The Pimco New York Municipal Bond Fund (PNF) and the Fidelity Spartan Mass Fund

Question

The Pimco New York Municipal Bond Fund (PNF) and the Fidelity Spartan Mass Fund (FDMMX) are tax-exempt municipal bond funds. In 2003, the Pimco fund yielded 8% while the Fidelity fund yielded 6%. You would like to invest a total of up to $90,000 and earn at least $6,600 in interest in the coming year (based on the given yields). Draw the feasible region that shows how much money you can invest in each fund. (Place PNF on the x-axis and FDMMX on the y-axis.)

Find the corner points of the region. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.)

Explanation / Answer

Note that 6% * $90,000 < $6,600, but 8 % * $90,000 > $6,600. This means that you can invest up to $90,000 in Pimco, the fund giving more interest, but you will have to invest at least a certain amount in Pimco in order to guarantee $6,600 in interest. If you are investing $90,000, you can figure the minimum amount that you invest in Pimco by solving the following. If we let the amount invested in Pimco in x, then the amount invested in Fidelity will be 90000 - x. .08 x + .06 (90000 - x) = 6600. .02 x + 5400 = 6600. .02x = 1200. x = 50 * 1200. x = 60000. y = 30000. If we only invested in Fidelity, in order to get 6600 in interest, .08 x = 6600 x = 12.5 * 6600 x = 82500. Thus, the feasible investment region will be, at a minimum, the line segment from (60000,30000) to (82500,0). This is the line that generates the minimum required return of 6600. x + 3/4 y = 82500, or y = 110000 - 4/3 x, on this line. If you would like, you can plug x and y from this line into the equation .08x + .06y and verify that the return is 6600. The maximum will be the line segment from (60000,30000) to (90000,0). This is the maximum investment amount line where the return is at least equal to the minimum. (x + y = 90000, or y = 90000 - x, on this line) These 3 points define the feasible region. The feasible region is the area inside and on the triangle.

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