In this online tutorial, we detail the application of some straightforward real-options valuation techniques to increase the power of expectations investing.

Specifically, we walk through the following real-options analytical tools:

*Imputed real-options value*. This tool allows us to calculate the real-options value implied by the difference between the market's valuation of a company and the value of a company's existing businesses.
*Project value and investment expenditure*. We can estimate how large the potential project value has to be to justify the imputed real-options value. We can also estimate the size of the investment expenditure required to exercise the real options.

We use the Amazon.com case study as of February 22, 2000--developed in Chapter 8 of the book--as the case study for this online tutorial.

Readers who want to apply real-options tools may wish to download the accompanying spreadsheet.

**What Inputs Do We Need For These Calculations?**

To use these real-options tools, we need to enter the following eight inputs into the spreadsheet:

1. *Company name*. Our case study focuses on Amazon.com. Enter this in cell C4 of the "Inputs" worksheet of the "Real Options" spreadsheet.

2. *Current share price ($, per share)*. Amazon.com's share price as of February 22, 2000 equaled $64.00. Enter this in cell C5 of the "Inputs" worksheet of the "Real Options" spreadsheet.

3. *Estimated value of existing businesses ($, per share)*. By estimating Amazon's Operating Value Drivers and Other Value Determinants--and assuming a Forecast Period of 10 years--our case study calculates that the market valued Amazon.com's existing businesses at $35.00 a share. Enter this in cell C6 of the "Inputs" worksheet of the "Real Options" spreadsheet.

4. *Shares outstanding (in millions)*. Amazon.com had 345.2 million shares outstanding as of year-end 1999. Enter this in cell C7 of the "Inputs" worksheet of the "Real Options" spreadsheet.

5. *Life of option (in years)*. The life of a real option is the length of time that a company can defer an investment decision without losing an opportunity. As of February 22, 2000, we estimated that Amazon's real options had a life of 2 years. Enter this in cell C8 of the "Inputs" worksheet of the "Real Options" spreadsheet.

6. *Risk-free rate of return (%)*. This is the interest rate on short-term government debt. We assumed a risk-free rate at 5.0%. Enter this in cell C9 of the "Inputs" worksheet of the "Real Options" spreadsheet.

7. *Project volatility (%)*. This measures the potential variability of a project's future value. We estimated Amazon's volatility to be 100%. Enter this in cell C10 of the "Inputs" worksheet of the "Real Options" spreadsheet.

8. *Estimate of potential project value [S/X] (%)*. The numerator of this metric (S) equals the present value of the project's expected free cash flow. The denominator of this metric (X) equals the onetime incremental investment required to exercise the option at the time of exercise. Various potential project values (S/X) equate to different scenarios for the profitability of the project created if and when a company exercises its real option to enter a new business:

*S/X equals one*. In this scenario, the net present value (NPV) of the project at the time of decision is zero.
*S/X less than one*. In this scenario, the NPV of the project at the time of decision is negative.
*S/X greater than one*. In this scenario, the NPV of the project at the time of decision is positive.

In our case study, we assumed the S/X of Amazon's real option equaled 75%. Enter this in cell C11 of the "Inputs" worksheet of the "Real Options" spreadsheet.

Company |
Amazon.com |

Amazon.com's current share price ($, per share) |
$64.00 |

Estimated value of Amazon.com's existing businesses ($, per share) |
$35.00 |

Amazon.com's shares outstanding (in millions) |
345.2 |

Life of option [ T for Time ] (in years) |
2.00 |

Risk-free rate [ r ] (%) |
5.00% |

Volatility [ s ] (%) |
100.0% |

Estimate of potential project value (S/X) |
75.0% |

**Using These Inputs To Perform Real-Options Analyses**

Using these inputs, we first estimate the market's imputed real-options value by calculating the difference between the market's total valuation of a company, and the value of a company's existing businesses:

Amazon.com's current share price ($, per share) |
$ 64.00 |

__Estimated value of Amazon.com's existing businesses ($, per share)__ |
$ 35.00 |

Imputed per-share value of Amazon.com's real options |
$ 29.00 |

__Amazon.com's shares outstanding (in millions)__ |
345.2 |

Total imputed value of Amazon.com's real options ($, in millions) |
$ 10,009.5 |

Next, we calculate the potential value of the project when the company exercises the real option (S), and the size of the investment expenditure necessary to exercise the real option (X). Using the Black-Scholes options pricing model, we obtain the following results:

Total imputed value of Amazon.com's real options ($, in millions) |
$10,009.5 |

Estimate of potential project value [S/X] (%) |
75.0% |

Asset price [ S ] ($, in millions) |
$21,074.7 |

Strike price [ X ] ($, in millions) |
$28,099.6 |

The last step in real options analyses is to assess the reasonableness of the numerical results for S and X. This topic is covered on pages 131 and 132 in Chapter 8 of the book.