# Calculating the Nominal Rate of Return of a dividend paying stock

How is the nominal rate of return for a dividend paying stock calculated. I understand that nominal return is calculated using the formula:

(Current Market Value - Original Purchase Price) / Original Purchase Price

But then I read Example #2 here ( https://www.wallstreetmojo.com/nominal-rate-of-return/ ) and cannot understand where they are getting the numbers from. Specifically where they multiply the annual dividend rate by quarterly dividend rate divided by the share price.

• Example #2 here makes no sense at all. Why does he sum the CD End Values in cell D9? The mutual fund numbers are gobledygook. \$150 invested at \$15 per share is 10 shares. If dividends reinvested, one owns more shares. Since not shown, the assumption is no DRIP. If share price is \$16.50 at the end of the year, the cap gain is 10 shares x \$1.50 or \$15. That alone is a 10% ROI and the dividend isn't accounted for. And the answer is 9.50% ??? The short answer is that an annual return of 5% in a CD equals a 5% return in a mutual fund (total return), regardless of the dividend. Commented Jul 26, 2019 at 0:13

The return over one period (day, week, month, etc.) for a stock is:

ret(t,t+1) = [P(t+1) + D(t+1) - P(t)] / P(t)

where P(t) is the stock price at the start of the period, P(t+1) is the stock price at the end of the period, and D(t+1) is the dividend paid at the end of the period.

If you're looking over a long enough period (e.g., year), you may have multiple dividends, in which case you can compute the IRR of your investment or the r such that the following is true.

P(0) = D(1) / (1+r) + D(2) / (1+r)^2 + ... + D(N) / (1+r)^N + P(N)

Unfortunately, this assumes that all of the dividends are reinvested at the same rate, r, which is highly unlikely.

Alternatively, you can follow the following recipe that is often used to compute the return on a coupon bond, which is also subject to reinvestment risk.

1. compute the future value of each dividend at the time the stock is sold using the appropriate reinvestment rates for each dividend.
2. Sum all of these future values.
3. Divide this sum by the price at which the stock is purchased.

This will produce a holding period return that you can then annualize if you want.

• I'm not clear on this statement: "Unfortunately, this assumes that all of the dividends are reinvested at the same rate, r, which is highly unlikely." Given this is a future forecast model, and a singular rate of return will be used for all periods, assuming the dividends are all invested at the same rate, is really the only way to do it. The result of this model should be the same effective return, as would be indicated for an identical company which pays no dividends. This of course assumes all dividends are reinvested in the same company - assuming otherwise is unnecessary complication. Commented Jul 17 at 12:56