So we've covered a range of very popular project evaluation techniques. But I don't want to mislead you into thinking that the role of the financial manager is to simply sit there and say yes or no as each new project comes along. We need to be able to value add more than that to the organization. This is where sensitivity analysis comes in. As we saw from these surveys, sensitivity analysis is quite often employed by managers around the world by CFOs when considering whether they should invest in new projects. So, let's discuss the technique. Sensitivity analysis involves testing how changes or errors in our estimates of variables, impact upon the final NPV calculation, which of course reflects the wealth that we expect to create from the project. Ultimately, sensitivity analysis is designed to provide us with additional tools beyond simply whether we should accept or reject a project. It can assist management in knowing the variables that they should collect more information for, prior to the commencement to the project, so we can get a better estimated of the NPV of the project. Then, once the project has started, we know where we should direct our particular attention. Because we need to remember, that managerial attention, managerial time is a scarce resource and it needs to be managed efficiently. So there are four simple steps to this approach. Firstly, we identify the variables that contribute to the project success, that is that feed into the NPV calculation. We then estimate optimistic and pessimistic values for each of those variables as opposed to simply using the expected values. Third, we calculate, in inverted commas, NPV numbers, but really they're just DCF calculations, on the basis of these optimistic and pessimistic values, allowing each variable in turn to swap between its optimistic and pessimistic whilst keeping all other variables at their expected values. We then rank the variables according to the change in NPV induced from changing from optimistic to pessimistic. Sounds very confusing, but it's quite simple. Let's do an example. Let's go through an example. Let's demonstrate the technique with the following example. We have a new production process which requires $8.5 million up-front and will last for 3 years. The appropriate discount rate is 10% per annum and all cash flows occur at year end. We've got an expected sales volume of 25,500 units per annum. An expected sales price per unit of $347. And an expected variable cost per unit of $193. So the difference between the sales price and the variable cost is what's known as a contribution margin, and that's generating our net cash flows. So we take the difference between those two numbers, multiply that by the number of units that we expect to sell and that gives us our expected cash flow on a per annum basis. We discount those cash flows at a risk-adjusted discount rate of 10% each year, that's accumulating to reflect the fact that we're waiting one, two or three years for it. And we offset that against the initial investment required. The NPV of this project is $1,265,868, so using the NPV approach to project evaluation, this project is acceptable, and we would accept it. But who cares? The role of the financial manager goes far beyond simply approving, or rejecting projects that are presented to them. The financial manager needs to have daily input into how the operations of the firm are conducted. So let's demonstrate how sensitivity analysis can aid us in that. What we've come up with here are pessimistic, and optimistic estimates of each of the variables in question. So, our pessimistic estimate of sales volume is $22,000 per unit. That's a 3,500 units per annum decrease relative to the expected value. The optimistic estimate, 3,500 units per annum more so. Sales price per unit, $290, is our pessimistic sales price. Our optimistic sales price, $380 per unit. Okay, and so on and so forth. For variable costs, $230, as a pessimistic variable costs per unit. They've increased from $193. Alternatively, an optimistic estimate has it then decreasing to $175. So the key to the sensitivity analysis approach is to recalculate the NPV of the project using pessimistic and optimistic estimates for each variable in turn, whilst keeping the other variables at their expected values. So working first with sales volume, we calculate an NPV that's pessimistic using 22,000 as opposed to 25,500 units per annum keeping the other variables at their expected values about $193 variable cost per unit and $347 as a sales price per unit. And when we do that, we end up with an NPV of minus $74,545. Now we've considered the optimistic estimate for sales volume. 29,000 units per annum. Keeping the other variables at their expected values once again, we have simply substituted these higher sales figures per annum, sales volume and we end up with an NPV of a bit over $2.6 million. So the take away here, what we do next, is compare the pessimistic NPV with the optimistic NPV. So subtract, minus $74,545 from 2,606,000 and we end up with a range of $2,680,000. Now what that reflects is the sensitivity of the project to move in-between optimistic and pessimistic estimates. When we repeat these for each of the three variables, moving between optimistic and pessimistic whilst keeping the other two variables at their expected values, we end up with this range of NPV estimates. The range of the ranges, if you like, are sales volume, was $2.68 million. Sales price, we end up with a range of NPVs of $5.7 million, and variable costs $3.487 million. So when we rank those according to their range of estimates, we say that the most important variable, firstly, is to collect more information about, and then to manage once the project commences, the sales price, then variable costs, then finally sales volume. The intuition from those numbers is demonstrated very clearly with the following graph where we plot the NPV generated using in turn pessimistic, expected, and optimistic outcomes for each of the variables. And we see that the greatest range in NPVs, the greatest vertical distance, if you like, is for sales price over variable costs over sales volume. So how do we use this information? Well, there's two ways. Firstly, prior to commencing with the project, we'll collect more information about sales price. Because we now know that sales price is a key variable in terms of the sensitivity of the wealth created from the project if we're to go forward with it. So we'll engage our marketers to get out there and collect more information about whether we can achieve the sales price that we expect to. If we decide to go ahead with what's clearly a positive NPV project then this will inform our sales strategy. We won't market this product as a discounted product. We market this product on the basis of, for example, high quality, to make sure that we can at least achieve our expected sales price figure. So we use the technique to direct managerial attention to where we can get our biggest bang for our buck. But where did our optimistic and pessimistic forecast come from? How optimistic is optimistic? How pessimistic is pessimistic? If you think about the technique, sensitivity analysis requires us to compare firstly for each variable an NPV using a pessimistic forecast with an NPV for that variable using an optimistic forecast of that variable. So, there needs to be a common basis of comparison within a variable, and then we compare those ranges between variables as well. So let's firstly deal with sales volume. What we have here is a probability distribution which simply plots each outcome that could occur to sales volume against the likelihood of it occurring. So for example, the likelihood of achieving sales volume of 27,000 units per annum is equal to 15%. So, the first stage having determined what the probability distribution looks like, the first stage is to determine your benchmark probability measure. And so my optimistic measure here is 29,000 units because there's a 5% probability, which I've determined somewhat arbitrarily but we'll come back to that point in a moment. There's a 5% probability that sales volume will be 29,000 units or greater. We can also do the same for the pessimistic outcome where if we set a value of 22,000 units per annum, we now have a probability of 5% in that left-hand tail. Switching to our two other variables, sales price per unit and variable cost per unit. We're now dealing, as you can see, with skewed distributions. But, once again, we've maintained our consistency, because we have 5% probability in our pessimistic forecast of sales price per unit, and 5% probability in our optimistic forecast as well. Similarly with the variable cost per unit. The key is that in order for us to compare optimistic and pessimistic outcomes for any individual variable, you need to set the probabilities equal to each other. That also enables you to then compare the range in NPVs between variables. Firms and financial analysts use a wide variety of project evaluation techniques, quite often more than one at the same time. Discounted cash flow techniques are the most popular as they're aimed at measuring value creation as opposed to simple profitability. Caution needs to be exercised when using these alternative techniques. We always need to check our answer against common sense and we should avoid fishing for the best metric that'll get the project done. So what next? Well, in this module, we're focused on the investment decision but there's some other very important decisions that CFOs face on a day to day basis including, how do we raise equity capital via an IPO? How do we determine the optimal mix of debt and equity? What impact will debt have on the risk and return of the firm's shareholders? And how do we determine the optimal payout policy to maximize returns to shareholders? These will be considered in the next module.