Two part question. First, say I invest 100K in an asset that throws off 10% interest income per year. I reinvest profits back into the asset at the end of every year. Also, say I can choose between Scenario 1: being taxed at 40% per year on my interest income and Scenario 2: have the asset accrue all pre-tax gains until the last year n, then have all my gains taxed at 40%. What is the mathematical intuition for why I would choose one over the other (I obviously get the gut intuition that the principle grows more slowly in the first scenario, but how do we know for sure that the cash taxes in the final year of the second scenario will always be smaller than the sum of all of the cash taxes in the first scenario…my algebraic sketch proof gets messy pretty quickly) ? And secondly, what would be an excel formula (not a native function) that would allow me to calculate the value of my holdings at year n given a tax rate t and an interest return r, assuming all proceeds are reinvested? I’ve only done this where I actually build a small “model” going out n years and add years if I need to look further in time. Is there an easier way to do this?
Q1: This is called “tax drag”. Intuitively, the account value growth is indeed being hindered by the annual taxation; tax deferral becomes far more valuable as n increases. This will be covered in excruciating exquisite detail when you hit Level III.
Q2. Use the FV function where your rate to input is gross yield * (1 - tax rate)
Breadmaker is correct. You’ll learn the difference at Level 3.
And Zerobonus is correct with almost everything. He is NOT correct when he says that the latter will always result in a higher return. That is only true if your holding period is more than one year. The two would have the same return if your holding period was only one year. (Minor detail, but could possibly manifest itself in an exam question nonetheless.)