money weighted vs time weighted

In a practice question for money weighted calculation, stock paid 2 dollars end of year 1 and year 2.

we have the cash flows as -50, 65 - div , 140 + divs,

where you do Cf0 = -50 , Cf1 = -63 , Cf2 = 144 CPT IRR 18.02

but when doing time money weight we do 65 + div / 50 , 140 + divs / 130 .

Then we multiply both rates and ^5.

a) I don’t understand why we go from subtracting the div in money weighted and adding the div in time weighed.

b) where is 130 coming from?

  1. in time weighted why do you do to the ^5? Is it always ^5?

For a time-weighted calculation, you treat each period as a separate investment.

Here:

  1. Your first investment was one share of stock: you bought it at 50, and at the end of the holding period you sold it and had 67 (= 65 + 2).
  2. Your second investment was two shares of stock: you bought them at 130 (= 65 × 2), and at the end of the holding period you sold them and had 144 (140 + (2 × 2)).

You’re raising the compound return to the ½ power because the compound return occurred over 2 periods and you want to know the one-period compound return. If you had had returns over three periods you would raise the compound return to the ⅓ power to get the single-period return. And so on.

Thank you.

Is there any better way to calculate this, maybe with financial calc? or even remember this?

I think the signs are mixing me up, money weight in different years we have them as negative because they are outflows i guess, but in time weighted these arent outflows?