Question

During the first quarter of 2015, Toronto Dominion Bank (TD) stock cost $45 per share, was expected to yield 4% per year in dividends, and had a risk index of 3.0 per share, while CNA Financial Corp. (CNA) stock cost $40 per share, was expected to yield 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to $25,000 to invest in these stocks, and would like to earn at least $778 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) 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?

Toronto Dominion Bank  shares:

CNA Financial Corp.  shares:

What is the minimum total risk index? (Round your answer to two decimal places.)

Answer 1

Answer:

Given that,

During the first quarter of 2015, Toronto Dominion Bank (TD) stock cost $45 per share, was expected to yield 4% per year in dividends, and had a risk index of 3.0 per share,

While CNA Financial Corp. (CNA) stock cost $40 per share, was expected to yield 2.5% per year in dividends, and had a risk index of 2.0 per share.

You have up to $25,000 to invest in these stocks, and would like to earn at least $778 in dividends over the course of a year.

TD:

Dividend per stock = 4% 45

=0.04 45

= 1.8

Return/risk :

= 1.8/3

= 0.6

CNA:

Dividend per stock = 2.5%45

=0.025 45

= 1.125

Return/risk:

= 1.125/3

= 0.375

As Return/Risk is better for TD, it will be preferred

Dividend required:

No. of shares of TD = 778/1.8

= 432.22

Investment:

No. of shares of TD = 25000/45 = 555.56 (as it is >432.22, requirement met within the total investment)

Total number of shares = 432.22 (as each additional share will increase risk)

Total risk index = 3432.22

= 1296.66