# Mid-Year Convention

Understand the Mid-Year Convention Concept

• What is the intended purpose of the mid-year convention?
• Why is the unadjusted, year-end assumption considered to be inaccurate?
• How does the mid-year convention impact the valuation of a company?
• When might mid-year discounting not be an appropriate measure?

## Mid-Year Convention Definition

In the context of DCF modeling, if the mid-year convention adjustment is not used, the implicit assumption is that the projected cash flows of the company are received at year-end (i.e. December 31, in the context of a calendar year).

The mid-year convention assumes the FCF generation of a company occurs evenly, therefore resulting in a steadier inflow of cash throughout the fiscal year.

Mid-year discounting accounts for the fact that the Free Cash Flows of a company are received throughout the year as opposed to only at year-end.

The mid-year convention can therefore be a necessary adjustment since, at times, the year-end assumption can be misleading in the portrayal of when cash flows are actually received.

In reality, the cash flows of a company are generated steadily throughout the year; however, the exact timing within a fiscal year tends to vary by the company in question (and industry).

Below is an illustrative diagram that depicts the mid-year convention in use – notice how 0.5 is subtracted from each time period:

## Valuation Implications of Mid-Year Convention

If the unadjusted, year-end assumption is used, the period number for the 1st year of the projection is straightforward (i.e., one).

But under the mid-year convention, the discount period of 1 is adjusted to 0.5 since the assumption is that half of a year has passed before the cash is considered to be in the hands of the company.

The adjusted discount factor formula is as follows:

• Discount Factor (Mid-Year Convention) = 1 / [(1 + Discount Rate) ^ (Period Number – 0.5)]

For mid-year discounting, the discount periods used are:

• 1st Year → 0.5
• 2nd Year → 1.5
• 3rd Year → 2.5
• 4th Year → 3.5
• 5th Year → 4.5

Since the discount periods are of lower value, this means the cash flows are received earlier, which leads to higher present values (and implied valuations).

Occasionally, the percentage increase from mid-year discounting could seem insignificant for smaller-sized companies, but at scale, the implications on the valuation and the gap between the two methods become far more pronounced.

Because each annual cash flow amount is implied to have been earned mid-year, this increases the valuation of the company in theory, as cash flows received earlier hold more value under the time value of money.

Despite the adjustment, the practice of mid-year discounting remains an imperfect approach, since it still does not take into account if cash flows reach the company more sporadically (rather than evenly) through a given year. Nevertheless, mid-year discounting is still typically more practical (and realistic) when compared to end-of-year discounting.

###### Mid-Year Convention: Seasonal / Cyclical Companies

While using the mid-year convention in DCF modeling has relatively become standard practice, it can be improper for highly seasonal or cyclical companies.

Companies with inconsistent sales trends with irregular fluctuations necessitate a closer look before using the mid-year discount.

For example, many retail companies experience seasonal patterns in consumer demand, and sales are disproportionately received in the 3rd and 4th quarters around the holiday season.

Here, the unadjusted, period-end assumption could be a more accurate representation of the cash flows of the retail company.

## Mid-Year Convention Calculator – Excel Template

We’ll now move to a modeling exercise, which you can access by filling out the form below.

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## Mid-Year Convention DCF Calculation Example

To add the mid-year convention into our stage 1 DCF model, we will first create a mid-year toggle switch as seen at the top right corner of the image.

Also from the formula, we see that the logic in the “Period” cell is:

• If the Mid-Year Toggle = 0, the output will be (Year # – 0.5)
• If the Mid-Year Toggle = 1, the output will be (Year #)

Next, the discount factor formula will add 1 to the 10% discount rate, and raise it to the negative exponent of 0.5 since the mid-year toggle is switched to “ON” here (i.e., input zero into the cell).

And to calculate the present value of the Year 1 cash flow, we multiply the .95 discount factor by \$100, which comes out to \$95 as the PV.

## Mid-Year Convention Output Sheets

In the final section of our post, the output for the model with the mid-year convention set to “ON” has been posted below:

And now, for comparison purposes, if the toggle was set to “OFF”:

Here, the periods are left unadjusted (i.e., no deduction of 0.5, implying the standard year-end discounting convention), which has the impact of making the discount factor lower and thereby decreasing the implied PV each year.

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