Discount rate/Tutorials

The present value of future costs and benefits

The present value V of a cost (or benefit) $c_{t}$ occuring after an interval of t years at a dicount rate of r is given by:

$V={\frac {c_{t}}{(1+r)^{t}}}$

The net present expected value of a future cost (or benefit) that has z possible values is given by calculating the value of $c_{t}$ in the above equation as:

${\mbox{c}}=\sum _{x=1}^{z}p_{x}c_{x}$

where $p_{x}$ is the probability of occurrence of the value $c_{x}$

The present value of a series of annual costs and benefits, ocurring after annual intervals 0 to n is given by:

${\mbox{V}}=\sum _{t=0}^{n}{\frac {c_{t}}{(1+r)^{t}}}$.

The social time preference rate

The social time preference rate, s, is given by:-

s = δ + ηg

where:

δ is the pure time preference rate (otherwise known as the utility discount rate);

η is the elasticity of marginal utility with respect to consumption; and,

g is the expected future growth rate of consumption.

Evidence based upon the structure of personal income tax rates in OECD countries suggests that the value of η for most developed countries is close to 1.4 . Estimates for the United Kingdom have ranged from 0.7 t0 1.5. .

The UK Treasury Green Book uses

δ = 1.5%, η = 1.0, g = 2%, yielding s = 3.5%

The Stern review uses

δ = 0.1%, η = 1.0, g = 2%, yielding s = 2.1%

The intergeneration transfer controversy

Sir Partha Dasgupta objected to the review's choice of eta on the grounds that it placed insufficient weight upon the comparative prosperity of current and future generations . Professor William Nordhaus also challenged the review's choice of eta and objected also to its arbitrary insistence on a zero pure rate of time preference.