You can indeed use the Gordon model. We can price the SP500 just after the exdividend date this year:
\(P_0 = \frac{Div_1}{r-g}\)
and just after the exdividend date next year
\(P_1 = \frac{Div_1(1+g)}{r-g}\)
therefore, the capital gains are
\(\dfrac{P_1}{P_0}-1=g\)
since returns are dividend yield plus capital gains, you get to the solution.
If you price the SP500 any other day, you will get the same result as long as the difference between dates 0 and 1 is one year.