The time value of money and the discount rate

You have used the word "discount" three times already without pausing on it. Now we stop and open it up, because the discount rate is the quietest and most powerful dial in all of valuation — the number that, more than any cash forecast, decides whether a business looks cheap or dear.

Start with the plainest possible fact. If someone offers you ₹100 today or ₹100 in five years, you take it today, and you are right to. Three reasons stack up. First, ₹100 today can be put to work — in a bank, a bond, another business — and grow, so by year five it is more than ₹100; the future ₹100 has missed all that growth. Second, prices tend to rise, so ₹100 buys a little less each year. Third, and often largest, a promise of ₹100 in five years might not be kept — the business could stumble, the plan could fail — while ₹100 in your hand is certain.

Together these make future money worth less than present money. That is the time value of money: the principle that a rupee today is worth more than a rupee later, because of growth foregone, inflation, and risk. And the number that converts "later" back into "today" — that captures all three reasons in a single annual percentage — is the discount rate. This module is about where that rate comes from, and why getting it a little wrong changes everything.

Every valuation on this shelf discounts future cash back to today, because value is the present worth of future cash. So the discount rate is not a technical footnote — it is half of what "value" means. It answers a real question: what annual return would you fairly demand to give up money now in exchange for uncertain money later?

Break the rate into its two jobs and it stops being mysterious.

The price of waiting. Even for perfectly safe money — say, lending to the government, which will not default in its own currency — you demand some return for the wait. That return is the risk-free rate: the return on a safe government bond, the reward for pure waiting with no default risk. In India you can read it straight off the yield on the 10-year government bond (the G-sec). It is the floor under every other rate — the pure time value of money, with no risk added.

The price of risk. A business is not the government. Its future cash is uncertain, so investors demand extra return on top of the risk-free rate to bear that uncertainty. For shares as a whole, this extra is the equity risk premium: the additional yearly return investors require for holding shares instead of a safe bond. Add it to the risk-free rate and you get the cost of equity: the total yearly return shareholders require for putting money into this business — the higher the risk, the higher this number climbs.

Most companies also borrow, and debt has its own price: the cost of debt, the rate a company pays to borrow, reduced by the tax it saves because interest is tax-deductible. Debt is usually cheaper than equity, both because lenders rank ahead of shareholders and because of that tax saving.

A company is funded by a mix of the two, so its overall discount rate is a blend of them, weighted by how much of each it uses. That blend is the weighted average cost of capital, or WACC: the company's overall cost of money, mixing the cost of equity and the after-tax cost of debt in proportion to how much of each funds the business. WACC is the discount rate most DCFs actually use. It is not a law of physics; it is an assembled estimate, and every piece of it is a judgement.

Let us build a WACC from the ground up, with round Indian numbers. illustrative

Start with the cost of equity. Say the 10-year G-sec yields 7% (the risk-free rate) and the equity risk premium is judged at 5%. For a business of ordinary riskiness, the cost of equity is roughly 7% + 5% = 12%. A riskier business would carry a larger premium and a higher cost of equity; a steadier one, less.

Now the cost of debt. Say the company borrows at 9%, and its tax rate is 25%. Because interest is deducted before tax, the real cost after the tax saving is 9% × (1 − 0.25) = 6.75%. Debt is markedly cheaper than the 12% equity.

Finally, blend them by the funding mix. Say the business is 70% equity and 30% debt:

WACC = (0.70 × 12%) + (0.30 × 6.75%) = 8.4% + 2.03% = ≈ 10.4%

That 10.4% is the discount rate this business's cash should be marked down by. Notice how many judgement calls went into it: the risk-free rate (readable, but it moves), the equity risk premium (an estimate, argued over endlessly), the company's specific riskiness, its borrowing rate, its tax rate, and its funding mix. Each is soft. The tidy "10.4%" is a tower of assumptions wearing one decimal place.

Now feel the power of that dial. Here is what happens to a single ₹100 as the rate and the waiting time change — the present value, the worth today, shrinking as either grows.

Read the bottom row slowly. ₹100 promised in twenty years is worth ₹21.5 today at 8%, but only ₹6.1 at 15% — a third as much, from nothing but a change in the rate. This is why the discount rate matters so enormously: it does not shave value evenly, it compounds against the future, so the cash furthest out — exactly the cash a DCF is least sure about — is the most violently affected by a number you merely estimated.

Watch how much rides on a rate that reasonable people disagree about. illustrative

Two careful analysts value the same steady business, agreeing exactly on its cash: about ₹100 cr of free cash a year, roughly forever. They differ only on the discount rate. The first argues the business is stable and well-financed, deserving a 10% rate. The second notes that the risk-free rate has risen and the business carries more debt than it looks, and lands on 12%. Neither is being unreasonable; both rates are defensible.

• At 10%: ₹100 cr ÷ 0.10 = ₹1,000 cr
• At 12%: ₹100 cr ÷ 0.12 = ₹833 cr

A two-point difference of opinion about the rate — not the cash, the rate — produces a ₹167 cr, or 20%, difference in value. And there was no error anywhere: both did the arithmetic perfectly, both had a fair case for their rate. The disagreement is real and it is unresolvable by more calculation, because the rate is a judgement about risk and required return, not a measurable fact.

The lesson is not that one analyst is right. It is that the rate is a judgement, it swings the answer hard, and so any honest valuation must show the answer across a range of reasonable rates rather than pretend one rate is the truth. It is better to be roughly right than precisely wrong applies to the rate above all: the roughly-right move is a value across 10–12%; the precisely-wrong move is a single figure built on a single rate.

The discount rate is indispensable and it is also where a great deal of false precision hides. Be honest about what it cannot do.

It cannot be measured, only estimated. Every ingredient — the equity risk premium above all, but also the business's specific riskiness and its true funding mix — is argued over by professionals who never fully agree. WACC looks like a measured quantity and is really an assembled opinion. The single decimal place is a costume.

It cannot capture risk that does not fit a formula. The textbook way of pricing a business's riskiness (its "beta", its wobble against the market) is a crude proxy at best, and misses the risks that actually sink investments — a fraud, a broken thesis, a technology shift. A neat rate can lull you into thinking risk has been handled when it has only been averaged.

It cannot fix bad cash forecasts. A perfect rate applied to fantasy cash flows gives a fantasy answer, delivered with confidence. The rate and the forecasts are two separate soft inputs; getting one exactly right does nothing for the other. The numbers need a story — including the story of why this business is as risky, or as safe, as your rate assumes.

It cannot stay still. The risk-free rate moves with the bond market; required returns shift with mood and cycle. A valuation built on today's rate is a snapshot, not a permanent truth, and re-running it in a different rate environment can change the answer without anything in the business changing at all.

The discount rate is where valuations are most often quietly rigged — sometimes on purpose, more often without noticing.

1. Using too low a rate on risky cash. A low, safe-asset rate applied to an uncertain business inflates the value by under-charging for risk. If the rate does not rise with the riskiness of the cash, the answer is flattering, not fair.

2. Treating WACC as a fact. The rate is an assembled estimate, every piece a judgement. Reporting it to a decimal place and trusting it closely mistakes tidiness for accuracy — the classic false precision this shelf warns against.

3. Forgetting how hard the rate hits the far future. Discounting compounds, so distant cash — the part a DCF is least sure of — is the most sensitive to the rate. A small change in the rate quietly rewrites the value that sits furthest out, including the terminal value you will meet soon.

4. Picking the rate to hit a desired answer. Because the rate swings the value so much, it is the easiest lever to nudge until the model agrees with what you already wanted to believe. A rate chosen to justify a price is not a discount rate; it is a rationalisation.

5. Showing one rate instead of a range. Reasonable people disagree on the rate by whole percentage points, and that disagreement is worth 20% of the value. An honest valuation runs the answer across a band of rates rather than pretending one is correct.