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Carolyn identified potential revenues and costs related to the purchase of the Jones Company, the project currently under consideration. She wanted to present to the board a traditional discounted cash-flow (DCF) analysis that focused on the estimated NPV of this acquisition. But, she also wanted to present an analysis of this investment proposal based on the use of a real-options valuation model that, she thought, wfuld incorporate the estimated valuc of any growth or flexibility options embedded in this proposed investment. The data that were generated to complete the traditional DCF analysis are shown in Table I. The revenues and expenses are expected to increase by 10 percent each year for years 2 and 3 (with the exception of depreciation and amortization, which will not change). From the third year on, the growth in after-tax cash flow for the acquisition target is expected to be 5 percent into perpetuity. The investment bankers hired by Jones had established an asking price of $2.5 million. Table 1 Year 1 Revenues Cost of goods sold (excluding depreciation) Depreciation of manufacturing equipment and plant Operating expenses (excluding depreciation and amortization) Depreciation and amortization - office equipment (straight-line basis) Income tax rate (combined federal and state) $450,000 $200,000 $120,000 $75,000 $15,000 40 percent Based on advice from an expert consultant who had experience with similar acquisitions in the past, Carolyn estimated that the growth in revenues would likely be normally distributed with a volatility (i.e. dispersion) of 25 percent. Similarly, she has estimated that the growth rate for costs would be approximately normally distributed with a volatility of 15 percent. She has also assumed that the growth rate for costs and the growth rate for revenues would be negatively correlated, at - 20 percent. The risk-adjusted discount rate (ie the weighted average, after-tax cost of capital) for Jones is assumed to be 13.18 percent. Assume for valuation purposes that the risk-free rate is 5 percent for all maturities. Of course, sensitivity analyses can be performed to determine the sensitivity of the decision model to these assumed rates Carolyn pondered about flexibilities or growth options that might be embedded in this potential acquisition. For example, because there was considerable uncertainty regarding the cash-flow projections, Carolyn felt that Smith Company should consider delaying the acquisition by two years. If the acquisition were delayed, she estimated that at that time Smith would have to pay $3 million for Jones, the acquisition target. Alternatively, she thought that if the acquisition were made today, Smith could become more informed about Jones's operations and prospects over the next three years and could therefore, at some future point, either expand or contract the operations of the target. If the Jones Company were purchased today, Carolyn thought that three years hence Smith might be able to expand capacity and after-tax cash flow by 50 percent, at an end-of-year three cost of $0.8 million. Similarly, three years from now, Smith could cut back 30 percent of capacity, with an estimated after-tax cash flow from disposal of assets of $0.5 million Carolyn is now faced with the decision to value this project for the purpose of presenting it to the BOD. She wonders whether the proposed acquisition would be desirable if analyzed on the basis of a traditional DCF (i.e. NPV) approach. She also wondered about how she could incorporate into the analysis the various options described above. Finally, she wondered about the sensitivity of her recommendation with respect to the assumptions she made in conjunction with her evaluation of the proposed acquisition. 4. Case requirements 1. Define the term "real options" and draw a contrast to "financial options." In what sense does the existence of real options add value to a proposed investment project? 2. Provide an overview of the major types of real options that can be embedded in capital investment projects. 3. Distinguish between a traditional DCF analysis of a capital expenditure proposal (e.g. NPV) and a real-options analysis of that same proposal. 4. On the basis of the data provided in the case: What is the estimated NPV of the acquisition that Smith Company is considering? On the basis of your analysis, is the acquisition desirable? Why or why not? . . How sensitive is your recommendation to the assumption regarding the volatility of returns? For each investment alternative, calculate the estimated NPV under each of the following assumed project-return volatilities: 89.75, 70, 50, and 30 percent. Are the results you obtain expected? What can you conclude based on this analysis? Carolyn identified potential revenues and costs related to the purchase of the Jones Company, the project currently under consideration. She wanted to present to the board a traditional discounted cash-flow (DCF) analysis that focused on the estimated NPV of this acquisition. But, she also wanted to present an analysis of this investment proposal based on the use of a real-options valuation model that, she thought, wfuld incorporate the estimated valuc of any growth or flexibility options embedded in this proposed investment. The data that were generated to complete the traditional DCF analysis are shown in Table I. The revenues and expenses are expected to increase by 10 percent each year for years 2 and 3 (with the exception of depreciation and amortization, which will not change). From the third year on, the growth in after-tax cash flow for the acquisition target is expected to be 5 percent into perpetuity. The investment bankers hired by Jones had established an asking price of $2.5 million. Table 1 Year 1 Revenues Cost of goods sold (excluding depreciation) Depreciation of manufacturing equipment and plant Operating expenses (excluding depreciation and amortization) Depreciation and amortization - office equipment (straight-line basis) Income tax rate (combined federal and state) $450,000 $200,000 $120,000 $75,000 $15,000 40 percent Based on advice from an expert consultant who had experience with similar acquisitions in the past, Carolyn estimated that the growth in revenues would likely be normally distributed with a volatility (i.e. dispersion) of 25 percent. Similarly, she has estimated that the growth rate for costs would be approximately normally distributed with a volatility of 15 percent. She has also assumed that the growth rate for costs and the growth rate for revenues would be negatively correlated, at - 20 percent. The risk-adjusted discount rate (ie the weighted average, after-tax cost of capital) for Jones is assumed to be 13.18 percent. Assume for valuation purposes that the risk-free rate is 5 percent for all maturities. Of course, sensitivity analyses can be performed to determine the sensitivity of the decision model to these assumed rates Carolyn pondered about flexibilities or growth options that might be embedded in this potential acquisition. For example, because there was considerable uncertainty regarding the cash-flow projections, Carolyn felt that Smith Company should consider delaying the acquisition by two years. If the acquisition were delayed, she estimated that at that time Smith would have to pay $3 million for Jones, the acquisition target. Alternatively, she thought that if the acquisition were made today, Smith could become more informed about Jones's operations and prospects over the next three years and could therefore, at some future point, either expand or contract the operations of the target. If the Jones Company were purchased today, Carolyn thought that three years hence Smith might be able to expand capacity and after-tax cash flow by 50 percent, at an end-of-year three cost of $0.8 million. Similarly, three years from now, Smith could cut back 30 percent of capacity, with an estimated after-tax cash flow from disposal of assets of $0.5 million Carolyn is now faced with the decision to value this project for the purpose of presenting it to the BOD. She wonders whether the proposed acquisition would be desirable if analyzed on the basis of a traditional DCF (i.e. NPV) approach. She also wondered about how she could incorporate into the analysis the various options described above. Finally, she wondered about the sensitivity of her recommendation with respect to the assumptions she made in conjunction with her evaluation of the proposed acquisition. 4. Case requirements 1. Define the term "real options" and draw a contrast to "financial options." In what sense does the existence of real options add value to a proposed investment project? 2. Provide an overview of the major types of real options that can be embedded in capital investment projects. 3. Distinguish between a traditional DCF analysis of a capital expenditure proposal (e.g. NPV) and a real-options analysis of that same proposal. 4. On the basis of the data provided in the case: What is the estimated NPV of the acquisition that Smith Company is considering? On the basis of your analysis, is the acquisition desirable? Why or why not? . . How sensitive is your recommendation to the assumption regarding the volatility of returns? For each investment alternative, calculate the estimated NPV under each of the following assumed project-return volatilities: 89.75, 70, 50, and 30 percent. Are the results you obtain expected? What can you conclude based on this analysis