separable programming model to be used in the following parts.
b. What is the optimal investment strategy for Charles?
c. What is fundamentally wrong with the advice Charles got from the investment advisor at the bank?
d. Now that Charles is considering investing in the certificate of deposit, what is his optimal investment strategy?
e. What would his optimal investment strategy for the fifth, sixth, and seventh years have been if he had originally invested DM 50,000?
Charles Rosen relaxes in a plush, overstuffed recliner by the fire, enjoying the final vestiges of his week-long winter vacation.
As a financial analyst working for a large investment firm in Germany, Charles has very few occasions to enjoy these private moments since he is generally catching red-eye flights around the world to evaluate various investment opportunities.
Charles pats the loyal golden retriever lying at his feet and takes a swig of brandy, enjoying the warmth of the liquid.
He sighs and realizes that he must begin attending to his own financial matters while he still has the time during the holiday. He opens a folder placed conspicuously on the top of a large stack of papers. The folder contains information about an investment Charles made when he graduated from college four years ago.
Charles remembers his graduation day fondly. He obtained a degree in business administration and was full of investment ideas that were born while he had been daydreaming in his numerous finance classes. Charles maintained a well-paying job throughout college, and he was able to save a large portion of the college fund that his parents had invested for him.
Upon graduation, Charles decided that he should transfer the college funds to a more lucrative investment opportunity. Since he had signed on to work in Germany, he evaluated investment opportunities in that country. Ultimately, he decided to invest 30,000 German marks (DM) in so-called B bonds that would mature in seven years. Charles purchased the bonds just four years ago last week (in early January of what will be called the “first year” in this discussion). He considered the bonds an excellent investment opportunity since they offered high interest rates (see Table 1 ) that would rise over the subsequent seven years and because he could sell the bonds whenever he wanted after the first year. He calculated the amount that he would be paid if he sold bonds originally worth DM 100 on the last day of any of the seven years (see Table 2 ). The amount paid included the principal plus the interest. For example, if he sold bonds originally worth DM 100 on December 31 of the sixth year, he would be paid DM 163.51 (the principal is DM 100 and the interest is DM 63.51).
Charles did not sell any of the bonds during the first four years. Last year, however, the German federal government introduced a capital gains tax on interest income. The German government designated that the first DM 6,100 a single individual earns in interest per year would be tax-free. Any interest income beyond DM 6,100 would be taxed at a rate of 30 percent. For example, if Charles earned interest income of DM 10,100, he would be required to pay 30 percent of DM 4,000 (DM 10,100 – DM 6,100) in taxes, or DM 1,200. His after-tax income would therefore be DM 8,900.
Because of the new tax implemented last year, Charles has decided to reevaluate the investment. He knows that the new tax
Table 1: Interest Rates over the Seven Years
TABLE 2: Total Return on 100 DM
Year _______________ DM
1 ……………………… 107.50
2 ……………………… 116.64
3 ……………………… 126.55
4 ……………………… 137.62
5 ……………………… 150.01
6 ……………………… 163.51
7 ……………………… 178.23
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