Discount rate

Definition

In economics, the concept of discounting, as used for the purpose of cost/benefit analysis, arises from the behavioural observation that people prefer immediate satisfaction to deferred satisfaction. Thus the term “discount rate” refers to the compensation in terms of increased utility that a person requires as inducement to defer consumption (usually as a percentage per annum). The discount rate that a person experiences assuming no expectation of changing circumstances, is sometimes termed his “pure time preference rate” - to distinguish it from the inducement that he would require if he expected his consumption to increase. In that case, he would take account of the fact that, as his total consumption increased, he would experience a reduction in the marginal utility of any further increase . The proportionate further compensation that a person requires to take account of its diminishing marginal utility is referred to as that person’s “elasticity of the marginal utility of consumption”. (The derivation of that concept is attributed to a 1928 paper by the economist Frank Ramsey . There is a note on the “Ramsey equation”, and the estimation of the associated elasticity measure, on the tutorials subpage.). A community’s discount rate, taking account of rising consumption, is termed its “social time preference rate”. The social discount rate of a compunity togeher with its liquidity prefernce are major determinants of its market interest rate.

In financial theory, the uses of the term “discount rate” include its application to a variety of interest rates, including the rate charged for loans made to a country’s banks by its central bank , and the rates of return that are used as investment criteria by companies and by government agencies .

Financial implications

"Time is money". Financial theory has tried to implement the fact that one cash flow received in the future is worth less than the same cash flow received today (i.e. one dollar in one year vs. one dollar received today). Any investor preferring to receive a cash flow sooner rather than later can put his money in a riskless saving account. The general formula for the discounting of a cash flow is given by:

$NPV_{0}={\frac {FV_{t}}{(1+k)}}$

where $NPV_{0}$ is the Net Present Value, $FV_{t}$ is the Future value (i.e. of a cash flow) received at time $t$ and $k$ is the discount rate.

Rearranging this equation we have that:

$k={\frac {FV_{t}}{NPV}}-1$

The discount rate is the interest rate that links a future cash flow received a time $t$ to the same cash flow received now, at $t=0$. It takes into account the length of the time period (the longer time it is, the higher it should be) and the risk related to the cash flow (the more uncertain it is, the higher the discount rate is).

Assume I have $80, and I buy a government bond that pays me $100 in a year's time. The discount rate represents the discount on the future cash flow:

${\frac {(100)}{80}}-1=25\%$

Economic Policy

One of the major issues in economics is what is an appropriate discount rate to use under various circumstances. For example, in assessing the impact of very long-term phenomena such as climate change, use of any discount rate much more than 1% per annum renders long-term damage (occurring in, say, 200 years time) of negligible importance now.

Conversely, governments often take a short-term view of things, effectively applying discount rates of perhaps 20% p.a. or higher, on the grounds that anything they do or fail to do which has detrimental effects in (say) 10 or more years' time won't prevent their re-election sooner than that.

In practice, discount rates such as 2%, 3%, 5% and 10% are widely used in economics. However there is little consensus on what value is appropriate in any given circumstance, and it often makes a significant difference.

Context Specific Uses

Credit cards

The discount rate is a percentage of the dollar amount of the transaction that a merchant is charged for each credit card transaction.

Monetary Policy

The discount rate is the rate that an eligible depository institution (such as a bank) is charged to borrow short term funds directly from the central bank through the discount window. This is also known as the base rate, repo rate and/or primary rate, as a profit-making bank will need to charge rates higher than this to its customers.

External links

• Instruments of the Money Market: Table of Contents
  • Instruments of the Money Market: Chapter 3 - The discount window