The "Font" class is read-only for the Range, so something like this
doesn't work:
Set ar = ActiveCell.Font
Set rng = ActiveCell.Offset(3, 0)
rng.Value = ActiveCell.Value
Set rng.Font = ar
There are about 10-15 properties of the Font class that you could set
individually, something like this:
Set ar = ActiveCell.Font
Set rng = ActiveCell.Offset(3, 0)
rng.Value = ActiveCell.Value
rng.Font.Background = ar.Background
rng.Font.Color = ar.Color
rng.Font.ColorIndex = ar.ColorIndex
rng.Font.FontStyle = ar.FontStyle
rng.Font.Italic = ar.Italic
(and so on, or maybe there are only a few values that you care about,
such as only using Bold)
Or you could use the copy and pastespecial(all) methods like this:
Set rng = ActiveCell.Offset(3, 0)
ActiveCell.Copy
rng.PasteSpecial xlPasteAll
Application.CutCopyMode = False
The downside here would be that you couldn't store the values to be
copied all at once, then paste, you'd have to copy-paste, copy-paste,
copy-paste (which may be what you're doing anyway).