Solution to problem sum

Here I shall reveal the calculations that I had based on the problem posted in this earlier post. I sort of figured out that nobody will be so bothered enough to go and try calculating the theoretical price of ARA after XA, so I might as well show the answers now. Thanks HH for trying it! Haha :)


Since in the real world, there are no teachers to check for you and no answers behind the textbook to assure that you're right, we always have to try solving the problem using different methods. If all the methods arrive at the same conclusion, then chances are, you're right until someone proves you wrong.

First method:

I tried using numbers to have a feel of how it works:
Let's say I have 10 lots of ARA shares @ $1.00 average price. Since the dividend is declared at $0.025 per share, or $25 per lot, I'll have $250 dividend for my 10 shares. The closing price a day before XA was $1.15, so I can calculate what's my profits so far.

My inventory before XA: 10 lots of ARA shares bought at $1.00

Sell price : 1.15

Profit from shares : (1.15 - 1) x 10,000 =  $1,500
Dividend : $250

Total profit before XA: $1,750 (1500+250)

Now, what happens after XA? The price of ARA drops because there are more shares floating around due to the 1 for 5 bonus issue. This means that for every 5 lots of ARA shares you own, you will now have 1 lot of bonus ARA shares. The price drops accordingly to reflect the fact that the market value of ARA remains the same. Do note that only the ordinary shares are entitled to dividend; Bonus shares are not entitled to this round of dividend but they are eligible for future dividends.

Let y be the price of ARA after XA.

My Inventory after XA: 10 lots of ARA bought at $1.00 PLUS 2 lots of bonus shares

Sell price : y

Dividend : $250

Profit from the original 10 lots of shares : (y - 1.00) x 10,000
Profit from the bonus share : y x 2,000
Total profit : 10,000y + 2,000y -10,000+ 250 = 12,000y - 9,750

Since y should represent the theoretical price such that my profit/loss before and after XA is to be the same, I equate the two profits,

12,000y - 9,750 = 1,750
Solving,           y = 0.95833

Hence $0.958 is the price such that my profits before XA and after XA is the same.

Second calculation:

I noticed that several terms can be removed without changing the answer. First of all, dividends doesn't matter as both sides of the equation contain the $250 divy term. Next, even if I tried different no. of shares bought at different price, it doesn't change the answer. I changed all the variables to algebra, and confirmed that the calculation remains the same. Without bothering you with the details, here's the much simplified formula:

Price = 5 x (closing price before XA) / 6

Since the closing price is 1.15,

Price = 5 x 1.15/6 = $0.958

Third calculation:

Not really a calculation. It's more like to show you that chartnexus had worked out what I had worked out in the morning. The chart clearly shows that the price before XA, on 28th Apr, had a closing of $0.958 whereas it was 1.15 just the day before the software updated the changes.

The closing price a day before XA clearly shows $0.958 instead of $1.15

The theoretical price is definitely different from the closing price. I cannot predict how the price will close and I know that the theoretical price will only be there for a fleeting moment. So, isn't it a waste of time trying to calculate something that only exists for a moment?

Not to me. I take great pleasure in such intellectual masturbation. It's like an unreachable itch behind the back, irritating me until I can solve it :)