ACCA FM December 2026: The Miller-Orr Mistake That Costs Easy Marks

If your Miller-Orr spread looks suspiciously small, you've probably mixed a daily variance with an annual interest rate. Convert the rate to daily first, or you throw away the marks.

The formula is easy. The units are not.

In FM, the Miller-Orr model appears in working capital and cash management questions. The formula is given on your formula sheet: spread = 3 x [(3/4 x transaction cost x variance of cash flows) / interest rate]^(1/3). The lower limit is set by management. The upper limit is the lower limit plus the spread, and the return point is the lower limit plus one third of the spread.

The trap sits in the interest rate. Questions usually give you the standard deviation of daily cash flows and an annual interest rate. The variance and the rate must be measured over the same period. Students square the standard deviation, drop in the annual rate, and cube-root their way to a confident wrong answer.

It is a method-mark killer too. A wrong spread flows into the upper limit and the return point, so one slip costs you three numbers. A clear working line showing the daily rate at least protects your own-figure marks.

Wrong vs right

Data: transaction cost $50, standard deviation of daily cash flows $400, annual interest rate 5%, lower limit $2,000.

Wrong: variance = 160,000. Spread = 3 x [(0.75 x 50 x 160,000) / 0.05]^(1/3) = $1,480. Upper limit $3,480, return point $2,493.

Right: daily rate = 5% / 365 = 0.0137%. Spread = 3 x [(0.75 x 50 x 160,000) / 0.000137]^(1/3) = $10,575. Upper limit $12,575, return point $5,525.

Same inputs, a spread seven times too small. The wrong version would have you transferring cash to and from the bank constantly, which is exactly the thing the model exists to avoid.

What to do

1. Write the daily rate as its own line. Before touching the formula, write "daily rate = annual / 365" (or 360 if the question says so). Make it a habit.

2. Square the standard deviation. The formula wants variance. If the question gives you a standard deviation, square it before you substitute.

3. Sense-check the answer. Higher transaction costs or higher volatility should widen the spread. A higher interest rate should narrow it. If your answer moves the wrong way, recheck your units.

Bottom line

Working capital is a regular source of calculation marks in FM, and Miller-Orr is one of the most mechanical. The formula is handed to you. Matching the units is on you.

Same period for variance and rate. Every time.