A DCF for beginners, worked in rupees

A rupee today is worth more than a rupee next year, because today's rupee can be put to work. ₹1,00,000 at 8% becomes ₹1,46,933 in five years.

Run that backwards and you have a discounted cash flow. Everything else is bookkeeping.

What follows is one built end to end for a synthetic Indian manufacturer, with every figure shown so it can be checked. The company is invented; the method is not.

The company

Kaveri Auto Components (synthetic) makes braking systems for commercial vehicles. Last year it reported:

Its marginal tax rate is 25%. It is funded 70% by equity and 30% by debt, and it borrows at 9%.

Step one: the cash flow to value

The cash flow a discounted cash flow discounts is not profit. It is the cash left after every operating cost, after tax, and after the spending needed to keep the business running and growing.

For an enterprise valuation the measure is free cash flow to the firm, which is measured before any payment to lenders, because it belongs to lenders and owners together.

Build it in four moves. Tax the operating profit at the marginal rate. Add back depreciation, because it took no cash. Subtract capital expenditure, because that did. Subtract the increase in working capital, because growth locks money in inventory and receivables before it comes back.

₹960 crore taxed at 25% is ₹720 crore. Add ₹380 crore of depreciation, subtract ₹460 crore of capital spending and ₹210 crore of working capital, and the company generated ₹430 crore of free cash flow to the firm.

The tax step is the one people get wrong. Taxing operating profit produces a higher charge than the company actually paid, because the real charge is computed after deducting interest. That is deliberate. The tax saving from debt belongs in the discount rate, not in the cash flow, and counting it in both places values the same benefit twice.

Step two: the discount rate

The rate has to compensate for waiting, for inflation, and for the chance the money never arrives.

Cost of equity. Under the capital asset pricing model it is the risk-free rate plus beta times the equity risk premium. Take the ten-year Indian government bond at 7%, a beta of 1.1 for a cyclical auto supplier, and an equity risk premium of 5.5%. That gives 13.05%.

Cost of debt. The company borrows at 9%. Interest is deductible, so the after-tax cost is 9% times one minus the 25% tax rate, or 6.75%.

The blend. Weight the two by how much of the funding each provides: 70% equity at 13.05% and 30% debt at 9% before tax. The weighted average cost of capital is 11.16%.

Round it. A weighted average cost of capital quoted to two decimal places carries an honest error of one or two percentage points, and pretending otherwise is the first place a beginner's model stops being honest. Working to 11.2% and running the whole thing again at 10% and 12.5% tells you more than any single answer.

The currency rule is the one that catches people. A rupee cash flow must be discounted at a rupee rate. Discount rupee cash flows at a dollar risk-free rate and the company will look extraordinarily valuable, and both numbers will look reasonable in isolation.

Step three: the explicit forecast

Assume the free cash flow grows 10% a year for five years. That is a decision, and it should be defensible: for a supplier to commercial vehicle makers it implies volumes and content per vehicle growing faster than the underlying industry, which needs a reason.

The five years are worth ₹2,084 crore today.

Five years is the market convention and it is often too short. The right length is however long it takes the business to reach a steady state, meaning stable margins, stable reinvestment and returns converging toward the cost of capital. A company earning far above its cost of capital will not be there in five years, and truncating the forecast forces the terminal assumption to carry a competitive position that has not yet faded.

Step four: the terminal value, which is where the answer actually lives

Everything after year five is collapsed into one figure.

Take the year-five cash flow of ₹693 crore, grow it one more period at the perpetual rate, and divide by the discount rate minus that rate. At 5% perpetual growth: ₹693 crore times 1.05, divided by 11.16% minus 5%, gives ₹11,804 crore at the end of year five.

Discount that back five years at 11.16% and it is worth ₹6,955 crore today.

Now look at the proportions. The explicit five years contributed ₹2,084 crore and the terminal value contributed ₹6,955 crore, so 77% of the answer sits in a single assumption about a year nobody can forecast. In a model built over ten years that share is usually higher still.

That is the honest fact about discounted cash flow models and it is the one most tutorials skip. The explicit forecast is where the work goes. The terminal assumption is where the answer is.

The rule that caps the growth rate

Nothing can grow faster than the economy forever, because it would eventually become the economy. A perpetual growth rate above long-run nominal economic growth is arithmetically impossible rather than merely optimistic.

For India that ceiling is somewhere around real growth plus inflation. For a mature American business, 2% to 3% is the working range.

The formula is also explosive as growth approaches the discount rate. At 11.16%, moving perpetual growth from 4% to 6% raises the terminal value by about 41%. A model that needs 6% to justify the current price is telling you something about the price rather than about the company.

Step five: from enterprise value to a share price

Add the two pieces: ₹2,084 crore plus ₹6,955 crore is ₹9,039 crore of enterprise value.

Subtract net debt of ₹1,020 crore and the equity is worth ₹8,019 crore. Across 50 crore shares that is ₹160.38 a share.

The bridge is where careful work is either done or skipped. Minority interests come out. Investments in associates and surplus cash that the operating cash flows excluded go back in. Each is a decision and each should be shown as a line rather than folded into a total.

What to do with the number

Not act on it.

The output of a discounted cash flow is not a target price. It is a statement of what has to be true for the current price to make sense, and the most useful thing to do next is to invert the model.

Take the market price as given and solve for the growth the price requires. If the shares trade at ₹200, the market is paying ₹10,000 crore for the equity and ₹11,020 crore for the enterprise, and the growth rate that produces that is the market's expectation. Write it as a sentence a domain expert could argue with: "the market expects this supplier to grow its cash flow 14% a year for five years and 5.5% forever."

That sentence is the investment case. A forward model asks you to predict, which nobody does well. A reverse model asks you to judge whether a stated expectation is plausible, which is a question a careful analyst can answer.

The three errors that ruin a beginner's model

Free growth. A terminal value assuming 5% perpetual growth at a 12% return on capital requires the business to reinvest about 41.7% of its operating profit forever. If the terminal cash flow does not reflect that reinvestment, the model has assumed growth without paying for it, and the valuation can be inflated by half.

Mismatched cash flow and rate. Free cash flow to the firm is discounted at the weighted average cost of capital and gives an enterprise value. Free cash flow to equity is discounted at the cost of equity and gives an equity value directly. Discounting a pre-interest cash flow at the cost of equity produces an answer that is wrong by roughly the size of the debt.

One number. A single point estimate presented to the rupee is a description of a spreadsheet. Run the model at three discount rates and three growth rates, present the range, and say which two assumptions the answer actually depends on.

The margin of safety

Suppose the model says ₹160 and the shares trade at ₹112.

That 30% gap is not a forecast of a 30% return. It is protection against the fact that the estimate was produced by a fallible person using assumptions that will turn out to be wrong, and it should be wider for a cyclical business whose earnings power depends on a price nobody can forecast than for a stable one with twenty years of steady returns.

A large margin on a business you have misjudged is not protection at all. That is the last thing a discounted cash flow cannot tell you, and it is why the model is the second half of the work rather than the first.

Sensitivity, and the only honest way to present the answer

One number to the rupee is a description of a spreadsheet. Present a grid.

Run the model at three discount rates and three perpetual growth rates and put the nine outcomes in a table. For this company, moving the discount rate between 10% and 12.5% and the perpetual rate between 4% and 6% produces a range running from about ₹6,713 crore to about ₹13,545 crore, which is a quarter below the mid-point and half above it.

That grid is not a hedge. It is the answer. It tells a reader which two assumptions the valuation depends on, which is more useful than any single figure, and it makes the research plan obvious: the two things worth spending a week on are the two that move the grid.

Most models have exactly two such assumptions. The rest of the spreadsheet is precision applied to inputs that barely matter.

Checking the model against itself

Three checks catch most beginner errors, and each takes a minute.

The reinvestment check. A terminal value assuming 5% perpetual growth at a 12% return on capital requires the business to reinvest about 42% of its operating profit forever. If the terminal cash flow does not reflect that reinvestment, the model has assumed growth without paying for it, and the valuation can be inflated by half. Growth is never free, and free growth is the single most common error in a first discounted cash flow.

The terminal share. Compute what proportion of the total value sits in the terminal figure. Where it is above about 80%, the explicit forecast is decoration and the valuation is really one assumption in a costume.

The implied multiple. Divide the terminal value by the terminal year's operating profit and see what multiple you have assumed. If the answer is 14 times for a business that has never traded above 10, the terminal assumption is doing work the analysis has not justified.

Three minutes, and they catch more than a week of extra forecasting.

Where the discount rate really comes from

The formula makes it look measured. It is not.

The equity risk premium is somewhere between 4% and 6% for a mature market depending on the method used, and the three standard methods disagree with each other. Beta is estimated from a regression whose answer changes materially with the period, the frequency and the index chosen, and for a thinly traded Indian mid-cap it is close to noise. The risk-free rate is observable and is the only input in the whole construction that is not an estimate.

So the honest position is that the cost of equity is a range, that the range is at least two percentage points wide, and that consistency across the companies you value matters far more than being right about the level. A valuation is a comparison, and a comparison survives a shared error better than an isolated one.

Build the rate once, document how, and apply it everywhere.

What a discounted cash flow is actually for

Not a target price.

It is a device for making assumptions explicit. Building one forces you to state the growth rate, the margin, the capital intensity and the durability of the returns, in numbers, where they can be argued with. That is the value, and it survives even when the output is wrong.

Feed the model your enthusiasm and it will hand your enthusiasm back to you dressed as an intrinsic value. That is the whole risk, and the reverse version is the defence, because it removes the answer you were trying to reach.

What the model is worth once it is built

A discounted cash flow is most useful in the hour it takes to build and least useful as a number afterwards. Building one forces every assumption into the open: what revenue does, what the margin does, how much capital the growth needs, how long the returns hold, and what an investor requires for bearing the risk. Each of those is a sentence somebody can disagree with, and disagreement is what an analyst is for. The output, by contrast, is a point estimate produced by compounding five uncertain assumptions over ten years, and treating it as a target price is the mistake that makes people distrust the whole method. Use the model to find out which two assumptions the answer depends on. Then go and do the research on those two, and let the number stay a range.

The spreadsheet is a thinking tool.

The answer is a range, always.

And the reverse version is the one to show somebody else.