Sensitivity analysis
Changing one critical input of a valuation model at a time, holding the rest constant, and tabulating how far the output value moves — a test of how fragile the answer is.
In plain language
A valuation model is only as good as what goes into it. Several of those inputs — the discount rate, the growth rate, the margin five years out — are assumptions, and a small change in any of them can move the answer a long way.
Sensitivity analysis makes that visible. Pick the critical variable, change it, keep everything else constant, and record what happens to the value. If a one-point change in the discount rate swings the fair value by a quarter, the reader of the report deserves to know that before acting on the target price.
How it works
Chapter 12 (section 12.6) describes the method: identify the critical variables in the model, and analyse how the valuation varies when a particular variable is changed keeping all other variables constant. Its example is the DCF discount rate — the rate must reflect the risks in the business, so the analysis is run at several discount rates and the impact on value is tabulated.
Scenario analysis is the related technique the same section mentions: a best case, worst case and most likely scenario, where several assumptions move together.
Chapter 10 makes the same point from the other side: DCF models "could also be very sensitive to some input factors", and valuers therefore typically present multiple scenarios showing the effect of a change in the primary variables on the output value.
The formula
Change in value (%) = (Value with changed input − Base value) ÷ Base value × 100
For the constant-growth dividend model used below:
P = D1 ÷ (k − g)
A worked example
Illustrative figures. A mature FMCG company is expected to pay a dividend of Rs 20 next year, growing at 6% a year. The analyst's base cost of equity is 11%.
Base value = 20 ÷ (0.11 − 0.06) = 20 ÷ 0.05 = Rs 400
Now move only the cost of equity:
| Cost of equity | k − g | Value | Change vs base |
|---|---|---|---|
| 10% | 4% | Rs 500 | +25.0% |
| 11% | 5% | Rs 400 | — |
| 12% | 6% | Rs 333 | −16.7% |
Then move only the growth rate, at k = 11%: growth of 7% gives 20 ÷ 0.04 = Rs 500; growth of 5% gives 20 ÷ 0.06 = Rs 333.
One percentage point in either input moves the value by a sixth to a quarter. If the stock trades at Rs 360, the analyst's "value 11% above price" conclusion survives only while the cost of equity stays below about 11.5% (where 20 ÷ (k − 0.06) = 360) — which is exactly the sentence the report should contain.
Why NISM asks about it
Chapter 12 (Fundamentals of Risk and Return) lists "Sensitivity analysis and Concept of Margin of Safety" among its learning objectives and defines the technique in section 12.6. Chapter 10 (Valuation Principles) explains why DCF outputs need it. Expect definition questions — especially the phrase "keeping all other variables constant" — and questions that distinguish it from scenario analysis and margin of safety.
Common exam traps
- One variable at a time. Change several together and you are doing scenario analysis (best, worst and most likely case), not sensitivity analysis.
- It does not make the valuation more accurate. It shows how much the answer depends on the assumption; the assumption is still an assumption.
- The swings are not symmetrical. In the example a one-point fall in k adds 25% while a one-point rise removes 16.7% — because k − g sits in the denominator.
- Sensitivity analysis is not margin of safety. Margin of safety is the gap between value and price; sensitivity analysis tells you how wide that gap needs to be.
- The narrower the spread between k and g, the more violent the sensitivity — a model with k − g of 1% is almost meaningless.
Where this is taught
- Series XXI-B · Chapter 17: Riskintroduced here
- Series XV · Chapter 12: Fundamentals of Risk and Returnintroduced here
Related terms
- Discounted Cash FlowA valuation method that estimates the cash a business will generate in future years and converts each year back to what it is worth today.
- Dividend Discount ModelA valuation that treats a share as worth the present value of every dividend it will ever pay, discounted at the return an equity investor demands for holding it.
- Intrinsic valueWhat an asset is actually worth — the present value of the cash it will generate over its remaining life, as against whatever price the market is quoting today.
- Margin of safetyThe gap between a security's estimated intrinsic value and the lower price paid for it — the cushion that protects the buyer when the estimate turns out to be wrong.
- Terminal valueThe value of everything a business earns after the end of the explicit forecast period, capitalised as a perpetuity or an exit multiple and then discounted back — usually most of a DCF answer.
- WACCThe blended after-tax rate a company pays on all its capital, equity and debt weighted by how much of each it uses — and therefore the discount rate for free cash flow to the firm.