ACCA AFM December 2026: The Black-Scholes Real Options Error That Doubles Your Answer

If a follow-on project's cash flows are valued at a future date, you cannot drop that number straight into Black-Scholes. Do it anyway and you will overstate the project by millions — and the marker will see it in one line.

Why real options keep costing marks in AFM

Real options are one of the highest-yield topics in AFM. They turn up attached to an NPV requirement, they are worth 6–10 marks, and the formula and tables are handed to you on the exam. Yet the AFM examining team keeps flagging the same pattern: candidates can quote the Black-Scholes inputs, but cannot map the scenario onto them.

AFM sat at 44% in March 2026 — below TX, FR and SBR. Real options are not why candidates fail, but they are exactly the kind of marks that separate a 48 from a 52.

The five inputs are fixed. Pa is the present value today of the future cash flows you gain by exercising. Pe is the cash you must pay to exercise, undiscounted. t is the years until the decision point. r is the risk-free rate — never the WACC. s is the volatility of the underlying cash flows.

Two of those five are where the marks leak. Pa must be discounted back to today. Pe must not be discounted at all, because the model discounts it for you inside the Pe × e^-rt term.

Worked example: the same scenario, two answers

A project has a base-case NPV of $(1.5)m. In three years the company can invest a further $30m in a follow-on project whose cash flows are worth $36.3m at that date. Cost of capital 9%, risk-free rate 4%, volatility 30%.

The wrong answer. Pa = 36.3 (the figure printed in the scenario). That gives d1 = 0.86, d2 = 0.34, and a call value of $12.4m. Add the base case and the project is worth +$10.9m. Recommend it.

The correct answer. That $36.3m sits at t=3. Discount it at 9%: 36.3 ÷ 1.09³ = $28.0m. That is Pa. Pe stays at 30 — do not touch it.

d1 = [ln(28/30) + (0.04 + 0.5 × 0.30²) × 3] ÷ (0.30 × √3) = 0.36
d2 = 0.36 − 0.52 = −0.16
N(d1) = 0.6406, N(d2) = 1 − 0.5636 = 0.4364
c = (28 × 0.6406) − (30 × e^-0.12 × 0.4364) = 17.94 − 11.61 = $6.33m

Project value = −1.5 + 6.33 = +$4.83m. Still accept — but you have not claimed $6m of value that is not there. The wrong answer more than doubles the option.

What to do

1. Write the five inputs out before you calculate anything. Pa, Pe, t, r, s, each with a one-line justification of where the number came from. Markers award those lines. It also forces you to notice that Pa is sitting at t=3.

2. Learn which option you are holding. Expand or delay is a call. Abandon or sell is a put — value the call first, then use put-call parity: p = c − Pa + Pe × e^-rt. Candidates lose whole answers by valuing an abandonment option as a call.

3. Always add the option value back to the base-case NPV. The option value on its own answers nothing. And write two sentences on the limitations — constant volatility, a single fixed exercise date, European-style exercise when management can really act at any time. Those sentences are worth as much as the calculation.

The bottom line

The formula is given. The tables are given. The only thing the exam is testing is whether you can read a scenario and put the right number in the right slot. Pa is discounted to today. Pe never is.

Get those two right and a negative-NPV project becomes a defensible accept — for the right reason.