Question

Your portfolio manager has suggested two high-yielding stocks: The Altria Group (MO) and Reynolds America (RAI). MO shares cost $50, yield 4.5% in dividends, and have a risk index of 2.0 per share. RAI shares cost $55, yield 5% in dividends, and have a risk index of 3.0 per share. You have up to $9,050 to invest and would like to earn at least $410 in dividends.
How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?

If no optimal solution exists enter no solution in each box.

Number of shares of MO = __________

Number of shares of RAI = __________

What is the minimum total risk index? $ __________

Answer 1

Answer:

Number of shares of MO = 8500

Number of shares of RAI = 550

The minimum total risk index $2.06

Explanation:

Let Investment in MO be "A"

Let Investment in RAI be "B"

A + B = 9050 ................................(1)

A(4.5%) + B(5%) = 410 .................(2)

From (1), A = 9050 - B,  Substitute for A in (2)

(9050-B)(4.5%) + 0.05B = 410

407.25 - 0.045B + 0.05B = 410

0.005B = 2.75

B = 550 = Number of shares of RAI

Substitute for "B" in (1)

A + 550 = 9050

A = 9050 - 550

A = 8500 = Number of shares of MO

                                    Shares Per Share Cost Value

Number of Share in MO  170                 50                  8500

Number of Share in RAI    10                 55                    550

                                                           Total                          9050

Total Risk Index  = 2*8500/9050 + 3*550/9050

Total Risk Index =  1.88 + 0.18

Total Risk Index = $2.06