Estimating Value per Share  355 into the value of operations, a valuation adjustment must be made for the por- tion of the subsidiary not owned by the parent company being valued. Because noncontrolling interests by other companies are to a certain extent the mirror image of nonconsolidated assets, the recommended valuation ap- proach for noncontrolling interests is similar to that of nonconsolidated assets, described earlier in this chapter. In the case of a minority carve-out (in which the consolidated but not fully owned subsidiary is publicly traded), deduct the proportional market value owned by outsiders from enterprise value to determine equity value. Alternatively, you can perform a separate valuation using a DCF approach, multiples, or a tracking portfolio, depending on the amount of information available. Remember, however, that a noncontrolling interest is a claim on a subsidiary, not the entire company. Thus, any valua- tion should be directly related to the subsidiary and not to the company as a whole. Estimating Value per Share The final step in a valuation is to calculate the value per share. Assuming that you have used an option-based valuation approach for convertible bonds and employee options, divide the total equity value by the number of undiluted shares outstanding. Use the undiluted (rather than diluted) number of shares because the full values of convertible debt and stock options have already been deducted from the enterprise value as nonequity claims. Also, use the most recent number of undiluted shares outstanding. Do not use the weighted average of shares outstanding; it is reported in the financial statements to de- termine average earnings per share. The number of shares outstanding is the gross number of shares issued, less the number of shares held in treasury. Most U.S. and European companies report the number of shares issued and those held in treasury under share- holders’ equity. However, some companies report treasury shares as an in- vestment asset, which is incorrect from an economic perspective. Treat them instead as a reduction in the number of shares outstanding. If you used the conversion and exercise value approach to account for em- ployee options and convertible debt and stock options, divide by the diluted number of shares. With intrinsic value per share in hand, you have completed the mechanics of your valuation. But the job is not done. The next two chapters discuss how to stress-test your valuation using integrated scenarios and trading multiples. 357 17 Analyzing the Results Now that the valuation model is complete, we are ready to put it to work. Start by testing its validity. Even a carefully planned model can have mechan- ical errors or flaws in economic logic. To help you avoid such troubles, this chapter presents a set of systematic checks and other tricks of the trade that test the model’s sturdiness. During this verification, you should also ensure that key ratios like return on invested capital are consistent with the econom- ics of the industry. Once you are comfortable that the model works, learn the ins and outs of your valuation by changing each forecast input one at a time. Examine how each part of your model changes, and determine which inputs have the largest effect on the company’s valuation and which have little or no impact. Since forecast inputs are likely to change in concert, build a sensitivity analy- sis that tests multiple changes at a time. Use this analysis to set priorities for strategic actions. Next, use scenario analysis to deepen the understanding that your valua- tion provides. Start by determining the key uncertainties that affect the com- pany’s future and use these to construct multiple forecasts. Uncertainty can take the form of a simple question (will a product launch be successful?) or a complex one (which technology will dominate the market?). Construct a com- prehensive forecast consistent with each scenario, and weight the resulting equity valuations by their probability of occurring. Scenario analysis will not only guide your valuation range but also inform your thinking about strategic actions and resource allocation under alternative situations. Validating the Model Once you have a workable valuation model, perform several checks to test the logic of your results, minimize the possibility of errors, and ensure that you understand the forces driving the valuation. Start by making sure that the