Sensitivity and Probability Analysis Sensitivity Analysis • Rationale: · To ascertain the riskiness of a project to changes in its input variables (i.e. sales volumes forecasts and direct unit cost forecasts) • Outcome: · The sensitivity (safety margin) of each input variable i.e. by how much it can vary before the investment decision changes from accept to reject or vice versa . The riskiest elements of the forecasts are those with the lowest absolute safety margins (i.e. nearest to zero) For a project with simple annuity cash flows: 1. Calculate the NPV of the project using forecasts of the input variables and the formulae: Annual contribution = (unit price - unit cost) x sales volume NPV = (annual contribution x annuity Factor) - initial investment 2. Calculate the value of each input variable in turn which would result in a project NPV of zero 3. The sensitivity of each input variable is the percentage change from its forecast to the value which would result in a project NPV of zero Example Input variables Forecasts Initial investment £50,000 Selling price £5.00 per unit Direct cost £3.50 per unit Sales volume 10,000 units per annum Project life 5 years Discount rate 10% Annual Contribution= (5-3.5)x 10000=15000 NPV=(15000×3.791)-50000=6865
Sensitivity to change in initial investment Set NPV to zero 0 =(15000 × 3.791) - Initial Investment Rearrange Formula and Solve for Initial Investment Initial Investment=15000 x 3.791 = 56865 Sensitivity Formula 56865-50000 =14% 50000 The initial investment can rise by 14% before NPV turns negative. Sensitivity to change in annual contribution Set NPV to 0 0=(C×3.791)-50000 Rearrange Formula 50000 C= 3.791 =13189 Sensitivity Formula 15000 13189-15000 =- 12% The annual contribution can fall by 12% before NPV turns negative. Sensitivity to change in project life 0=(15000 x AF)-50000 Solve the annuity factor AF= .50000 15000 =3.333 Interpolate to calculate breakeven project life. Breakeven is between 4 and 5 years, but where exactly between? 3.333- Lower project life anuuity =Breakeven Project Lifetime Higher project life annuity - lower project life ann 4+ =4.26 3.791-3.170 3.333-3.170 Sensitivity Formula 4+ (4.26-5.00)=5.00 =- 15%
The project life can be shortened by 15% before the NPV turns negative. Sensitivity to change in the discount rate 0=(15000 x AF)-50000 Solve the annuity factor AF= 15000 50000 =3.333 Per annuity factor table using a 5-year project life, 3.333 falls between 15% and 16%. 15+ 3.352-3.274 3.352-3.333 =15.2 Sensitivity Formula =52% 10 15.2-10 The discount rate can increase by 52% before the NPV turns negative. Input variable Initial investment £50,000 Forecast (NPV=£6,865) Breakeven (NPV=£0) £56,865 Annual contribution £15,000 Sensitivity +14% £13,189 -12% Project length 5 years 4.26 years -15% Discount rate 10% 15.2% +52% The project is: . Most sensitive to a change in the annual contribution · Least sensitive to change in the discount rate Actions Accept risks and proceed; or Conduct further analysis into the riskiest input variables i.e. check assumptions, conduct market research; or Avoid risks and seek a better alternative But consider timing of and control over the