# Simple math question

Just got a little confused and I am perhaps thinking a little slow today. But just wanted to ask what is the correct way to calculate fractions. I am going through this tutorial

1. You have 53,2 shares issued and the overallotment percentage is 15%, meaning it should be 15% of those 53,2 shares.
2. In a tutorial I am going through here they calculate this as 53,2/(1+0,15) = 6,9. However, if you divide 6,9/53,2 you get to 13%… Why does he not take 0,15*53,2 to arrive at 8m shares?

Which way is correct?

The 53.2 shares include the original shares planned (S) + overallotment of 15%

53.2 = S + (S \times 15\%)

53.2 = S \times (1 + 0.15)

So, the original number of shares that they planned to issue was:

S = \frac{53.2}{1.15} = 46.26 shares

And the overallotment is:

15\% \times 46.26 = 6.939 shares

To check:

\frac{6.939}{46.26} \approx 15\%

Thanks a lot! Another silly one:

• The implied post money valuation @ trading is 3079
• The IPO discount is 15%.
• They calculate the post money valuation @ pricing to be 3079/(1+0,15) = 2677
• This means that the discount is 401,6.

However that discount is 15% of the post money valuation @ pricing value of 2677. Why do they not calculate the discount as 3079 * 0,15 = 462 and then the post money valuation @ pricing would equal 2617?

Seems strange that the IPO discount is 15% of the post money valuation @ pricing and not the post money valuation @trading?