Why does cash flow actually arrive throughout the year rather than as a lump sum, and how does mid-year convention approximate that reality?
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The answer
Cash flow arrives throughout the year because companies generate revenue and pay expenses continuously every week, not in a single lump sum on December 31st. Discounting as if all cash lands at year-end systematically discounts it for too many periods, which understates its present value.
The mid-year convention approximates this reality by assuming each year's cash flow effectively arrives at the midpoint of the year rather than the end. Mechanically, that means I discount using an exponent of t minus 0.5 instead of t, which shrinks the discounting period by half a year for every cash flow. Because the exponent is smaller, the discount factor is larger, and the present value of every cash flow increases.
This purely timing-driven adjustment typically raises total DCF value by roughly 3 to 5 percent relative to end-of-year discounting. I apply the same convention consistently to the terminal value by using the same n minus 0.5 exponent as the final explicit year, since the terminal value represents summarized cash flows generated on that same continuous timeline.
The convention is a useful approximation, but I recognize that highly seasonal businesses don’t generate cash evenly, so in that case I would flag the assumption and might model quarterly cash flows explicitly instead.
DCF timeline
| Line item | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Free cash flow | 50 | 54 | 58 | 63 | 68 |
| PV of free cash flow | 45 | 45 | 44 | 43 | 42 |
| Terminal value (Year 5 exit) | 1,001 |
| PV of terminal value | 621 |
| Implied enterprise value | 840 |
Also asked as
- Write the standard end-of-year discounting formula and the mid-year convention version. What single change distinguishes them?
- Does mid-year convention increase or decrease enterprise value relative to end-of-year discounting, and roughly by how much for a typical WACC?
- A cash flow of $40mm is expected in year 4. WACC is 8%. Compute its present value under both end-of-year and mid-year convention.
- Derive, algebraically, the exact percentage uplift that mid-year convention produces relative to end-of-year discounting, as a function of WACC alone.
- Explain what a stub period is and why it requires both a prorated cash flow and a different discount exponent than a full year would.
- You are valuing a company on October 1st with a December 31st fiscal year-end. The current fiscal year's full-year FCF is projected at $200mm and next fiscal year's is $220mm. Compute the stub-period FCF and its discount exponent, and the following full year's discount exponent, assuming mid-year convention and ratable cash generation.
- Explain the theoretical argument for NOT applying mid-year convention to an exit-multiple-based terminal value, even while applying it to the explicit forecast period. What kind of business event does the exit multiple represent that makes this argument coherent?
- A DCF has explicit-period PV of cash flows of $500mm and an unadjusted (end-of-year, full n=6) terminal value PV of $2,100mm at WACC 9%. Recompute the terminal value's PV under mid-year convention (n − 0.5 = 5.5) and quantify the total enterprise value difference in dollars and percent versus the end-of-year figure.
- A ski resort's cash flows are heavily concentrated in Q4 and Q1 (winter season), with almost no cash generated in Q2-Q3. Explain specifically why the standard mid-year convention is a poor approximation for this business, and describe the more rigorous alternative you would build instead.
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The rest of this topic
The DCF: cash flow, discount rate, terminal value