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 suggests that the value of η for most developed countries is close to 1.4 .

The present value of future cash flows

cThe 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:

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

The present value of a series of annual cash flows after annual intervals 0 to n is given by:

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