Present value and discounting

In simple terms

Would you rather have ₹1,000 today or ₹1,000 in five years? Almost everyone chooses today, for good reasons:

• Opportunity: money today can be invested and earn a return.
• Inflation: prices may rise, so future money buys less.
• Risk: a promise of future money may not be kept.

This is the time value of money. It means that to compare money at different times, you must convert it to the same point in time. Converting future money to its value today is called discounting, and the result is its present value.

Future value and present value

The compounding lesson showed how money grows:

Discounting is simply compounding in reverse. The rate used is called the discount rate. The number 1 ÷ (1 + rate)^years is the discount factor: what each future rupee is worth today.

Discounting a series of cash flows

Businesses produce cash flows year after year. To value a series, discount each cash flow by its own number of years and add them up.

The difference between the present value of the inflows and the cost today is the net present value (NPV). A positive NPV means the investment earns more than the discount rate.

How the discount rate changes the answer

The discount rate has a large effect, especially on distant cash flows.

This is why valuations of companies whose cash flows lie far in the future, such as young, fast-growing businesses, are so sensitive to the discount rate and to interest rates in the economy. When rates rise, the present value of distant cash flows falls sharply.

Choosing the discount rate

The discount rate is the return you require for waiting and for bearing the risk that the cash may not arrive. Riskier cash flows deserve higher rates. For valuing a company's shares, the rate is the cost of equity; for valuing the whole business, it is usually the weighted average cost of capital. The next two lessons, on the cost of equity and WACC, explain how analysts estimate them.

Why it matters

Every valuation method, explicit or not, discounts the future. A P/E ratio is a shortcut that hides assumptions about growth and discount rates; a DCF makes them visible. Understanding present value lets you compare money at different times, judge investments, and see why changes in interest rates move share prices.

Limitations

Present value calculations are only as good as the cash flows and discount rate put into them. Real cash flows are uncertain and arrive through the year, not neatly at year-end. The discount rate is a judgement, and small changes in it produce large changes in value. Use present value as a disciplined way of thinking, not as a source of false precision.

Common mistakes

• Adding up future cash flows without discounting them.
• Dividing by rate × years instead of compounding, for example dividing by 1.5 instead of 1.61 for 10% over five years.
• Using the same discount rate for very different risks.
• Forgetting how sensitive distant cash flows are to the rate.

Try it yourself

1. Work out the present value of ₹10 lakh received in 10 years at discount rates of 8%, 10% and 14%.
2. Take three years of made-up cash flows, such as ₹5 lakh, ₹6 lakh and ₹7 lakh, and calculate their total present value at 12%.
3. Change the rate to 9% and recalculate. How much does the value change?
4. Write a sentence on why a higher interest rate in the economy might lower the price investors pay for shares.