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–Not very systematic
•10% ±on most uncertain parameters
–Why 10%?
Sensitivity Analysis
•Break even analysis
–Conventionally used to estimate break even production level (capacity utilisation)
–Can also be used for other parameters –‘switching values
•Range of Estimates
–‘Best’
–‘Optimistic’
–‘Pessimistic’
–Not very systematic
•10% ±on most uncertain parameters
–Why 10%?
Sensitivity Analysis
•±likely order of variation
•Break even tests (switching values)
–What % change →NPV = 0
–Only accurate when the relationship between change in variable and change in NPV is linear
•Linear/Non-Linear tests
–Linear-% change in price or quantity
–Non-Linear–delay in implementation, removal of component, use of different material etc.
Linear Relationship (e.g. price)
•If relationship between variable and NPV is linear we can estimate switching values:
–e.g. if a 10% fall in sales price reduces the NPV from 6539 to –11195 then the switching value is:
%100*121121PPPNPVNPVNPV%7.3%100*10.829.710.8)6539111956539
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TABLE 15.1 SENSITIVITY TESTS FOR PROJECT EXAMPLE
NPV Change in NPV Switching Value
Discount Rate 4% 8% 12% 4% 8% 12% 4% 8% 12%
NPV at Market Prices
Base Value of NPV 17352 6539 -733
Sales Price -10% -5342 -11195 -14853 -22693 -17734 -14120 -7.6% -3.7% 0.5%
Production -10% 9358 391 -5552 -7993 -6147 -4819 -21.7% -10.6% 1.5%
Machinery Price +10% 14994 4310 -2845 -2358 -2229 -2113 73.6% 29.3% -3.5%
Cotton Lint Price +10% 10261 932 -5247 -7091 -5607 -4514 24.5% 11.7% -1.6%
Labour Costs +10% 13122 3213 -3397 -4230 -3326 -2664 41.0% 19.7% -2.8%
NPV to Equity Capital
Base Value of NPV 7936 3346 294
Sales Price -10% -10279 -11195 -11509 -18215 -14542 -11803 -4.4% -2.3% -0.2%
Production -10% 2248 -1101 -3250 -5688 -4447 -3543 -14.0% -7.5% -0.8%
Machinery Price +10% 5932 1726 -1044 -2005 -1620 -1338 39.6% 20.7% 2.2%
Cotton Lint Price +10% 2837 -788 -3113 -5100 -4135 -3407 15.6% 8.1% 0.9%
Labour Costs +10% 4905 909 -1699 -3032 -2437 -1993 26.2% 13.7% 1.5%
Source: Project Planning and Analysis for Development p. 314
Limitations of Sensitivity Analysis
•It tells us the impact of particular changes but not the probability that they will occur
•It looks at one change at a time but what happens if a combination of factors occur?
•This can be partially taken into account through scenario analysis (e.g. optimistic, best, pessimistic estimates for combination of variables)…..
•…but this still does not tell us about probability –for this we need to do a risk analysis
Responses to Uncertainty
•Delay decision and collect further information to reduce uncertainty
–Increase certainty of estimates or…….
–Undertake risk analysis
•Change project design e.g.
–Use alternative raw materials
–Use alternative sources of energy
–Adopt smaller scale of operation
–Use contracts
–Diversify production
Summary
•Nothing is certain –all estimates have a margin of error
•Different enterprises have different attitudes t