Discount Rate

Discount rate is a term with two distinct meanings. In central banking, it is the interest rate a central bank charges commercial banks that borrow from it directly, most famously at the US Federal Reserve's "discount window". In finance and economics, it is the rate used to convert money expected in the future into its value today, the basis of every bond price, loan valuation and investment appraisal.

The two meanings share a root. Early central banks lent by "discounting" bills: they bought a bill of exchange for less than its face value, and the gap was their interest. The rate applied was the discount rate, and the same arithmetic of shrinking a future sum to a present one became the general tool of valuation. The term also differs from the merchant discount rate (MDR) charged on card payments, which is a fee, not an interest rate.

A promise of Rs 1,000 a year from now is worth less than Rs 1,000 in your hand today, because cash today could be saved and earn interest, and because promises carry some risk. The discount rate is the yardstick that tells you how much less. At 10%, next year's Rs 1,000 is worth about Rs 909 now.

The central bank meaning is simpler still. When a bank runs short of cash and nobody else will lend, it can go to the central bank, the "bank for banks". The price of that emergency borrowing is the central bank's discount rate.

In the United States, the Federal Reserve lends to depository institutions through its discount window. The main programme, primary credit, is available to sound banks against collateral, usually overnight. Since 2003 the primary credit rate has been set above the Federal Open Market Committee's target for the federal funds rate, so that banks look to the market first; since March 2020 it has been set at the top of the target range. A secondary credit rate, set higher, applies to banks that do not qualify for primary credit. Because the Fed stands ready to lend at this rate, it acts as a ceiling on overnight rates and as the practical form of the lender of last resort role.

Other central banks use different names for the same idea: a marginal lending facility, a standing lending facility, or a "Bank Rate". In Pakistan, the State Bank of Pakistan's historical "discount rate" was the rate on its 3-day repo facility, the window where short banks could borrow. In August 2009 that facility was turned into an overnight reverse repo facility, which became the ceiling of a new interest rate corridor, with an overnight repo facility as the floor. In May 2015 the SBP introduced a separate policy (target) rate for the overnight money market, and that policy rate, not the old discount rate, is now the headline figure announced at each monetary policy meeting. Older Pakistani texts and data series still use "discount rate" for the earlier period.

In finance, the present value of a single future payment is:

• $PV$ is the present value, what the future payment is worth today.
• $FV$ is the amount to be received in the future.
• $r$ is the discount rate per period, as a decimal.
• $t$ is the number of periods until the payment.

Example: a payment of Rs 100,000 due in three years, discounted at 10% a year, is worth $100{,}000 \div 1.1^{3} = 100{,}000 \div 1.331 \approx 75{,}131$ today. For a stream of payments, each one is discounted separately and the results added; this is how bond prices, net present value and discounted cash flow valuations are worked out. Discounting is the mirror image of compound interest: compounding grows Rs 75,131 at 10% for three years back to Rs 100,000.

The right rate depends on the use. Common building blocks include:

• The risk-free rate, usually the yield on government bills or bonds of matching maturity, such as Market Treasury Bills (MTBs) for short rupee cash flows.
• A risk premium for uncertain cash flows, such as a company's cost of capital or a lender's credit spread.
• An allowance for inflation when cash flows are in nominal terms.
• Social discount rates, set by governments to compare costs and benefits of public projects over decades.

Small changes in the rate move values a lot, especially for distant cash flows. This is why bond prices fall when interest rates rise, and why share prices of fast-growing companies, whose profits lie far in the future, are especially sensitive to rate changes. It also links the two meanings: when a central bank raises its policy and discount rates, the market rates used for valuation tend to rise too.

Related ideas on the wiki include the coupon rate on bonds, yield, and monetary policy more broadly.

• Federal Reserve: Discount Rate
• Federal Reserve Discount Window