## Risk Analysis in Capital Budgeting

There is also, of course, the situation of complete certainty. This relates to a decision over which the decision maker has complete control, and is thus likely to be confined to the production sphere. This is so because the existence of external agents in marketing and distribution means that knowledge is incomplete, and the creative aspect of R&D means that outcomes are unknown in advance. Capital budgeting is a part of Investment decision. Capital budgeting deals with long-term decisions.

Cash flow is basis of a sound capital budgeting technique.If a finance manager predicts how a project will turn out, he is likely working under conditions of certainty. For example, if one invests ₹20,000 in five-year central government bonds that are expected to yield a 7% tax-free return, the return on investment @ 7% can be calculated fairly accurately. Risk is described as a situation in which the chances of an occurrence are known and can be determined objectively or subjectively.

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For example, if ₹10 lakhs is invested in the stock of a company (that extracts coal from a mine), the likely return cannot be calculated with 100% certainty. Because of this high uncertainty, the rate of return on the above investment may range from minus 100% to some incredibly high amount. As a result of this high variability, the project is considered relatively risky. The risk of an investment is then linked to the uncertainty of the project’s expected future returns: the more variable the expected future returns from the project, the riskier the investment.

When an incident is non-repetitive and special in nature, and the finance manager is unsure about the odds themselves, confusion reigns supreme. Uncertainty is a personal experience. No conclusion can be drawn from frequency distributions in such a case. We have no idea what the odds of the various outcomes are.

As a result, the expected value of any decision cannot be calculated if the odds are absolutely uncertain or even meaningfully unknown. So far, no widely accepted methods for dealing with situations of uncertainty have been developed, whereas there are a variety of techniques for dealing with risk.

### Risk Analysis

It would have been a lot simpler if the results of the events had been known ahead of time. However, this is not the case in practise. The results of many activities are uncertain, and there is a significant amount of risk involved as the projects near completion and even after completion. Even if all of the characteristics of capital budgeting programmes are carefully considered, the project’s success cannot be assured.

Projects are correlated with various forms of risks, such as risk related to funding, risk related to execution and monitoring, and so on. An organisation’s primary goal is to make a profit at the end of the day. Risk-adjusted discount rate is used in discounted cash flow strategies to analyse a capital budgeting decision. The impact of time on the investment returns is taken into account by using discounted cash flow techniques.

When such an analysis is done with a discount rate, it is possible to change the inflation rate as well as the necessary rate of return. The higher rate of return is used to discount the riskier projects. The company may also set two different discount rates, one for routine projects and the other for high-risk projects. Different discount rates may also be assigned to different projects, depending on the level of risk associated with each project.

## Sources of Risk

Inflation, increased interest rates and changing general economic conditions impact all businesses and sectors. There are several methods for incorporating risk perception into capital budgeting project assessment. Risk arises from different sources, depending on the type of investment being considered, as well as the circumstances and the industry in which the organisation is operating. Some of the sources of risk are as follows:

### Size of the Investment

A large project requiring larger investments entails more risk than a small project because if the large project fails, the business will experience a much greater loss and will be forced to liquidate. Furthermore, in many instances, the cost of a project is known ahead of time. There is always the possibility that the final price will differ from the estimate. It’s impossible to predict exactly how much building, debugging, design, and development would cost.

Rather than settling for a single estimate, it seems more practical to specify a cost range and the likelihood of each value within the range occurring. The wider the range, the less trust the decision maker has in his calculation. Forecasting possible returns from a project will not be a simple task. Instead of making an investment decision based on a single estimation of cash flow, a number of estimates would be preferable.

### Reinvestment of Cash Flows

Reinvestment risk refers to the possibility of risk that an investor will not be able to reinvest the cash flows he receives from an investment at a rate comparable to their current rate of return. The rate of interest at which an investor reinvests his cash flows is called reinvestment rate.

The rate of return available for reinvesting the profits from the 20%, 2-year cycle determines whether an organisation can consider a project that offers a 20% return for 2 years or one that offers a 16 percent return for 3 years. The risk of the business not being able to reinvest funds when they become available is a persistent risk in the management of fixed assets and cash flows.

### Life of the Project

In capital budgeting projects especially the long-term projects. In projects, the risks may occur at any stage of the project life cycle or they may also appear throughout the project. For instance, over the entire life of a projects, various risks such as operational and maintenance risks, legal and regulatory risks, delays in project development, technology risks, political and social risks, financial risks, market risks, and commercial risks may occur. For example, the COVID-19 pandemic severely impacted the construction activities which can be considered as an operational risk.

## Techniques of Risk Analysis

One of the most difficult elements of capital budgeting is risk analysis. There have been several different methods proposed, and no technique can be considered the strongest in all cases.

Some of the prominent techniques of risk analysis and management include:

- Probability
- Variance and Standard Deviation
- Coefficient of Variation
- Risk-Adjusted Discount Rate
- Certainty Equivalents
- Sensitivity Analysis
- Scenario Analysis

Let us discuss a few of these techniques.

### Probability

Probability can be described as the likelihood that an event will occur. If an event is most likely to occur, we assume that it has a probability of 1. If an event is extremely unlikely to occur, we assume that it has a probability of 0. As a result, the likelihood of all events occurring is between 0 and 1. An objective likelihood is a probabilistic prediction that is based on a large number of observations. Personal or subjective probabilities are probability assignments that represent a person’s state of conviction rather than empirical data from a large number of trials.

In case of projects and capital budgeting, the expected cash flows are calculated as the sum of likely cash flows of the project multiplied by the probability of these cash flows.

Expected Net Cash Flow ENCF NCF P

Expected net present value = Sum of present values of expected net cash flows

ENPV = 1 k = + ∑

Where, t = period and k = discount rate

**Example:** The initial investment for projects X and Y is ₹12,000.

The cash flows for to projects X and Y at end of first year and their probabilities are as follows:

Project X | Project Y | |||
---|---|---|---|---|

Possible Event | Cash Flow (₹) | Probability | Cash Flow (₹) | Probability |

A | 12000 | 0.20 | 12000 | 0.20 |

B | 16000 | 0.30 | 15000 | 0.30 |

C | 18000 | 0.30 | 18000 | 0.30 |

D | 2000 | 0.20 | 19000 | 0.20 |

If the discount rate is 10%, what is the expected net present value of the projects and which project should be chosen?

**Solution:** Calculating Expected Value

Project X | Project Y | |||||
---|---|---|---|---|---|---|

Possible Event | Cash Flow (₹) | Probability | Expected Value (₹) | Cash Flow (₹) | Probability | Expected Value (₹) |

A | 12000 | 0.20 | 2400 | 12000 | 0.20 | 2400 |

B | 16000 | 0.30 | 4800 | 15000 | 0.30 | 4500 |

C | 18000 | 0.30 | 5400 | 18000 | 0.30 | 5400 |

D | 2000 | 0.20 | 400 | 19000 | 0.30 | 3800 |

ENCF | 13000 | 16100 |

Now, calculating the net present value for both projects.

The present value factor for 1 year at 10% discount rate is 0.9091.

Therefore,

Net Present Value of Project X = (13000 × 0.9091) – 12000 = 11818.3 – 12000 = – 181.7

Net Present Value of Project Y = (16100 × 0.9091) – 12000 = 14636.51 – 12000 = 2636.51

Accept Project Y.

### Sensitivity Analysis

You are already aware that projects rely heavily upon the cash flow forecasts which in turn depend upon the revenues and costs incurred in a project. The revenue earned by a project depends on factors like sales and market share. For calculating the NPV or IRR of the project, we need to make the accurate predictions of independent variables.

Any change in the independent variables can change the NPV or IRR of the project. In sensitivity analysis, the degree of responsiveness of the dependent variable (i.e., cash flow) for a given change in any of the dependent variables (i.e., sales and market share).

Sensitivity analysis basically consists of three steps, which are as follows:

- Identifying all variables that affect the NPV or IRR of the project
- Establishing a mathematical relationship between the independent and dependent variables
- Studying and analysing the impact of the change in the variables

In sensitivity analysis, we get three different estimates of cash flows under the following three circumstances, which are as follows:

**Worst or pessimistic conditions:**Refers to the most unfavorable economic situation for the project**Normal conditions:**Refers to the most probable economic environment for the project**Optimistic conditions:**Indicates the most favorable economic environment for the project

**Example:** A manager needs to choose between two projects A and B when he is given the following information:

Particulars | Project A | Project B |
---|---|---|

Initial Cash Outlays | 250000 | 300000 |

Cash Inflow Estimates | ||

Most Optimistic | 50000 | 70000 |

Expected or Most Likely | 40000 | 50000 |

Most Pessimistic | 20000 | 30000 |

Required Rate of Return | 0.10 | 0.10 |

Economic Life | 10 years | 10 years |

**Solution:** Present Value Annuity Factor for 10 years at 10% discount rate is 6.145. Now, calculating the NPV of each of the project:

Expected Cash Inflows | Present Value | NPV |
---|---|---|

Most Optimistic | 307250 | 57250 |

Most Likely | 245800 | – 4200 |

Most Pessimistic | 122900 | – 127100 |

Expected Cash Inflows | Present Value | NPV |
---|---|---|

Most Optimistic | 430150 | 130150 |

Most Likely | 307250 | 7250 |

Most Pessimistic | 184350 | – 115650 |

In this case, the manager should choose Project B.

### Scenario Analysis

Scenario analysis extends the concept of sensitivity analysis to consider the impact of parameters on probability distributions of the input variables in capital budgeting analysis. In scenario analysis, the effect of changes in more than one variable at a time can be seen and analysed.

The scenario analysis helps in making changes in more than a single variable at a time. The management of an organisation can assess the variability in outcomes of a project under different scenarios and assess the risk of a particular project. However, one drawback of this method is that it is quite complex and involves multiple variables.

**Example:**

Bolt Inc. is a company that specializes in building tracks for high-speed trains in Electrasia. The company is the process of bidding for a new interstate train project. The chief bidding engineer has come up with a net present value estimate of ₹814.5 million. His inputs include the company’s weighted average cost of capital of 8%, cash inflows of ₹2 billion which are expected at the end of 3rd year, annual expenditures for year 1, 2 and 3 of ₹300 million per year. You are the chief investment officer and CFO has asked you to conduct a scenario analysis.

Find the best-case scenario and worst-case scenario.

**Solution:**

For the best-case scenario, assume a WACC of 6.5%, cash inflows of ₹2.1 billion at the end of 2nd year and cash outflows of ₹400 million at the end of 1st year and $500 million at the end of second year.

For the worst-case scenario, assume a WACC of 9%, cash inflows of ₹1.2 billion at the end of 4th year and cash outflows of ₹200 million at the end of each year for 4 years. The initial investment is 0 in all scenarios.

For the best-case scenario, the net present value (NPV_{B}) is ₹1,035 million while for the worst-case scenario, the net present value (NPV_{W}) is ₹202 million.

NPV_{B} = – ₹400 million + ₹2,100 million −₹500 million − 0 = ₹1,035 million

(1 + 6.5%)1 (1 + 6.5%)2

NPVW= -₹ 200 million × 1 – (1 + 9%)-4 + ₹1,200 million − 0 = ₹202 million

9% (1 + 9%)4

From this scenario analysis, we find that the net present value of the project is expected to be between ₹202 million and ₹1,035 million with the most likely figure to be ₹814.5 million.

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