Two operations carry the whole idea. Compounding carries a present amount forward: invest it for one period at a rate and it grows by that rate, then grows again on the enlarged amount. Discounting runs the arithmetic backwards: to find what a future payment is worth today, divide it by one plus the rate, raised to the number of periods. Future value and present value are the same relationship read from opposite ends, and every other tool in the kit, annuities, perpetuities, bond prices, loan repayment schedules, is a sum of those single steps. CFA Institute's refresher reading on the subject applies it straight away to pricing bonds and shares, because valuing any asset means adding up what its future payments are worth today.
What sits inside the discount rate
- Opportunity cost: the return available elsewhere on money not committed here.
- Inflation: the loss of purchasing power while waiting; the Bank of England describes real interest rates as nominal ones adjusted for expected inflation.
- Risk: a less certain payment is discounted at a higher rate, which is why equity cash flows are discounted more heavily than government bond coupons.
- Timing and frequency: the same annual rate compounded monthly produces a different result from one compounded once a year.
One principle, four tools
Almost everything in corporate finance and valuation rests on this page. Net present value is the principle applied to a single project, a discounted cash flow valuation applies it to a whole business, the company-wide WACC is one way of choosing the rate, and compound interest is its forward-running face on a savings account.