Cash Flows & DCFintermediate

The Mid-Year Convention

Standard discounting assumes each year’s cash flow lands in a single lump at year end. In reality a firm collects cash throughout the year, so the year-end assumption discounts it slightly too hard. The mid-year convention corrects this by treating each year’s cash flow as if it arrives at the middle of the period, at $t - 0.5$ rather than $t$ . Because the cash is assumed to arrive sooner, every present value rises a little, and so does the valuation. It is a timing refinement on the same cash flows, not a change to the cash flows or the accounting behind them.

Why it matters

Picture a shop taking money every day. Lumping a whole year of those daily takings at December the thirty-first pretends you waited the full year for cash you were actually banking all along. The mid-year convention splits the difference. It assumes the cash, on average, lands at mid-year, which is closer to the truth. Pulling each cash flow half a year nearer to today lifts its present value, so a mid-year DCF is always a touch higher than the year-end version on identical forecasts.

Formulas

Year-end versus mid-year present value

\text{PV}_{\text{mid}} = \frac{\text{CF}_t}{(1 + r)^{\,t - 0.5}} \;>\; \frac{\text{CF}_t}{(1 + r)^{t}} = \text{PV}_{\text{end}}

Discounting at t minus 0.5 instead of t shortens every horizon by half a year, so each present value is higher. The same logic shifts the terminal value half a period closer as well.

Worked examples

Scenario

A cash flow of US$1,000 arrives in year 3. The discount rate is 10 percent. Compare the present value under the year-end and mid-year conventions.

Solution

Under the year-end convention, discount over the full 3 years. PV is 1,000 divided by 1.10 cubed, about 1.331, which is roughly US$751. Under the mid-year convention, discount over 2.5 years. PV is 1,000 divided by 1.10 to the power 2.5, about 1.269, which is roughly US$788. The mid-year value is about US$37 higher on the very same cash flow, because the cash is assumed to arrive half a year sooner. Across a full forecast this lift compounds into a meaningfully higher valuation.

Common mistakes

✗The mid-year convention changes the cash flows. It changes only the assumed timing of the same cash flows, not their size. The forecasts are untouched.
✗Mid-year discounting lowers the valuation. It raises it, because each cash flow is treated as arriving half a year earlier, which increases every present value.
✗The convention applies only to the explicit forecast years. The same half-period shift should be applied consistently, including to the terminal value, or the valuation is internally inconsistent.
✗Year-end discounting is simply wrong. It is a convention, not an error. Mid-year is a refinement that better reflects cash arriving across the year, and either is defensible if applied consistently.

Revision bullets

•Year-end discounting assumes cash arrives in one lump at the period end
•Firms actually collect cash throughout the year
•The mid-year convention discounts at t minus 0.5 instead of t
•Assuming cash arrives sooner raises every present value
•A mid-year DCF is always slightly higher than the year-end version
•Apply the same half-period shift to the terminal value for consistency

Quick check

Compared with year-end discounting, the mid-year convention generally produces a valuation that is

Connected topics

NPV & Additivity Discounting Terminal Value Enterprise DCF

Sources

Titman & Martin, Ch. 2
Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
Discusses the timing of cash flows within the period and the mid-year discounting refinement.

How to cite this page

Dr. Phil's Quant Lab. (2026). The Mid-Year Convention. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-mid-year-convention

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