Question

3. Following is the stock price for three stocks for time 0 and time 1. Time 0 Time 1 #Shares 50 100 80 Stock A splits 2-for-1 between time 0 and 1 Stock Stock Price Price # Shares $55 $100 $60 A $30 $115 $40 A 100 B 100 80 C C What is the value of a price weighted index including all three stocks at time 0? (3 points) a) b) What is the new divisor for a price-weighted index after stock A's 2-for-l split? (4 points) c) What is the value of a price weighted index at time 1? (4 points)

Answer 1

a) Value of price weighted index = [55*55/215]+[100*100/215]+[60*60/215] = 77.33

b) The new divisor for a price weighted index after stock split is = 30+115+40 = 185

c) value of price weighted index at time 1 = [30*30/185]+[115*115/185]+[40*40/185] = 85

d) Rate of return for time 1 = (85-77.33)/77.33 = 9.92%

e)

RA - Excel (Product Activation failed) File Insert Page Layout Formulas Data Review View Tell me what you want to do... Home % Cut Calibri General Be Copy -A À === - A- 333 Paste - 11 BIU - - Font Din Wrap Text 3 Merge & Center - Alignment Format Painter Clipboard $ - %, Number 14 F m A B C D E 1 Calculation of value weighted index TIME 1 3 Price($) Number Market cap Weights Market cap* weights 100 3000 0.17 508.47 115 11500 0.65 7471.75 40 80 32000.18 578.53 17700 8558.76 30 + 100 0 0 0 11 50 2750 TIME O 10 Price(s) Number Market cap Weights Market cap*weights 55 0.16 427.26 12 100 100 10000 0.56 5649.72 13 60 80 4800 0.27 1301.69 17550 7378.67 Sheets Sheet1 14 Ready 1 Search the web and Windows o e е x

So return = (8558.76-7378.67)/7378.67 = 16%

f) After stock split as market cap is in value weighted index. Hence value is increased and rate of return increased from 9.92% to 16%.