Question

The following three defense stocks are to be combined into a stock index in January 2013 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance): Suppose that Douglas McDonnell shareholders approve a 2-for-1 stock split on January 1, 2014.

             

	Price
	Shares (millions)		1/1/13			1/1/14			1/1/15
Douglas McDonnell	420		$	63		$	67		$	84
Dynamics General	450			53			47			61
International Rockwell	250			82			71			87

            

a.	What is the new divisor for the index? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

  

New divisor

  

b.	Calculate the rate of return on the index for the year ending December 31, 2014, if Douglas McDonnell’s share price on January 1, 2015, is $24.36 per share. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

   

Rate of return

%

Answer 1

a)

Given Douglas McDonnell’s share price = $67

Given 2-for-1 stock split

Share price after the stock split is $67/2 = $33.5

On January 1, 2014 Index value without split = (67 + 47 + 71) / 3 = 185/3 = 61.666....

Index value on 1/1/14 without the split is 61.667.

Let new divisor be d

(33.5 + 47 + 71) / d = 185/3

d = 151.5/ (185/3) = 2.4567 = 2.457 (rounded off to three decimal places)

New divisor = 2.457

b)

Given Douglas McDonnell’s share price on January 1, 2015 = $24.36 per share

On January 1, 2015 Index value = (24.36 + 61 + 87) / 2.457

= 70.151

Rate of return = (2015 index value – 2014 index value) / 2014 index value

Rate of return = (70.151- 61.667)/ 61.667 = 0.13757 = 13.76 %