ModeldrillMid-year convention
The mid-year convention assumes cash flows arrive evenly through each year, so year t is discounted by (1 + r)^(t - 0.5) instead of (1 + r)^t. It raises the present value slightly. In Excel, use a 0/1 switch: =CF / (1 + r)^(year - 0.5 * switch).
Syntax
PV = CF_t / (1 + r)^(t - 0.5)| Part | What it is |
|---|---|
t | Forecast year number (1, 2, 3, ...) |
r | Discount rate |
switch | 1 for mid-year, 0 for end-of-year, so one model can show both |
Examples
100 in year 1 at 10%, end of year vs mid-year
=100/(1+10%)^1 and =100/(1+10%)^0.5Result: 90.91 and 95.35
100 in year 2 at 10%, mid-year
=100/(1+10%)^1.5Result: 86.68
Switch in B2 (1 or 0), year in C3, rate in B1
=C5/(1+$B$1)^(C3-0.5*$B$2)Result: mid-year when B2 = 1, year end when B2 = 0
Common mistakes
- Applying the half-year shift to an exit multiple terminal value: the sale is assumed at year end, so discount that TV by a full n years.
- Using mid-year on a company whose cash is seasonal and clearly year-end weighted, where the convention overstates value.
- Mixing conventions in a sensitivity table so one case uses t and another t - 0.5.
Practice Mid-year convention
These drills check your answer on live data, free, no account needed.
- Mid-year convention switchCash usually arrives through the year, not on the last day. Add a switch: when B3 is 1, discount each year half a year less (year minus 0.5); when it is 0, use the full year. Fill the discount period (row 7), discount factor (row 8), present value (row 9) and the total in B10.
- Discount factors and present valuesFill the discount factor for each year (row 6: 1 divided by (1 + rate) to the power of the year), the present value of each cash flow (row 7) and the total present value in B8.
Questions
Does the mid-year convention apply to the terminal value?
Common practice: with the perpetuity growth method, discount TV at n - 0.5 because it is built from mid-year cash flows; with an exit multiple, discount at n. State which you used.
How much does the mid-year convention change a DCF?
It raises PV by roughly (1 + r)^0.5 - 1 on the cash flows, about 4.9% at a 10% rate, so a few percent of total value.
Related
- Discount factorA discount factor converts a future cash flow into present value: DF = 1 / (1 + r)^t. Worked examples, the Excel formula with absolute references, mid-year.
- DCF model stepsThe six steps of a DCF: forecast unlevered free cash flow, set WACC, compute terminal value, discount it all, bridge to equity value and divide by shares.
- Terminal valueTerminal value captures all cash flows after the forecast period. Perpetuity growth and exit multiple formulas with examples, and how to discount it right.
- NPV in ExcelExcel NPV discounts every value one period, so the time zero investment goes outside the function: =NPV(rate, cash flows) + initial. Exact examples, errors.