Risk Analysis in Capital Investment
Investment
Risk Analysis in Capital Investment
Syllabus tag: KASNEB CPA | Advanced Level | CA33 Advanced Financial Management | Topic 3 Risk Analysis in Capital Investment
Lesson objectives
By the end of this topic, you will be able to:
- Distinguish risk from uncertainty
- Compute and interpret sensitivity for each variable
- Apply expected values, standard deviation and the coefficient of variation
- Explain simulation and decision trees
- State the limitations of each technique
Why this matters
CA22 computed a single NPV from a single set of forecasts. Every one of those forecasts was an estimate. This topic asks which of them the decision actually depends on, and what happens if they are wrong.
Risk and uncertainty
Risk exists where the possible outcomes are known and probabilities can be attached — from experience, from data, or from judgement.
Uncertainty exists where the outcomes themselves cannot be listed, so no probability can be assigned. A genuinely novel product faces uncertainty, not risk.
The distinction matters because the techniques below all require probabilities. Where there are none, expected values cannot be computed, and sensitivity analysis becomes the only tool available.
Sensitivity analysis
Sensitivity = NPV / Present value of the variable being tested
It answers: by what percentage can this variable move before NPV reaches zero?
A project costing KES 25,000,000 with inflows of 9,000,000 a year for four years, discounted at 12%:
| KES | |
|---|---|
| PV of inflows (9,000,000 × 3.0373) | 27,336,144 |
| Initial outlay | (25,000,000) |
| NPV | 2,336,144 |
Initial outlay: 2,336,144 / 25,000,000 = 9.34% Annual inflows: 2,336,144 / 27,336,144 = 8.55% Discount rate: the IRR is 16.37%, so the rate can rise by (16.37 − 12) / 12 = 36.40%
The lowest percentage is the most critical variable. Here the annual inflow can only fall 8.55% before the project fails, so that is where management attention and further investigation belong.
Note that the discount rate can move a great deal without the decision changing. Arguing at length about the cost of capital while accepting the revenue forecast unexamined would be effort spent in the wrong place — and sensitivity analysis is what reveals that.
Limitations. It changes one variable at a time, when in practice variables move together. It attaches no probability — a 5% sensitivity on a stable variable may be less worrying than 30% on a volatile one. And it identifies critical variables without saying what to do about them.
:::checkpoint A project shows sensitivity of 4% on sales volume and 45% on the discount rate. A director proposes renegotiating the bank facility to reduce the cost of capital. Explain why this is the wrong priority. :::
Expected values
Where probabilities can be assigned, compute the probability-weighted average.
| Outcome | Probability | NPV (KES) | Weighted |
|---|---|---|---|
| Poor | 0.30 | (6,000,000) | (1,800,000) |
| Expected | 0.45 | 14,000,000 | 6,300,000 |
| Good | 0.25 | 30,000,000 | 7,500,000 |
| Expected NPV | 12,000,000 |
Two warnings. The expected value of 12,000,000 is not a possible outcome — no scenario produces it. And there is a 30% probability of a negative NPV, which the single figure conceals entirely.
Expected values suit repeated decisions, where outcomes average out over many trials. For a one-off decision that could threaten the company, the spread matters more than the average.
Standard deviation and coefficient of variation
Standard deviation measures the spread. For the figures above it is KES 13,416,408.
Coefficient of variation = SD / Expected value = 13,416,408 / 12,000,000 = 1.12
The CV is what allows projects of different sizes to be compared. A large project will have a larger standard deviation simply because it is larger; the CV expresses risk per unit of expected return, so a small project with a CV of 2.0 is riskier than a large one at 1.1.
Simulation
Monte Carlo simulation assigns a probability distribution to each variable and runs the model thousands of times, producing a distribution of NPVs rather than a single figure.
Its advantage over sensitivity analysis is that it varies all variables simultaneously and can build in correlations between them — a rise in volume that raises variable cost, for instance.
Its limitations: it is only as good as the distributions assumed; correlations are hard to specify; and it produces a distribution rather than a decision. Management still has to choose.
Decision trees
Where decisions are sequential — invest in a pilot now, expand later if it succeeds — a decision tree maps the choices and chance events in order.
The tree is evaluated by rolling back from the right: compute the expected value at each chance node, then at each decision node select the branch with the higher value.
Decision trees are the natural bridge to real options, because the ability to expand or abandon after seeing how the pilot performs has value that a single-shot NPV ignores entirely.
Other adjustments
Risk-adjusted discount rate — add a premium to the discount rate for a riskier project. Simple, and it implicitly assumes risk increases with time, which may not be true.
Certainty equivalents — convert risky cash flows to the certain amount the decision-maker would accept instead, then discount at the risk-free rate. More theoretically sound and harder to apply, because the equivalents are subjective.
Payback as a risk measure — a shorter payback means less exposure to distant, less predictable cash flows. Crude, and still widely used for exactly that reason.
:::checkpoint A project has an expected NPV of KES 12 million with a 30% chance of a negative outcome that would breach the company's loan covenants. Explain why the expected value alone should not decide the matter. :::