Sensitivity analysis(6)Cost of capital
−50,000 +{5,000 ×[10 −(4 +3)] ×A} = 0where Ais the annuity factor.
A==3.333The annuity table (Appendix 2) for five years shows that 3.333 falls between the 15 per
cent figure (3.352) and the 16 per cent one (3.274). Thus a 1 per cent increase in the discount
rate (from 15 per cent to 16 per cent) causes a reduction in the annuity factor of 0.078 (from
3.352 to 3.274). The value of 3.333 lies 0.019 below the 15 per cent value, so the discount
rate applying to 3.333 is about 15^19 –– 78 per cent, that is, about 15.24 per cent.
(7)Life of the project
Of course, the same 3.333 annuity value must be used to deduce the life of the project, this
time assuming that the discount rate remains at 10 per cent (the original estimate).
The 10 per cent column in the annuity table shows that 3.333 falls between the four-year
figure (3.170) and the five-year one (3.791). This means that an extra year causes the annuity
factor to increase by 0.621 (from 3.170 to 3.791). The value of 3.333 lies 0.163 above the
four-year figure, so the period applying to 3.333 is about 4^163 –– 621 , that is, about 4.26 years.
(Note that this approach to finding the cost of finance and the life of the project is not
strictly correct as the relationship between these factors (cost of capital and time) and the
annuity factor is not linear. It is, however, fairly close to linear over small ranges so the above
figures are a reasonable approximation. An alternative to using this approach in this par-
ticular case (because it is an annuity) is to use the equation for an annuity, introduced in
Chapter 4, page 86.)
The results can now be tabulated, as follows:
Difference as percentage
Original Value to give of original estimate for
Factor estimate zero NPV the particular factor ( %)
Initial investment £50,000 £56,865 13.7
Annual sales volume 5,000 units 4,396 units 12.1
Sales revenue/unit £10 £9.64 3.6
Labour cost /unit £4 £4.36 9.0
Material cost /unit £3 £3.36 12.0
Cost of capital 10% 15.24% 52.4
Life of the project 5 years 4.26 years 14.8
From this it can be seen at a glance how sensitive the NPV, calculated on the basis of the
original estimates, is to changes in the variables in the decision. This provides some basis
on which to assess the riskiness of the project. If the decision makers concerned can look
at the table confident that all of the actual figures will fall within a reasonable safety margin,
then they would regard the project as much less risky than if this were not the case. If, on
the other hand, they felt that all other factors seemed safe but that they were doubtful about,
say, labour costs, the fact that only a 9 per cent rise would cause the project to become
unfavourable might reduce their confidence in the investment.
50,000
5,000 × 3