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Merck & Company

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From the case material we can see that the value of licensing arrangement consists of three parts: Initial investment, Milestone Payment and Royalty Fee.
In Phase 1, Merck has to pay LAB 5 million initial investment no matter whether Davanrik will get approved by FDA in future.
In Phase 2, Merck has to pay LAB 2.5 million Milestone payment if Davanrik successfully complete Phase 1 with a probability of 60%.
In Phase 3, the amount of milestone payment Merck has to pay depends on the result of Phase 2. If Davanrik successfully complete phase 2 and was effective only for depression with the probability of 10%, then Merck has to pay 20 million to LAB. If Davanrik successfully complete phase 2 and was effective only for weight loss with the probability of 15%, then Merck has to pay 10 million to LAB. If Davanrik successfully complete phase 2 and was effective for both depression and weight loss with the probability of 5%, then Merck has to pay 40 million to LAB.
When finishing all three phases and getting approval by FDA, Merck has to pay Royalty fee to LAB based on the sales with 5% fee rate. After finish all three phases, there is a chance of 85% that Merck can launch Davanrik if the Phase 3 showed that it was only effective for depression and the commercialized present value is 1.2 billion. The chance decreased to 75% if Merck can only be effective for weight loss with 345 million commercialized present value. If Davanrik is effective for both, the chance of successfully launch is 70% with 2.25 billion commercialized present value. Under this scenario, there was 15% chance of a successful outcome for depression only and a 5% chance for weight loss only.
The probability mentioned above must be transformed to joint probability before calculation. For example, the probability of paying milestone payment in Phase 3 if Davanrik was effective only for depression is 6% (100%*60%*10%) instead of 10%. The final result showed that the initial investment is 5 million, the milestone payment is 4.8 million and the royalty fee is 6.88 million. So the expected value of the licensing arrangement is 16.68 million. (5+4.8+6.88). Table below is the detailed calculation process of cash flow in each stage. You can also check Appendix X for more details about the decision tree structure.

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