MAKING DECISIONS AT BIO-IMAGING, INC. In 2004, the company Bio-Imaging, Incorporated was formed by James Bates, Scott Tillman, and Michael Ford, in order to develop, produce, and market a new and potentially extremely beneficial tool in medical diagnosis. Scott Tillman and James Bates were each recent graduates from Massachusetts Institute of Technology (MIT), and Michael Ford was a professor of neurology at Massachusetts General Hospital (MGH). As part of his graduate studies at MIT, Scott had developed a new technique and a software package to process MRI (magnetic resonance imaging) scans of brains of patients using a personal computer. The software, using state of the art computer graphics, would construct a three-dimensional picture of a patient's brain and could be used to find the exact location of a brain lesion or a brain tumor, estimate its volume and shape, and even locate the centers in the brain that would be affected by the tumor. Scott's work was an extension of earlier two-dimensional image processing work developed by James, which had been used extensively in Michael Ford's medical group at MGH for analyzing the effects of lesions on patients' speech difficulties. Over the last few years, this software program had been used to make relatively accurate measurements and diagnoses of brain lesions and tumors. Although not yet fully tested, Scott's more advanced three-dimensional software program promised to be much more accurate than other methods in diagnosing lesions. While a variety of other scientists around the world had developed their own MRI imaging software, Scott's new three-dimensional program was very different and far superior to any other existing software for MRI image processing. At James' recommendation, the three gentlemen formed Bio-Imaging, Incorporated with the goal of developing and producing a commercial software package that hospitals and doctors could use. Shortly thereafter, they were approached by the Medtech Corporation, a large medical imaging and software company. Medtech offered them $150,000 to buy the software package in its then-current form, together with the rights to develop and market the software world-wide. The other two partners authorized James (who was the "businessman" of the partnership) to decide whether or not to accept the Medtech offer. If they rejected the offer, their plan was to continue their own development of the software package in the next six months. This would entail an investment of approximately $200,000, which James felt could be financed through the partners' personal savings.|f BioImaging were suocEsful in their effort to make the three-dimensional prototype program fully operational, they would face two afte rnative development strategiE. 0ne alternative would be to apply after six months\" time for a $300,000 Small BusinEs Innovative Research {SEIIFI} grant from the National Institutes of Health {NIH}. The SBIR money would then be used to further develop and market their product. The other afternative would be to seek further capital for the project from a venture capital firm. In fact, Michael had had several discussions with the venture capital firm Nugrowth Development. Nugrowth Development had proposed that if BioImaging were successful in producing a three-dimensional prototype program, Nugrowth would then offer $1,000,000 to BioImaging to finance and market the software package in exchange for 80356 of future profits after the three-dimensional prototype program became fully operational. {Because NIH regulations do not allow a company to reoeive an NIH grant and also receive money from a venture capital firm, Bio-Imaging would not be able to receive funding from both sources.:| James knew that there was substantial uncertainty conoeming the likelihood of receiving the SEIIFI grant. He also knew that there was substantial uncertainty about how sucoessful Bio Imaging might be in marketing their product. He felt, however, that if they we re to aocept the Nugrowth Development offer, the profitability of the product would probably then be higher than if they were to market the prod uct themselves. If Bio-Imaging was not sucoessful in making the threedimensional prototype program fully ope rational, James felt that they oou Id still apply for an SBIR grant with the two-dimensional software program. He realiIed that in this case, they would be less likely to be awarded the SBIR grant. Furthermore, clinical tests would be needed to ne-tune the two-dimensional program prior to applying for the grant. James Etimated that the cost of these additional tam would be around $100,000. The decision problem faced by Bio-Imaging was whether to accept the offer from Medtech or to continue the research and development of the three-dimensional software package. If they were su coessful in producing a threedimensional prototype, they would have to decide either to apply for the SBIR grant or to accept the offer from Nugrowth. If they we re not sucoessful in producing a threedimensional prototype, they would have to decide either to further invest in the twodimensional product and apply for an SEJIFI grant, or to abandon the project altogether. In the midst of all of this, James also wondered whether the cost of the Nugrowth offer {80% of future prot: might be too high relative to the benefits {$1,000,000 in muchneeded capital}. Clearly James needed to think hard about the decisions Bio-Imaging was facing. Data Estimates of Revenues and Probabilities Given the intense competition in the market for medical imaging technology, James knew that there was substantial uncertainty surrounding the potential revenues of Bio-Imaging over the next three years. James tried to estimate these revenues under a variety of possible scenarios. Table 1.2 shows James' data estimates of revenues under three scenarios {"high profit,\" "medium prot,\" and r'Iow profit\"] in the event that the threedimensional prototype were to become operational and if they were to receive the SBIR grant. Under the "high prof'rt\" scenario the program would presumably be very suocessful in the marketplaoe, yielding total revenues of $3,000,000. In the "medium profit\" scenario, James estimated the revenues to be $500,000, while in the "low profit\" scenario, he estimated that there would be no revenues. James assigned his estimated probabilities of these three scenarios to be 20%, 40%, and 40% for the "high profit," r'medium prot,\" and r'low profit" scenarios, respectively. Table 1.3 shows James' data estimates of revenues of Bio-Imaging in the event that the threedimensional prototype were to become operational and if they were to accept the financing offerfrom Nugrowth Development. Given the higher resources that would be available to them {$1,000,000 of capital}, James estimated that under the \"high prot" soenario the program would yield total revenues of $10,000,000. In the \"medium profit\" scenario, James estimated the revenues to be $3,000,000,- while in the r'low profit\" scenario, be estimated that there would be no revenues. As before, James assigned his estimated probabilities of the three scenarios to be 2056, 40%, and 40% for the \"high profit," r'medium prot,\" and "low profit\" scenarios, respectively. Table 1.4 shows James' data estimates of revenues of Bio-Imaging in the event that the threedimensional prototype were not successful and if they were to receive the SEIIR grant for the two-dimensional software program. In this case James considered only two soenarios: "high profit\" and \"low prot.\" Note that the revenue estimates are cru'rte low. Under the r'high prof'rt\" scenario the program would yield total revenues of $1,500,000. In the r'low profit\" soenario, James estimated that there would be no revenues. James assigned his estimated probabilities of the scenarios to be 2556 and 15% forthe "high profit\" and the "low profit\" scenarios, respectively. James also gave serious thought and analysis to various other uncertainties facing Elio Imaging. After consulting with Scott, he assigned a 0096 likelihood that they would be su coessful in producing an operational version ofthethree-dimensional software program. Moreover, after consulting with Michael Ford, James also estimated that the likelihood of winning the SEIIR grant after suocessful completion of the three-dimensional software program to be T056. However, they estimated that the likelihood of winning the SBIR grant with only the two-dimensional software program would be only 20%. TABLE 1.2 Scenario Probability Total Revenues Estimated revenues High Profit $3,000,000 $500,000 of Bio-Imaging, if the Medium Profit 40% Low Profit 40% three-dimensional prototype were operational and if Bio-Imaging were awarded the SBIR grant. TABLE 1.3 Scenario Probability Total Revenues Estimated revenues High Profit 20% $10,000,000 Medium Profit 40% $3,000,000 of Bio-Imaging, if the Low Profit 40% 50 three-dimensional prototype were operational, under financing from Nugrowth Development. TABLE 1.4 Scenario Probability Total Revenues Estimated profit of High Profit 25% 51.500,000 75% $0 Bio-Imaging, if the Low Profit three-dimensional prototype were unsuccessful and if Bio-Imaging were awarded the SBIR grant. Find the optimal decision strategy and compute for the EMV