Calculating returns for a mutual fund with dividends

Question

I'd like to calculate returns for a given mutual fund (in this case, PRWCX from troweprice). When I look at their published performance, it says the Calendar Year Total Returns for 2013 is 22.43% but when I try to calculate that using with a formula (end.price + dividend - start.price)/start.price I get something different.

The price on 12/31/13 is 25.66 (adjusted close is the same), there was a dividend of 1.54 on 12/13/13, the close price on 1/2/13 is 22.56 and the adjusted close is 21.25. If I calculate the return using the close price, I get 0.2056, and if I calculate based on adjusted close, it's 0.28. The fund has an expense ratio of 0.71% (as of 12/31/13) and even if I subtract 0.71% from my results, I don't get anywhere close to 22.43%. Does anyone know what I could be doing wrong?

Also, I'm wondering if someone could tell me how Average Annual Total Return (for say 5 years or 10 years) is calculated.

My goal is to compare returns of this mutual fund to returns based on the S&P500 or individual stocks.

Answer 1

When we hear that the Dow is up for the day, it is not relative to the open, but rather to yesterday's close. Accordingly, I believe the yearly returns for 2013 are calculated, using the yearly adjusted closing prices, as $(C_{2013} - C_{2012}) / C_{2012}$.

I looked up adjusted closing prices on finance.yahoo.com: substituting $C_{2012} = 20.96$ and $C_{2013} = 25.66$ I get 22.42%, which is very close to their published performance.

Regarding your second question, average annual return (as opposed to annualized return) is probably calculated using a straightforward simple average of the annual returns of the last five or 10 years. If that does not seem to work, please refer us to where you have seen this terminology. Thanks!