I really don’t get your case study on linking and annualizing returns. Take a look at my attached spreadsheet which illustrates my understanding of your scenario. Here are my issues:
1. You are compounding returns that are instantaneously granted through the discount stock purchase program. But, this is a one-time granted return and it only affects the initial purchase amount. It does not compound against the purchases previously made.
2. You assume there is no price appreciation over the purchase period, so what is there to compound? There are no market returns that affect the prior invested amounts.
a. I added a column that randomly generates returns within +/- 10% per quarter. However, you can overlay this with zero returns if you wish.
3. I treat the initial purchase as something that grows instantaneously at the beginning of the period, and then at the end of the period the additional amount is added. This allows the initial purchase to get the discount adjustment gain, and then be subject to market price change. Again, the market change can be switched off.
4. I calculate a simple gain against the average invested amount (it’s like a Dietz return) and it equals the 60% you state in your question. It’s a reasonable and intuitive measure of value gained from the discount program.
5. I also calculate an IRR that is “annualized” although I don’t think that either compounding or simply multiplying are perfect. You’ll note that neither of these are close to your compounded value of near 75%. Again, I think your error is because you are continuing to compound the original 15% gained at purchase against the entire accumulating amount. This is wrong, as the discount only applies to a single purchase. That said, there really is no compounding here. The mechanics have gotten ahead of the question and the investment scenario.
I don't know how to attach a spreadsheet to a post (or even if this is possible), so if you want to see Steve's spreadsheet, send me a note and I'll pass it to you.
I greatly appreciate Steve taking the time to chime in, and have no disagreements with his arguments.