Math Question on stock sales and value over time

I hold stocks that appreciate 20% annually. What is cheaper for me, if i sell 6 shares now to purchase something outright or if i pay 1 share every year for 8 years (so i pay 8 shares instead of 6) but i get the benefit of the 20% increases in annual share value on the time i get to wait until i sell the balance of the shares. Which option is cheaper in the end?

This is hypothetical, right, so you know they’ll continue this exact rate of appreciation indefinitely? And you’ll be selling those future stocks at their appreciated value, right?

Your question as asked doesn’t make much sense. If you are paying in shares, the seller is getting the increased value of the share, you’re just forcing them to wait a little longer.

correct, its privately held stock with a long history of 20% annual gains so just assume the future gains for the hypothetical.

I set up a simple spreadsheet, with some assumptions:

  1. You start with ten shares, valued at $100 each.
  2. In your second scenario, you are selling one share each year at its appreciated value (so instead of paying $600 total, you’re paying the value of 8 shares, each appreciated up to the year it’s sold, or a total of $1649.60).

Assuming I set everything up right–an enormous assumption–with no sales, by the end of 10 years, your value is $5159.78. With six of your ten shares sold the first year, your ending value is $2063.91. With eight of your ten shares sold, one/year, your ending value is $1,031.96.

Keep in mind, though, if you’re selling the stock at the appreciated value, it doesn’t matter what year you sell it, really: all you do is figure out what the value is of (initial shares-8) * 1.2 * years of appreciation.

it does because its 20% one year, then its 20% higher the next year etc so the longer you can wait to sell the more 20% annual increases you pocket. But the appreciating im gaining by spreading out the sales inm losing by having to sell 8 in the long run instead of 6, so which one is a better deal

If you are paying in shares, rather than in dollars, it doesn’t matter if the shares appreciate or depreciate. At the end of eight years, you’re out six shares in the first scenario and eight in the second. the first is always better.

If you mean that you are paying the current value of each share each year for eight years, but to keep the appreciation you get, then your question makes more sense. I can’t figure out how to put a picture of the spreadsheet into this message, but it is a fairly simple financial modeling problem, and the answer is that paying out the value of 8 shares over 8 years is better than paying over 6 shares now.

It matters if the first payment is made now, and the last payment seven years from now, or if you are making the first payment at the end of a year and the last eight years from now. But either one is better than the paying the value of six shares now.

thank you Mighty Mouse

This. It is amazing how often the solution to a mathematical problem is obvious once you look at it correctly. I am currently dealing with such a problem in which my collaborator refuses to see it correctly.

My other comment is that if I had a stock that was appreciating 20% a year, I would strain a gut not selling any of it. You could make a loan at 3% (they tell me) and use the stock as collateral. You will be way ahead even if you have to sell a couple of shares in 8 years to pay off the loan.

Shares of private stock do not make good collateral for loans. There is typically restrictions on who can get them.