Question

Capital adjustments for a share are described below. The last sale price is immediately after the shares have gone “ex” the event described in the final column. For example, the price of $4.50 at the end of June is the share price ex-rights.

March	$4.50
April	$4.00	ex 1:10 bonus issue
May	$4.00	ex a dividend of 10 cents per share
June	$4.50	ex 1:5 rights issue at $3.00

Based on the information in the above table:

Calculate the monthly rate of returns (%), from holding the share over the one-month periods:

from the end of March to the end of April              

from the end of April to the end of May   

from the end of May to the end of June

Calculate the monthly geometric mean return (% per month) from the end of March to the end of June.  

Answer 1

Price at end of March = 4.5

Effective price at end of April after 1:10 bonus = 1.1*4 = $4.4

% return = (4.4-4.5)/4.5 = -0.0222 =-2.22%

Price at the aend of April = $4

Price at the end of May after dividend = $ 4.10

% return =(4.10-4)/4 = 0.025 =2.5%

Let us assume you had 10 shares of the business, price at end of May =10*4 = $40

Now you got 1:5 rights issue and got 2 shares at $3 = 2*3 = $6, total = $46

Price per share = 46/12 = $3.833333

Price after ex-dividend = $4.50

% return = (4.50-3.83333)/3.83333 =0.1739 = 17.39%

Geometric return =( (1-0.0222)*(1+0.025)*(1+0.1739))^(1/3) -1 = 0.0557 = 5.57% per month