Discounted Cash Flow (DCF)
Discounted cash flow values a property by projecting its cash flows over a holding period, including the eventual sale, and discounting each back to today at a required return. A gross rent multiplier is a compressed representation of the same idea: one year of gross rent and one market-derived multiplier standing in for the whole forecast.
DCF captures what GRM cannot: expenses, financing, rent growth, a renovation in year two, and the price at exit. Its outputs are net present value and internal rate of return. Its inputs are all forecasts, which is both its strength and its weakness.
GRM sits at the other extreme. It needs two observable numbers and no forecast, and it is only as good as the assumption that the subject's future looks like its comparables'. The two agree when expenses are typical, growth is steady and the exit resembles the entry. Use GRM to decide which properties deserve a DCF, and DCF to decide between them.
Further reading: Discounted Cash Flow (DCF) on Wikipedia.