Question

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'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'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 (t = 1 to 7). NPC will know for sure one year from today whether the competitor's product has been approved.

NPC will proceed with the investment today to take advantage of the untapped market potential and at the end of the project's life, after finding out about the FDA's decision about the demand for competitor's product, they will decide whether or not to renew the patent and rerun the project. The project rerun's up-front cost (at t=7) will remain at $1500, and the subsequent cash flows will remain unchanged and will be received for seven additional years (t=8...14).

They will only rerun the project if the rerun of the project adds value. Assuming that all Cash Flows are discounted at 10%, what is the NPV of the project with and without the growth option?

Answer 1

All financials are in $ '000

All Cash Flows are discounted at R = 10%

Upfront cost at t = 0 will be, C₀ = 1,500

Case 1: There is a p₁ = 75% chance that the competitive product will be rejected, in which case NPC's expected cash flows, C = $500 at the end of each of the next N = 7 years

NPV in case 1 = NPV₁ = -C₀ + C / R x [ 1 - (1 + R)^-N] = -1,500 + 500 / 10% x [1 - (1 + 10%)^-7] = $  934.21

Case 2: There is a p₂ = 25% chance that the competitor's product will be approved, in which case the expected cash flows, C = $25 at the end of each of the next N = 7 years

NPV in case 2 = NPV₂ = -C₀ + C / R x [ 1 - (1 + R)^-N] = -1,500 + 25 / 10% x [1 - (1 + 10%)^-7] = - $ 1,378.29

Hence, expected NPV = p₁ x NPV₁ + p₂ x NPV₂ = 0.75 x 934.21 + 0.25 x (-1,378.29) = $ 356.08

Hence, the NPV of the project without the growth option = $  356.08

=======================

Project with growth option:

They will only rerun the project if the rerun of the project adds value.

In case 1: The NPS is positive, the project thus adds value. Hence, the company will undertake rerun. Since financials remain unchanged, NPV of rerun at t = 7 will be same as NPV₁ = $ 934.21

NPV_{rerun, t = 0} = NPV₁ / (1 + R)^N = 934.21 / (1 + 10%)⁷ =  479.40

Hence, NPV with growth option = NPV₁ + NPV_{rerun, t = 0} = 934.21 + 479.40 =  1,413.61

In case 2: The NPV was negative hence the company will not undertake the rerun.

Hence NPV₂ with growth option = same as NPV₂ = -1,378.29

Hence, NPV with growth option = 0.75 x 1,413.61 + 0.25 x (-1,378.29) = $ 715.63