 In capital budgeting process, a financial analyst is also required to consider the project riskiness. What is risk? Risk is a variation in the expected outcome. Then, how risk is measured? Risk is measured through the dispersion in the outcome. So far as the project riskiness is considered, the riskiness of a project is measured through dispersion in its NPVs or the IRRs. To determine stand-alone riskiness of a project, we have three different tools that is sensitivity analysis, scenario analysis and simulation analysis. For that purpose, we have a certain example with us where we have unit price, annual unit sales, variable unit cost, fixed capital investment, networking capital investment, project life, depreciation on straight-line basis, expected solvage value, tax rate and the required rate of return. When using these variables to determine basic capital budgeting criteria, we have initial cash outflows of $350,000, operating cash flows of $104,000 and terminal non-operating cash flows of $86,000. Now using these figures, we have a project NPV of $121,157. Come to the sensitivity analysis. We know that in sensitivity analysis, we change only one input variable at one time and we see the effect of this one changed input variable on the expected outcome. On the screen, you can see we have six variables as input variables. We have a base value that we used earlier to determine the project NPV. We have a change in terms of low value and in terms of high value. Now you can see that we have a change for every variable, for the six variables in both of the classes, low value and high value. In this way, we have 12 changes as input variables. Now we can expect 12 different NPVs. If we see the lower half of the project NPV, we see that for the base case, we have equal amount of project NPV. And for the low estimates, we have a changing NPV for each of the variables because we change every time the variable and we observe the outcome. This means for the low estimates, we have six changes and we have six values. Similarly, for the high estimates, we have six changes and we have correspondingly six values of the NPVs. Now what is the riskiness of these high-low estimates that is shown in terms of the ranges? To determine range, we deduct lower value from the higher value and see the difference. If we see the difference, we can see that due to change in unit price, the variation is $98,674 whereas due to the change in required rate of return, we have a change of $57,890 in NPV. From this schedule, we can infer that the change in NPV is highly related with the change in unit price and the unit sales, but it is least related with the change of required rate of return. Then there is scenario analysis. In scenario analysis, we change many of the input variables at one time. So there is a difference between sensitivity analysis and scenario analysis. In sensitivity analysis, only one input variable is changed at one time, whereas in scenario analysis, several or all of the input variables are changed at a time. We have three different scenarios. You can see pessimistic, most likely, and the optimistic. Most likely scenario is the scenario that we have already used as our basic capital budgeting model. Now if you use the values of pessimistic and optimistic, we have different values for NPV and IRR. For pessimistic, we have a negative NPV, but for optimistic, we have the higher NPV than the most likely. For pessimistic option, we have IRR of 12.40 for 9% and for optimistic valuation, we have IRR of 34.24%. So being an optimistic analyst, we have positive NPV and higher IRR over the two other scenarios. The third analysis technique for risk analysis of a project, we have and that is the simulation analysis. In simulation analysis, we adopt a certain procedure for estimating the probability distribution of the outcomes. And in project, we have our output in terms of project NPV and IRR. So in simulation, we go for computing the distributions of project NPVs and project IRRs. Then in this simulation analysis, we have several variables that can be assumed being stochastic for their given distribution. They are on distributions and then we have iterations using these variables in terms of hundreds or even thousands of time. And that many iterations yield a good estimate to determine an acceptable NPV or IRR for the project. Dear students, you can see on the screen that there is an exercise for conducting simulation analysis. This exercise uses certain variables like fixed capital investment, expected life of the project, depreciation policy, unit sales, sales growth rate, sale price per unit, cash operating expenses, discount rate and tax rate using certain criterion. Then what is requirement of this exercise that is to determine NPV and IRR using the expected value of all the input variables. And once we have expected value of NPV and IRR, then we go for the simulation analysis and we will be having probability distributions for NPV and IRR. In scenario one, we determine the project NPV and the project IRR using the point estimates and this point estimates have been used as the basic capital budgeting technique. Now we have solution two after running the basic capital budgeting technique. In solution two, we will run a simulation model to develop so many iterations so that we can have certain distributions for project NPVs and the project IRRs. For that purpose, we use software at the rate of risk. This is the software that is used to run iterations for the simulation. And we have run 10,000 iterations. For each iterations, we have selected values for the five stochastic variables of our input variables and who are price output, output growth rate, cash operating expenses and solvage value of the project. We have derived assumed distributions of these variables using the 10,000 iterations while running the software that is at the risk. Then we compute NPVs and IRRs from these observations. Dear students, you can see the probability distribution graph of NPV and IRR after the 10,000 iterations. You can see that the peaks of these two distributions show that they are normally distributed and these are not peaked and not flat. And also we can see that both of these distributions for project NPV and IRR these are the relatively positive but skewed to the right side. On the screen, we can see the results of our iterations and these are the summary statistics for NPV and IRR. We first see the mean value of NPV and mean value of IRR and we can understand that there is no much difference from the actual value. The mean is relatively closer to the actual values. Then we have standard deviation of these two values. The skewness of these two values shows that both of the values in their probability distribution are positively secured and the values show they are slightly skewed to the right side. The values of cortices on these two NPV and IRR are almost closer to the point 3. This means that the probability distributions of these two values are not peaked and also not flat. Then we have a 90% confidence interval which shows that 90% values of NPV would fall from negative $379 to positive $7,413. Then for IRR we can see that 90% of the IRR values would fall from 11.38% to 25.13%. If we determine the correlation between input variables and NPV, between input variables and IRR, we see that we have higher correlation of NPV and IRR with the output as independent variable and which is 0.71 for NPV and output and 0.72 for IRR and output. We also have a good correlation between NPV and IRR with the output growth rate. But we have least correlation of these two output variables with the solvage value and that is 0.06 for NPV and 0.05 for IRR.