A project with an up$-$front cost at $t=0$ of $$1500$ is being considered by Nationwide Pharmaceutical Corporation $($NPC$).($All dollars in this problem are in thousands.$)$ The project's subsequent cash flows are critically dependent on whether a competitor's product is approved by the Food and Drug Administration. If the FDA rejects the competitive product, NPC$\text{'}$s product will have high sales and cash flows, but if the competitive product is approved, that will negatively impact NPC$.$ There is a $75\%$ chance that the competitive product will be rejected, in which case NPC$\text{'}$s expected cash flows will be $$500$ at the end of each of the next seven years $(t=1$ to $7).$ There is a $25\%$ chance that the competitor's product will be approved, in which case the expected cash flows will be only $$25$ at the end of each of the next seven years to $7).$ NPC will know for sure one year from today whether the competitor's product has been approved.

NPC is considering whether to make the investment today or to wait a year to find out about the FDA's decision. If it waits a year, the project's up$-$front cost at $t=1$ will remain at $$1,500,$ the subsequent cash flows will remain at $$500$ per year if the competitor's product is rejected and $$25$ per year if the alternative product is approved. However, if NPC decides to wait, due to the patent expiration, the subsequent cash flows will be received only for six years