Why valuation should use ranges
A share price can be observed to the paise. A valuation cannot. It requires estimates of future sales, margins, reinvestment, risk and how long an advantage can survive. None of those future numbers is known when the spreadsheet is built.
The formula may calculate perfectly. That does not make its inputs certain. Put an uncertain growth estimate into an exact formula and the output remains an uncertain estimate — even if the software prints two decimal places.
A single value such as ₹487.60 therefore claims more knowledge than the analyst possesses. A range such as ₹420–₹560 makes a narrower, more useful claim: these are the values produced by the plausible futures we examined, and these are the assumptions that separate one end from the other.
Precision in the calculation is useful. Precision in the conclusion must be earned.
One uncertain input, three exact answers
Return to the stripped-down constant-growth model from 15.01.01. Hold the first year's owner-cash proxy at ₹25 and the required return at 10%. At 4% perpetual growth the model produces ₹417. At 5% it produces ₹500. At 6% it produces ₹625.
Every result is mathematically exact under its assumption. None proves that the growth rate will occur. A single percentage point in an unobservable future input moves the answer sharply; another decimal place would not repair that uncertainty.
This is sensitivity analysis: change one input while holding the others still, and watch the answer. It reveals which assumption can overturn your conclusion. It does not decide which assumption is true.
- 4% perpetual growth
- ₹417 — rounded to about ₹420
- 5% perpetual growth
- ₹500
- 6% perpetual growth
- ₹625
A range is an argument with two visible edges
An honest range is not a favourite answer with an arbitrary 10% or 20% added and subtracted. Each end must come from a business future you can state, value and later check.
Near the lower end for Bharat Foods, growth may slow, margins may face pressure, reinvestment may earn less, or the return demanded for risk may rise. Near the upper end, growth may last longer, margins may hold, reinvestment may work and risk may remain contained. The exact inputs belong beside the spreadsheet; the business reasons belong in the written conclusion.
Do not manufacture a lower case by making every input disastrous, or an upper case by making everything perfect. Those are fantasies at opposite ends. Useful scenarios must be internally consistent and plausible. Also avoid counting one risk twice — once by cutting the cash flows and again by adding an arbitrary penalty to the discount rate.
Open the range
Select the lower case, today's market price or the upper case. Each marker means something different — and each has a limit.
The band displays selected plausible outcomes. It does not say every number is equally likely, or that the true value must remain inside.
Sensitivity and scenarios do different jobs
Sensitivity analysis asks: what happens if this one input is wrong? Change growth while holding margins, reinvestment and the required return fixed. Then test another input. The output shows which assumption makes the model fragile.
Scenario analysis asks: what is the business worth if this connected future occurs? Slower sales may bring weaker margins, poorer factory use and greater financing risk together. Those inputs describe one future and should be valued together.
A disciplined range normally needs both. Sensitivity finds the fragile inputs; scenarios assemble them into coherent business futures. More advanced work may use probability distributions and simulation, but three labelled scenarios are not a statistical confidence interval merely because a spreadsheet drew a band around them.
What ₹420–₹560 says — and what it refuses to say
It says that the selected plausible cases produced values from about ₹420 to ₹560, that the assumptions behind the ends can be audited, and that new evidence can move, narrow or widen the range.
It does not say that the true value must stay inside, that every point is equally likely, or that the midpoint is the real answer. It does not carry an 80% or 95% probability unless somebody actually built and explained a probability model. And it does not turn ₹420 into a buy instruction or ₹560 into a sell instruction.
A wide range can be the honest answer for a young, cyclical or fragile business. A narrow range is useful only when stable economics and strong evidence justify it. Neatness is not confidence.
How to compare a price with a range
Bharat Foods trades at ₹500, inside the illustrative ₹420–₹560 range. The defensible conclusion is limited: valuation alone has not shown a clear gap under these assumptions. You now have to decide which scenario deserves more weight and what evidence could change it.
If the price moves below ₹420 or above ₹560, audit the valuation before declaring an opportunity. The business may have changed, the range may be stale, or the model may have omitted something. A price outside the range is a reason to investigate, not an automatic instruction.
Update the range when evidence changes sales, margins, reinvestment, risk or the duration of growth. A price move by itself changes the comparison; it does not change your estimate. If the move followed new business information, analyse the information and update the assumptions it affects.