Question

Problem 24-6

XYZ stock price and dividend history are as follows:

  

Year	Beginning-of-Year Price				Dividend Paid at Year-End
2013	$	100			$	4
2014		120				4
2015		90				4
2016		100				4

  

An investor buys three shares of XYZ at the beginning of 2013, buys another two shares at the beginning of 2014, sells one share at the beginning of 2015, and sells all four remaining shares at the beginning of 2016.

  

  

b.

What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the fourdates corresponding to the turns of the year for January 1, 2013, to January 1, 2016. If your calculator cannot calculate internal rate of return, you will have to use trial and error.) (Round your answers to 4 decimal places. Negative amount should be indicated by a minus sign. Omit the "%" sign in your response.)

  

Dollar-weighted rate of return

%

Answer 1

At t = 0 ( i.e beginning of 2013) ......... relavant cashflows = 3 shares * 100 = - 300

At t = 1 ( i.e beginning of 2014) ......... relavant cashflows = 2 shares * 100 + dividend on 3 shares * 4

= - 200 + 12 = - 188 Net cash outflow

At t= 2 ( i.e beginning of 2015 )... sold one share and received dividend on 5 shares = 90 + 5 *4 = 110

At t= 3 ( i.e beginning of 2016) ... sold all the FOUR shares = 4 * 100 + 4 * 4 = 416

Year	CF	DF	PF
0	-300	1	-300
1	-188	0.970874	-182.524
2	110	0.942596	103.6856
3	416	0.915142	380.6989
IRR	= 3%		1.860208

In the above table a value of 1.86 is negligible. Hence at 3% discount rate we have NPV = 0

Thus Dollar - weighted rate of return = 3 %