IFT Notes for Level I CFA^{®} Program

**Ranking ****conflicts between NPV and IRR**

For single and independent projects with conventional cash flows, there is no conflict between NPV and IRR decision rules. However, for mutually exclusive projects the two criteria may give conflicting results. The reason for conflict is due to differences in cash flow patterns and differences in project scale.

For example, consider two projects one with an initial outlay of $1 million and another project with an initial outlay of $1 billion. It is possible that the smaller project has a higher IRR, but the increase in firm value (NPV) is small as compared to the increase in firm value (NPV) of the larger project.

In case of a conflict, we should always go with the NPV criterion because:

- The NPV is a direct measure of expected increase in value of the firm.
- The NPV assumes reinvestment of cash flowsat the required rate of return (more realistic), whereas the IRR assumes reinvestment of cash flows at the IRR rate (less realistic).
- IRR is not useful for projects with non-conventional cash flows as such projects can have multiple IRRs , i.e., there are more than one discount rates that will produce an NPV equal to zero.

**Comparison between NPV and IRR**

NPV |
IRR |

Advantages |
Advantages |

Direct measure of expected increase in value of the firm. | Shows the return on each dollar invested. |

Theoretically the best method. | Allows us to compare return with the required rate. |

Disadvantages |
Disadvantages |

Does not consider project size. | Incorrectly assumes that cash flows are reinvested at IRR rate. The correct assumption is that intermediate cash flows are reinvested at the required rate. |

Might conflict with NPV analysis. | |

Possibility of multiple IRRs. |

Analysts and corporate managers should understand the logic and practicalities of different capital allocation methods.

If a company can invest in a project that earns more than its opportunity costs of funds, then the investment creates value and will increase shareholder wealth. Conversely, if the project earns less than the company’s opportunity cost of funds, then the investment decreases value and will reduce shareholder wealth. The return on invested capital (ROIC) is a measure that is often used to make these comparisons.

**Relationship between NPV and Stock Price**

- The value of a company can be measured as the existing value plus the present value of its future investments. NPV is a direct measure of the expected change in the firm’s value from undertaking a capital project.
- A positive NPV project should cause a proportionate increase in a company’s stock price. But, if the project’s profitability is less than expectations, then the stock price may be negatively impacted.

**Example**

A company is undertaking a project with an NPV of $500 million. The company currently has 100 million shares outstanding and each share has a price of $50. What is the likely impact of the project on the stock price?

**Solution:**

NPV of the project = $500 million. The overall value of company should increase by $500 million because of the project. Since there are 100 million shares outstanding, each share should go up by 500/100 = $5. The share price should increase from $50 to $55.

**Effects of Inflation on Capital Allocation process**

Capital allocation analysis can be done either in ‘nominal’ terms or ‘real’ terms. Nominal cash flows include the effects of inflation. Whereas, real cash flows are adjusted downward to remove the effect of inflation. Nominal cash flows should be discounted at a nominal discount rate, and real cash flows should be discounted at a real rate. In general, the relationship between real and nominal rates is:

(1 + Nominal rate) = (1 + Real rate) (1 + Inflation rate).

Inflation reduces the value of depreciation tax savings. This is because the depreciation charge is based on the asset’s original purchase price and it is not adjusted to match the current inflated price. Higher-than-expected inflation increases the corporation’s real taxes and shifts wealth from the corporation to the government.

Inflation does not affect all revenues and costs uniformly. The company’s after-tax cash flows will be better or worse than expected depending on how particular sales outputs or cost inputs are affected.

Inflation complicates the capital allocation process.

Real options are options that allow managers to make decisions in the future that change the value of capital investment decisions made today. As with financial options, real options are contingent on future events. The difference is that real options deal with real assets.

Types of real options include:

__Timing options__: A company can delay investing until it has better information.__Sizing options__: If a company can invest in a project and then abandon it if its financial results are weak, it has an abandonment option. Conversely, if the company can make additional investments when financial results are strong, it has a growth option.__Flexibility options__: Once an investment is made, operational flexibilities such as changing the price (price setting option), or increasing production (production flexibility option) may be available.__Fundamental options__: In this case, the whole investment is an option. For example, the value of an oil well or refinery depends on the price of oil. If oil prices are low, a company may not drill a well. If oil prices are high, the company may pursue drilling.

There are several approaches to evaluating capital allocation projects with real options. Four common sense approaches to real options analysis are presented below:

- Use DCF analysis without considering options. If the NPV of the project without considering options is positive, then we can go ahead and make the investment. The presence of real options will simply add even more value. Therefore, it is not necessary to determine the value of the options separately.
- If NPV is negative without considering options, then calculate project NPV as: Project NPV = NPV (based on DCF alone) – Cost of options + Value of options. Check if the project NPV turns positive after the options are considered.
- Use decision trees. They can help in many sequential decision-making problems.
- Use option pricing models. These models are complex and the company may need the help of special consultants.

**Example: **Production-flexibility option

(*This is Example 3 from the curriculum.*)

Sackley AquaFarms estimated the NPV of the expected cash flows from a new processing plant to be –$0.40 million. Sackley is evaluating an incremental investment of $0.30 million that would give management the flexibility to switch between coal, natural gas, and oil as an energy source. The original plant relied only on coal. The option to switch to cheaper sources of energy when they are available has an estimated value of $1.20 million. What is the value of the new processing plant including this real option to use alternative energy sources?

__Solution__:

NPV, including the real option = NPV based on DCF alone – Cost of options + Value of options

= -0.40 million – 0.30 million + 1.20 million = 0.50 million.

Without the flexibility offered by the real option, the plant is unprofitable. The real option to adapt to cheaper energy sources adds enough to the value of this investment to give it a positive NPV.

Common mistakes that managers make when analyzing capital allocation projects are:

*Not incorporating economic responses into the investment analysis*: For example, if a project is successful, competitors can enter and reduce the project’s profitability.*Misusing capital budgeting templates*: Many companies have standard capital budgeting templates. The manger may select a template that is not suitable for the project.*Pet projects*: Pet projects are projects backed by senior management. They may contain overly optimistic projections that overstate the project’s profitability.*Basing investment decisions on EPS, net income, or return on equity*: The compensation of mangers is sometimes tied to EPS, net income, or ROE. They may therefore reject even strong positive NPV projects that reduce these accounting numbers in the short run.*Using IRR to make investment decisions*: For mutually exclusive projects, the NPV and IRR criteria may give conflicting results. Since the NPV criterion is more economically sound than IRR, in case of conflicts decisions should be based on NPV.*Bad accounting for cash flows*: For a complex project, it is easy to make mistakes such as omitting relevant cash flows, double counting cash flows, etc.*Overhead costs*: Overhead costs such as management time, information technology support, financial systems etc. may be over or underestimated.*Not using the appropriate risk-adjusted discount rate.**Spending all of the investment budget just because it is available.**Failure to consider investment alternatives.**Handling sunk costs and opportunity costs incorrectly.*