This is “Approaches for Dealing with Risk”, section 13.7 from the book Finance for Managers (v. 0.1). For details on it (including licensing), click here.

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## 13.7 Approaches for Dealing with Risk

PLEASE NOTE: This book is currently in draft form; material is not final.

### Learning Objectives

1. Explain risk in capital budgeting.
2. Describe and implement scenario analysis.
3. Describe and implement sensitivity analysis.

We have estimated the potential earnings from our projects, but what about the risk involved? What’s the likelihood that we estimated these cash flows properly? What the numbers are much worse? Ideally, the sytematic risk involved with our project has been accounted for by our WACC used (see previous chapter for discussion of this), but managers still need to account for projection errors and evaluate the potential range of outcomes. There are several ways to deal with risk in capital budgeting. We present two of the most common here: scenario analysis and sensitivity analysis.

Sensitivity analysisIndicates how much NPV will change if we change one particular variable. measures the sensitivity of our project to a change in one variable. Also called “what-if” analysis, it looks at how sensitive our outcome is to a change in one variable (for example, projected sales). Intuitively we know that our outcome is more dependent on certain inputs to our equation than to other inputs. If we change just that one variable (holding everything else constant), how much does the outcome change? Sensitivity analysis tells us by how much are we more sensitive to a change in sales than we are to a change in, say, WACC or some other variable. We can then dedicate resources to ensure a more accurate estimate for the inputs with the larger effects.

Scenario analysisUses several possible scenarios to determine the range of possible NPV outcomes. gives us several different ‘scenarios’ or likely outcomes for our project. We can analyze what will happen if we have a best-case, worst-case and most-likely-case scenario. This measures the variability of the returns and can present us with a variety of situations and financial outcomes so that we are adequately prepared for each one. In scenario analysis we can change many variables and estimate a new outcome. We can then look at the ‘range’ of possible outcomes by analyzing the difference between the best-case and worst-case scenarios.

For Project A, we had annual cash inflows (after-tax) of \$15,000 for five years. But what if our worst-case scenario occurred and the annual cash flows were only \$10,000 per year? Or what if, best case, we earned \$20,000 per year? What would our NPV be under each of these different scenarios? Let’s calculate.

Table 13.4 Gator Lover’s Ice Cream: Best Case, Worst Case, and Likely Scenarios

Project A
Initial Investment (\$48,000) r = 10%
Operating Cash Inflows
Year Best Case Most Likely Worst Case
1 \$20,000 \$15,000 \$10,000
2 \$20,000 \$15,000 \$10,000
3 \$20,000 \$15,000 \$10,000
4 \$20,000 \$15,000 \$10,000
5 \$20,000 \$15,000 \$10,000
Total \$100,000 \$75,000 \$50,000
NPV \$27,815.74 \$8,861.80 (\$10,092.13)

From Table 13.4 "Gator Lover’s Ice Cream: Best Case, Worst Case, and Likely Scenarios", we see that our previous NPV calculation was the most likely case and it had a positive NPV of \$8,861.80. The best case provides NPV equal to \$27,815.74 and the worst-case has a negative NPV of \$10,092.13. The NPV rangeThe difference between the best-case scenario and the worst-case scenario NPV. is the difference between the best case and the worst-case or in this situation a range of \$37,907.87. We can hopefully earn somewhere between a negative \$10,092 and a positive \$27,815. Obviously we hope for the \$27,815! But it’s helpful to know that we may lose \$10,092 under the worst-case scenario.

There are several other techniques a company can use to deal with risk in capital budgeting. Other, more sophisticated techniques exist (such as simulation analysis), but they are beyond the scope of this text.

### Key Takeaways

Risk is important to consider in capital budgeting. Fortunately we have several techniques to deal with risk.

• Sensitivity Analysis tells us how sensitive our NPV is to changes in one key input.
• Scenario Analysis gives us a NPV range between the best and worst case scenarios, and models the most likely outcomes.

### Exercises

1. Project J costs \$100,000 and is projected to earn \$50,000 each year for five years, with a discount rate of 10%. Calculate how sensitive NPV is to our discount rate if it might be as high as 12%.
2. Compute the NPV for the best case scenario if Project J earns \$75,000 per year and the discount rate is only 9%.