Question

In 2008, the company Imaging Dragons, Inc. was formed by three entrepreneurs, to develop, produce, and market a new and potentially extremely beneficial tool in medical diagnosis. Two of the partners were graduates of the John’s Hopkins School of Medicine, and one a PhD student in epidemiology at the University of Florida. The Hopkins graduates had, together, developed a new technique and related software package to process MRI scans of the 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. Their work was an extension of earlier two-dimensional image processing work developed by one and which had been used extensively in the other’s medical practice for analyzing the effects of various lesions, on a patients' speech. 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, the more advanced three-dimensional software program promised to be much more accurate than any other methods in diagnosing lesions. Whilst a variety of other scientists around the world had developed their own MRI imaging software, this new three-dimensional program was very different and far superior to any other existing software for image processing.

Whilst surfing, the three gentlemen decided that they would form Imaging Dragons, Inc., with the goal of developing and producing a commercial software package that hospitals and doctors could adopt for radiologic interpretations. Shortly thereafter, they were approached by the Phantogramic Corporation, a large medical imaging and software company. Phantogramic 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. Being the most mathematical of the group, the UF graduate student was asked by the others to use the most advanced statistical tools available to decide whether or not to accept the Phantogramic offer. They agreed that if the offer was rejected, their plan would be to continue their own development of the software package in the next six months. This would entail an investment of approximately $200,000, which they felt could be financed through the partners' personal savings.

If Imaging Dragons were successful in their effort to make the three-dimensional prototype program fully operational, they must also decide amongst two alternative development strategies. One alternative would be to apply after six months time for a $300,000 Small Business Innovative Research (SBIR) grant from the National 1nstitute of Health (NIH). The SBIR money would then be used to further develop and ·market their product. The other alternative would be to seek further capital for the project from a venture capital firm. In fact, they had successfully chatted up the venture capital firm Nugrown Development. Nugrown Development had proposed that if Imaging Dragons were successful in producing a three-dimensional prototype program, Nugrown would then offer $1,000,000 to Imaging Dragons to finance and market the software package in exchange for 80% of future profits after the three-dimensional prototype program became fully operational. (Because NIH regulations do not allow a company to receive an NIH grant and also receive money from a venture capital firm, Imaging Dragons would not be able to receive funding from both sources.)

The partners knew that there was substantial uncertainty concerning the likelihood of receiving the SBIR grant. They also knew that there was substantial uncertainty about how successful Imaging Dragons might be in marketing their product. He felt, however, that if they were to accept the Nugrown Development offe1 the profitability of the product would probably then be higher than if they were to mark.et the product themselves.

If Imaging Dragons were not successful in making the three-dimensional prototype program fully operational, they felt that they could still apply for an SBIR grant with the two-dimensional software program. He realized that, in this' case, they would be less likely to be awarded the SBIR grant. Furthermore, clinical tests would be needed to fine-tune the two-dimensional program prior to applying for the grant. They estimated that the cost of these additional tests would be around $100,000.

The decision facing Imaging Dragons was whether to accept the offer from Phantogramic or to continue the research and development of the three-dimensional software package. If they were successful in producing a three-dimensional prototype, they would have to decide either to apply for the SBIR grant or to accept the offer from Nugrown. If they were not successful in producing a three-dimensional prototype, they would have to decide either to further invest in the two-dimensional product and apply for an SBIR grant, or to abandon the project altogether. In the midst of all of this uncertainty, they also wondered whether the cost of the Nugrown offer (80% of future profits) might be too high relative to the benefits ($1,000,000 in much-needed capital). Clearly the partners needed to think carefully and rationally about the decisions Imaging Dragons was facing.

Estimates of Revenues and Probabilities

Given the intense competition in the marketplace for medical imaging technology, they knew that there was substantial uncertainty surrounding the potential revenues of Imaging Dragons over the next three years. They tried to estimate these revenues under a variety of possible scenarios. Table 1 shows their data estimates of revenues under three possible scenarios ("high profit," "medium profit," and "low profit") in the event that the three-dimensional prototype was to become operational and if they were to receive the SBIR grant. Under the "high profit" scenario the program would presumably be very successful in the marketplace, yielding total revenues of $3,000,000. In the "medium profit" scenario, they estimated the revenues to be $500,000, while in the "low profit" scenario they estimated that there would be no revenues. They as­ signed the following estimated probabilities of these three scenarios: 20%, 40%, and 40% for the "high profit," "medium profit," and "low profit" scenarios, respectively.

Table 2 shows the data estimates of revenues of Imaging Dragons in the event that the three-dimensional prototype became operational and they were to accept the financing offer from Nugrown Development. Given the higher resources that would be available to them ($1,000,000 of capital), they estimated ·that under the "high profit" scenario the program would yield total revenues of $10,000,000. In the "medium profit" scenario, they estimated the revenues to be $3,000,000; while in the "low profit" scenario, they estimated that there would be no revenues. As before, the partners estimated probabilities for the three scenarios to be 20%, 40%, and 40% for the "high profit," "medium profit," and "low profit" scenarios, respectively.

Table 3 shows data estimates of the revenues generated by Imaging Dragons, in the event that the three-dimensional prototype was not successful and if they were to receive the SBIR grant for the two-dimensional software program. In this case, they considered only two scenarios: "high profit" and "low profit." Note that the revenue estimates are quite low. Under the "high profit" scenario the program would yield total revenues of $1,500,000. In the "low profit" scenario, they estimated that there would be no revenues. The three partners estimated probabilities of the scenarios to be 25% and 75% for the "high profit" and the "low profit" scenarios, respectively.

They also gave serious thought and analysis to various other uncertainties facing Imaging Dragons. After consulting with several physicians, they assigned 60% likelihood that they would be successful in producing an operational version of the three-dimensional software program. And, they further estimated that the likelihood of winning the SBIR grant after successful completion of the three-dimensional software program to be 70%. However, they estimated that the likelihood of winning the SBIR grant with only the two-dimensional software program would be only 20%.

Table 1.

Scenario         Probability            Total Revenues

High profit             20%              $3,000,000

Medium profit 40%              $500,000

Low Profit              40%              0

Table 2.

Scenario         Probability            Total Revenues

High profit             20%              $10,000,000

Medium profit 40%              $3,000,000

Low Profit              40%              0

Table 3.

Scenario         Probability            Total Revenues

High profit             20%              $1,500,000

Low Profit              40%              0

Answer 1

In order to solve this question, we will be creating a decision tree. This decision tree will entail the profits/losses made by the company in each of the scenarios presented to it. Please find the decision tree attached in a picture below:

Using the decision tree, we will now evaluate the profits received by the company in each scenario.

Scenario 1: Company accepts the Phantogramic offer. It will receive $150000.

Scenario 2: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for SBIR Grant and reaps High profit.

In this case, the company will have profit = 0.6(0.7)(+300000)(0.2)(3000000) - 200000 = 75,599,800,000.

Scenario 3: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for SBIR Grant and reaps Medium profit.

Profit = 0.6(0.7)(+300000)(0.4)(500000) - 200000 = 25,199,800,000.

Scenario 4: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for SBIR Grant and reaps Low profit.

Profit = 0.6(0.7)(+300000)(0.4)(0) - 200000 = -200000.

Scenario 5: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for Venture Capitalist and reaps 20% of the High profit. It was decided that the Venture Capitalist would take 80% of the profits. Therefore, the company will be left with 20% of the profits.

Profit = 0.6(0.3)(+1000000)(0.2)(0.2)(10000000) - 200000 = 71,999,800,000.

Scenario 6: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for Venture Capitalist and reaps 20% of the Medium profit. It was decided that the Venture Capitalist would take 80% of the profits. Therefore, the company will be left with 20% of the profits.

Profit = 0.6(0.3)(+1000000)(0.2)(0.4)(3000000) - 200000 = 43,199,800,000.

Scenario 7: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for Venture Capitalist and reaps 20% of the Low profit. It was decided that the Venture Capitalist would take 80% of the profits. Therefore, the company will be left with 20% of the profits.

Profit = 0.6(0.3)(+1000000)(0.2)(0.4)(0) - 200000 = -200000

Scenario 8: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is unsuccessful. The company applies for SBIR grant for the 2D device and reaps High profit.

Profit = 0.4(0.2)(0.25)(+1500000) - 200000 = -170000.

Scenario 9: Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is unsuccessful. The company applies for SBIR grant for the 2D device and reaps Low profit.

Profit = 0.4(0.2)(0.25)(0) - 200000 = -200000.

Thus, from the above scenarios, we can see that the company will make the highest profits in Scenario 2 that is, when Company does not accept Phantogramic offer and spends $200000 to develop the 3D prototype. The development of 3D device is successful. The company applies for SBIR Grant and reaps High profit.