**Why Should We Care About Real Options?**

Ignoring real options in a project often leads to an underestimation of the true project value. Because real options are not explicitly linked to cash flows, they may seem difficult to identify. Here are some typical examples of real options.

- The option to expand an existing investment project.
- Research and development (R&D) is an example of a growth option.
- The option to delay an investment project.
- The option to abandon a project that has already been undertaken.

From the above examples, we find that real options reflect the flexibility inherent in any capital investment process, which is often ignored by the DCF analysis because flexibility is hard to quantify in terms of cash flows. Fortunately, the breakthrough in option pricing theory provides us with the tools to find the value of these real options.

**Types of Reserves**

MW Petroleum’s estimated reserves can be classified into four major categories:

- proved developed reserves
- proved undeveloped reserves
- probable reserves
- possible reserves

Exhibits 3-6 tell us the production and cash flow projections for each of the four types of reserves.

**Risk-adjusted Discount Rate (RADR)**

For valuation purposes, we need an estimate of MW’s WACC to discount cash flows. Unfortunately, the case does not provide many details. This presents a very realistic problem that is often faced when attempting to do analysis in the real world. For example, because MW is a subsidiary of Amoco, its (market) equity value is not available. We do not have a clear idea about the debt and equity mix of MW either. However, we do have the following information:

The average asset (unlevered) beta for Oil companies = 0.64 (footnote b of Exhibit 2).

Given this information, we can use the CAPM to calculate the cost of equity for MW.

*Cost of equity = risk-free rate + beta * market risk premium*

For the risk-free rate, we can use the 1990 year-end 30-year US government bond yield given in the MW case in Exhibit 10. We choose the 30-year bond because the time horizon of the cash flows given in the case is 15 years (US government bonds are available in 10-year and 30-year maturities, but none in-between). Remember, projects in this industry are long-term and, therefore, call for a longer-term Treasury yield to proxy for the risk-free rate.

To determine the market risk premium, we can rely on a report that is maintained by the Stern School of Business at New York University. This report maintains historic annual returns on stock, T-bonds, and T-bills from 1928 – Current. The report also maintains the historical market-risk premium (MRP), starting in 1960. To be consistent with our risk-free rate, we want to use the historical market-risk premium for 1990 in the following report:

Next, we assume that Miller Equilibrium holds. This implies:

- The WACC, which is the risk-adjusted discount rate for discounting free cash flows, is the sum of the after-corporate-tax yield on taxable risk-free debt and a risk premium.
- The risk premium is the product of the asset beta (relative to the market portfolio of equity securities) and the market risk premium.
- The market risk premium is measured relative to the after-corporate-tax yield on taxable risk-free debt.

If taxes are zero, the WACC is independent of capital structure. Therefore, WACC = cost of equity.

**Identifying the Real Options**

Your first task is to identify the real options associated with these reserves. The fundamental characteristic of an option is that the option-holder has the RIGHT but not the obligation to do something (such as buy a stock or invest in a project). Clearly, the proved developed reserves of MW are assets-in-place rather than options. One way to verify this is to look at the capital expenditure in Exhibit 3, which is relatively small even in the early years compared with the cash from operations.

On the other hand, for proved but undeveloped reserves, the capital expenditure (shown in Exhibit 4) in the first two years are much larger than the cash from operations, which suggests that the proved undeveloped reserves should be treated as real options, as these large capital expenditures represent the investment needed to begin this project (i.e., the strike price on the real option). In addition, on the fourth page of this case, the case writer states that “MW could leave these (proved but undeveloped) reserves undeveloped while retaining the RIGHT to develop them later.” This clearly indicates that the proved undeveloped reserves should be valued using the option approach. Therefore, the following discussion will focus on MW’s proved undeveloped reserves and you will extend the analysis to the remaining types of reserves that represent real options.

**Valuing the Options**

Before we can apply the Black-Scholes model, we need to map project characteristics to parameters for the Black-Scholes model.

- Exercise Price (X)

In the real options context, the exercise price is equivalent to the expenditures required to acquire the assets. Note that total capital expenditure may include some routine expenditure. These should not be used when calculating X. Only extraordinary expenditure should be included. For proved undeveloped reserves (Exhibit 4), the capital expenditure for the first two years is $17.5 million and $17.7 million, respectively. These are significantly higher than the expenditure for the other years. Hence, the exercise price (X) should be the present value of these two cash flows.

We discount the two cash flows using the risk-free rate (8.24%). The argument here is that the risk associated with the capital expenditure is largely unsystematic (from the CAPM perspective). Note that we use 8.24% to be consistent with the early calculation regarding the discount rate. Strictly speaking, we should use the one-year and two-year risk-free rates from the yield curve. However, these numbers are not provided by the case.

- Underlying Asset Value (S)

The underlying asset value is analogous to the role of stock price in the Black-Scholes model. In this case, we can estimate S by discounting the projected net cash flows reported in Exhibit 4. The caveat is that we should exclude the extraordinary capital expenditures already identified with X, but include all other routine capital expenditures. We should use the risk-adjusted discount rate when calculating S.

- Time to Maturity (T)

Page 4 of the case states that “MW could wait 5-7 years…”. Therefore, we will need to do a sensitivity analysis, assuming that T ranges from 5 to 7 years.

- Risk-free Rate (r)

As mentioned above, we have chosen the 30-year government bond yield as the risk-free rate r.

- Volatility ()

The volatility of S is clearly linked to the volatility of oil and gas prices in this case. Exhibit 8 shows the annualized volatility in oil and gas prices. The volatilities are very high, ranging from 20% to 60%. In addition, the operating leverage due to fixed costs in the production process tends to amplify the volatility of S. Hence a reasonable assumption is to assume that volatility will range from 30% to 70% (this will be part of the sensitivity analysis).

The final step is to calculate real option values based on the estimates of the five parameters using the Black-Scholes model.

Hint: Instead of using Z-Tables for N(d1) & N(d2), Excel has a function for this, *NORMSDIST*. Excel is more accurate because it does not round.

Note: A (two-dimensional) sensitivity analysis is needed since both time to maturity (T) and volatility can take multiple values. You will construct a *Sensitivity Analysis Table (SAT)* that presents an analysis of what is projected to happen to the call option value under the different possible values for time to maturity (T) and volatility (). To construct the SAT requires that you use the “What-If Analysis” tool that is located under “Data Tools” on the “Data” tab. You will use the “Data Table” option under “What-If Analysis”. Part of the assignment is learning how to use this tool for sensitivity analysis. Therefore, if you have not used this previously, you will need to research its use.

**Required:**

1) Read the MW Petroleum Case in order to familiarize yourself with the proposed transaction and the challenges that are faced by Apache with respect to the valuation of MW Petroleum and how that affects the ability to secure financing.

2) You will calculate the real option values for all types of reserves for which you identify real options in the MW Petroleum Case using the Black-Scholes Option Pricing Model (BSOPM) as described above. Adding them together will give you the total option values for MW as a whole. Then, you will compare the DCF value of MW with and without real options (the firm without real options is represented by the Aggregate MW Production and Cash Flow Projection in Exhibit 7). Finally, you will compute the percentage change between the two. I have put together a MW Petroleum Case Excel spreadsheet template to help guide you.

3) You will draft a brief report on your analysis of the value of MW Petroleum. In your report, you will tie together the opportunities and challenges of the deal (found in the case study) with the conclusions of your valuation. How does your valuation affect these opportunities and challenges?

- You will turn in the report as a word document along with the spreadsheet. You will use the following guidelines:
- The report is required to be a minimum of 1 full page and a maximum of 2 full pages EXCLUDING any tables, graphs, or references. If you have any of these, you can use another page(s). You will use Times New Roman (12 pt.) font with ‘multiple’ spacing at 1.15. The ‘before’ and ‘after’ spacing will be set at 0 pt. and margins will be set to ‘normal’.
**Do not skip a line between paragraphs**

- If you are unsure about any of these settings, please ask!

**ALL work submitted is assumed to be the original work of the student, in the student’s own words, and any material copied from other sources needs to be properly cited and in quotation marks, where appropriate. When referencing online sources, only use well-known established sources and be wary of sites that have an agenda (i.e., political, financial, etc.). Please refer to the ‘Academic Integrity Policy’ in the syllabus for further details on plagiarism and penalties for minor and major infractions.**

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