I understand for mid-year convention in a DCF, you would use 0.5 for year 1, 1.5 for year 2, etc. (Cash flow is in the middle of the year, instead of at the end of the year)

But what does it mean for there to be a "stub period"?
i.e. if the stub period is Q4 of year 1 - what does this mean? And how would you calculate discount periods with stub?

Thanks.

### Stub Period DCF

Below is an explanation for valuation in a stub stub period. You can also find an example of a mid year DCF lbo/stub"> here.

from @nelly"

Calculation is pretty straight forward. For the stub period, you adjust the cash flow and assume that it is received during the middle of the stub period. For all full future periods, cash is assumed to flow during the middle of the fiscal period. This must be adjusted based on the valuation date of your DCF.

All examples assume a 30/360 days convention for simplicity.

Ex.1: Valuation date of 12/30/13; 12/30/13 FYE w/o mid-year convention
FY2014 - Discount period = 1.000
FY2015 - Discount period = 2.000
FY2016 - Discount period = 3.000
etc.

Ex.2: Valuation date of 12/30/13; 12/30/13 FYE w/ mid-year convention
FY2014 - Discount period = 0.500
FY2015 - Discount period = 1.500
FY2016 - Discount period = 2.500
etc.

Ex.3: Valuation date of 9/30/13; 12/30/13 FYE w/ mid-year convention (Q4 = stub)
FY2013 (Q4) - Discount period = (0.000 + 0.250) / 2 = 0.125
FY2014 - Discount period = (1.000 + 0.250) - 0.500 = 0.750
FY2015 - Discount Period = (2.000 + 0.250) - 0.500 = 1.750
etc.

In terms of excel, you can typically use the following, with "midyear" serving as a mid-year convention toggle:
"=IF(midyear, MAX(YEARFRAC(start date, period date,1)-0.5, YEARFRAC(start date, period date,1)/2), YEARFRAC(start date, period date,1)"

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I'm not sure I totally understand what you're asking, but I think what you mean is the fact that if, for example, AT&T buys T-Mobile and the deal closes on 9/30/11, AT&T should only get credit for the last quarter's earnings and cash flow - everything prior to that is attributable to T-Mobile shareholders. So when you run the DCF, only that last quarter of FCF should be counted when valuing the acquired T-Mobile.

http://macabacus.com/lbo-model/stub-period

Stub period = partial period.

So, if I model out the Q4 of 2011 and the deal actually closes on Oct 31, 2011, the the stub period is 2/3rds of the quarter.

One formula that might be useful is the "yearfrac" formula when you encounter stub periods.

I guess I'm more confused on what this question is asking: "What discount period numbers would I use for the mid-year convention if I have a stub period (Q4 of year 1) in my DCF?"

Going along with MittRomney, does this just mean there is a period of 1 quarter (3 months) between when the deal closes and the next fiscal year?

Thanks.

Did this on a fairness opinion recently. Believe you use .25, 1.25, 2.25 etc for your discounting periods - so basically just an adjusted midyear convention.

Partial Period Adjustment = YearFrac[12/31/X, Start date, 1]

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Best Response

Calculation is pretty straight forward. For the stub period, you adjust the cash flow and assume that it is received during the middle of the stub period. For all full future periods, cash is assumed to flow during the middle of the fiscal period. This must be adjusted based on the valuation date of your DCF.

All examples assume a 30/360 days convention for simplicity.

Ex.1: Valuation date of 12/30/13; 12/30/13 FYE w/o mid-year convention
FY2014 - Discount period = 1.000
FY2015 - Discount period = 2.000
FY2016 - Discount period = 3.000
etc.

Ex.2: Valuation date of 12/30/13; 12/30/13 FYE w/ mid-year convention
FY2014 - Discount period = 0.500
FY2015 - Discount period = 1.500
FY2016 - Discount period = 2.500
etc.

Ex.3: Valuation date of 9/30/13; 12/30/13 FYE w/ mid-year convention (Q4 = stub)
FY2013 (Q4) - Discount period = (0.000 + 0.250) / 2 = 0.125
FY2014 - Discount period = (1.000 + 0.250) - 0.500 = 0.750
FY2015 - Discount Period = (2.000 + 0.250) - 0.500 = 1.750
etc.

In terms of excel, you can typically use the following, with "midyear" serving as a mid-year convention toggle:
"=IF(midyear, MAX(YEARFRAC(start date, period date,1)-0.5, YEARFRAC(start date, period date,1)/2), YEARFRAC(start date, period date,1)"