Pension Funds A pension fund has decided to invest $50,000 in the four high-yield stocks

Chapter 5, Problem 21

(choose chapter or problem)

Pension Funds A pension fund has decided to invest $50,000 in the four high-yield stocks listed in the table below. Price Price/ per share Earnings Stock 4-12-10 Yield Ratio Duke Energy Corp. $16.26 5.90% 19.79 H. J. Heinz $45.99 3.65% 16.33 General Electric Co. $18.71 2.14% 18.23 Ferrellgas Partners LP $23.14 8.64% 37.78 Source: TD Ameritrade. The pension fund has decided to invest at least 10% of the $50,000 in the H. J. Heinz stock and at least 20% in each of the other three stocks. Further, it has decided that at most 50% of the $50,000 can be invested in the Duke Energy Corp. and the General Electric Co. combined. Determine how many shares of each stock should be purchased in order to minimize the average price/earnings ratio of the stocks purchased, while conforming to the above requirements. Note that to minimize the average price/earnings ratio of the stocks purchased, it is sufficient to minimize the sum of the four products obtained by multiplying the price/earnings ratio for each stock and the amount invested in that stock. What is the average price/earnings ratio (rounded to the nearest hundredth) for the optimal investment plan? What is the annual yield in dollars for the optimal investment plan? Assume that it is possible to purchase a fraction of a share.