Question

The following three defense stocks are to be combined into a 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.

		Price
	Shares (millions)		1/1/16			1/1/17			1/1/18
Douglas McDonnell	545		$	80		$	83		$	98
Dynamics General	460			70			63			77
International Rockwell	190			99			88			91

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

  

  
b. Calculate the rate of return on the index for the year ending December 31, 2017, if Douglas McDonnell’s share price on January 1, 2018, is $30.04 per share. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

a) What is the new divisor for the index?

01/01/2017: Index Value = (83 + 63+ 88)/3 = 78

Index value on 01/01/2017 without the split is 78

(27.66 + 63 + 88) / d = 78

d = 178.66 / 78

d = 2.29

b) Calculate the rate of return on the index for the year ending December 31, 2017 if Mcdonnell share price on January 1, 2018 is $30.04

01/01/18: Index value = ( 30.04 + 77 + 91 ) / 2.29 = 86.48

The index value in 2018 is 86.48

From this, the 2018 return = (86.48 – 78) / 78 = 10.87 %