What discount period numbers would I use for the mid-year convention if I have a stub period – e.g. Q4 of Year 1 – in my DCF?

The rule is that you divide the stub discount period by 2, and then you simply subtract 0.5 from the “normal” discount periods for the future years. Example for a Q4 stub: 

Q4 Year 1 Year 2 Year 3 Year 4 Year 5

Normal Discount Periods with Stub: 0.25 1.25 2.25 3.25 4.25 5.25

Mid-Year Discount Periods with Stub: 0.125 0.75 1.75 2.75 3.75 4.75