Calculation of a risk-adjusted rate
A company has a provision for which the expected value of the cash outflow in three years’ time is £150, and the risk-free rate (i.e. the nominal rate unadjusted for risk) is 5%. However, the possible outcomes from which the expected value has been determined lie within a range between £100 and £200. The company is risk averse and would settle instead for a certain payment of, say, £160 in three years’ time rather than be exposed to the risk of the actual outcome being as high as £200. The effect of risk in calculating the present value can be expressed as either:
(a) discounting the risk-adjusted cash flow of £160 at the risk-free (unadjusted) rate of 5%, giving a present value of £138; or
(b) discounting the expected cash flow (which is unadjusted for risk) of £150 at a risk-adjusted rate that will give the present value of £138, i.e. a rate of 2.8%.