Question

The following three defense stocks are to be combined into a price-weighted stock index in January 2016 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance): Suppose that Douglas McDonnell shareholders approve a 3-for-1 stock split on January 1, 2017 and that the company enacts the stock split on January 2, 2017.

Price

Shares (millions) 1/1/16 1/1/17 1/1/18
Douglas McDonnell 430 $108 $114 $41.08
Dynamics General 535 38 34 48
International Rockwell 210 67 56 70

a. What is the new divisor for the index?
b. Calculate the rate of return on the index for the year of 2017.

Answer 1

Answer:

24.42%

Explanation:

(a) Index on the day immediately before the split (on 1 Jan 2017)

= (114+ 34 + 56 ) / 3

= 204/3 =68

Price of Douglas McDonnel stock just after the split (on 2 Jan 2017)

= 114/3 = $38

New divisor for the index

= (38 + 34 + 56)/68

= 128/68

=1.88

(b) Index on 1 Jan 2017 = 68

Index on 1 Jan 2018 = (41.08+ 48+ 70) / 1.88

= 159.08/1.88

=84.61

Hence:

Rate of return on the index for the year

2017

= (84.61 - 68) / 68 × 100

16.61/68×100

= 24.42%