CAGR and Dividend Yield

Question

I am brand new to this, but am looking for some guidance when it comes to calculating the estimated FV of an investment in stocks with dividends reinvested in the same company. I'm going to be really green right now and use everyone's favourite case study, McDonalds, as an example.

It's 2013, I have $1000 to invest and at the close MCD is 96.92. I promptly buy up 10 shares in the company totalling $96.92 (excluding commissions). I keep my shares in MCD for five years and their current share price is 184.01 and the dividend yield was 2.5% per year.

To calculate the growth rate, I use the CAGR formula:

If I am correct, this means that MCD price has risen by an average 13.68% per year. This would therefore result in the 10 shares I bought being worth 1840.10 today. Where I run in to trouble is calculating the effect that the dividend yield being reinvested.

Currently, my thinking was to use the future value of a time series with the variable PMT linked to the 2.5% yield. In the example below r is the interest rate, n is the number of compounds per period and t is the duration of the investment.

The problem, $24.23 or 2.5% of the starting price is reinvested every year instead of increasing over time with the price of the share. I can iterate through the years one by one, as illustrated in the screenshot below, but would prefer a mathematical approach to calculating the future value:

Can anyone point me in the direction of a better way to calculate this? Also, please understand that this is purely theoretical.

Answer 1

When dividends are paid as a fixed percentage, the formula for total return is just price return + div yield. So in your case the total return would be 13.68% + 2.5% = 16.18%

You can verify that by thinking of the dividends as a payment that grows by G% each year (where G is the rate of price growth after dividends are paid). So every year, your total return is G% from the growth of the underlying stock, plus D% in dividends. Since the dividend yield does not change, that growth rate will be the same each year, so the total return will just be G + D.

In your example, dividends are paid at the end of the period, so your dividends are shifted by one period from your starting price, and your dividend "yield" (as a function of the starting price of the period) is D(1+G), meaning your end formula is G + D(1+G), or 13.68% + 2.5%(1.1368) = 16.522%. If you calculate the CAGR of your first table you should get exactly that value.