decomposed into a risk-free rate, which is a compensation for the time value of money,
and a risk premium, which rewards investors for risk.Hence, the discount rate is:
Discount rate = Risk free rate + Risk premium
Suppose the risk free rate is 10% and the required risk premium is 5%, then we obtain
the following relationship between the discount rates and the time horizon:Table2
Details Period 1 Period 2 Period 3 Period 4
Discount factor
at 10%
0.91 0.83 0.75 0.68
Discount factor
at 15%
0.87 0.76 0.66 0.57
Difference 0.0395 0.0703 0.0938 0.1113
% Difference 4.35 8.51 12.48 16.29
The picture emerges quite clearly from table 2: the risk premium reduces the value of
one Leone at the end of period 1 from Le0.91 to Le0.87, or by 3.95 cents or 4.35%.
However, Leone at the end of period 2 is reduced substantially more by 7.03 cents or
8.51%, and the reduction increases with the time horizon.Hence, our NPV criterion, with appropriately set discount rates already accounts for the
fact that risk increases with the time horizon. In addition to this, we know much less
about the more distant future than the immediate future, and we would typically change
the design of a project if circumstances change in the future.Hence, we need to reflect the fact that one project commits our money for a short period
and another one for a long period in our analysis, because projects with longer time
horizons give us somewhat less flexibility, because flexibility has economic value.However, the appropriate tool for analyzing flexibility is decision tree analysis or
option analysis (so-called ‘real options’). We can extend NPV analysis and allow us to
quantify the value of flexibility and of ‘money at risk’ by using decision trees and real
option analysis. Using payback period is an illegitimate shortcut.PROFITABILITY INDEX