Discount rate/Tutorials

The Ramsey equation

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 present value of future cash flows

The present value V of a cash flow $c_{t}$ 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 cash flow 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 cash flows after annual intervals 0 to n is given by:

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