Question

1. 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 $550 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 $20 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 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 $550 per year if the competitor’s product is rejected and $20 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 (t = 2 ... 7).

Assuming that ALL cash flows are discounted at 10%, if NPC chooses to wait a year before proceeding, how much will this increase or decrease the project’s expected NPV in today’s dollars (i.e., at t = 0), relative to the NPV if it proceeds today? (Find NPV of the project with and without the option and take a difference, i.e. find the value of the timing option)

Answer 1

Given are two scenarios-

1) If the competitors product is rejected,

2) If the competitiors product is approved.

Interest rate- 10%

Accordingly, we compare NPV of above scenarios, given if the project investement starts today(t=0) versus project investment starts after 1year(t=1).

Key point to remember-

• A positive NPV number means present value of revenues exceeds the present value of costs which means a profitable project.
• A negative NPV means present value of costs exceeds the present value of revenues which means loss making project.

Scenario 1-

To calculate NPV, we need to calculate Present Value of each cash flow, for which we use formula given below:

Present Value = Future Value/(1+Interest rate)^number of year

Project investment stating today (t0):

t0= -1,500/(1+10%)^0 = -1500; t1= 550/(1+10%)^1 = 500; t2= 550/(1+10%)^2 = 454.55; t3=550/(1+10%)^3 = 413.22; t4= 550/(1+10%)^4 = 375.66; t5= 550/(1+10%)^5 = 341.51; t6= 550/(1+10%)^6 = 310.46; t7= 550/(1+10%)^7 = 282.24

NPV = -1,500 + 500 + 454.55 + 413.22 + 375.66 + 341.51 + 310.46 + 282.24 = $1,177.63

Project investment starting after 1 year (t1):

t1= 1,500/(1+10%)^1 = -1,363.64; t2= 550/(1+10%)^2 = 454.55; t3=550/(1+10%)^3 = 413.22; t4= 550/(1+10%)^4 = 375.66; t5= 550/(1+10%)^5 = 341.51; t6= 550/(1+10%)^6 = 310.46; t7= 550/(1+10%)^7 = 282.24

NPV = -1,363.64 + 454.55 + 413.22 + 375.66 + 341.51 + 310.46 + 282.24 = $813.99

Scenario 2-

Project investment stating today (t0):

t0= -1,500/(1+10%)^0 = -1,500; t1= 20/(1+10%)^1 = 18.18; t2= 20/(1+10%)^2 = 16.53; t3=20/(1+10%)^3 = 15.03; t4= 20/(1+10%)^4 = 13.66; t5= 20/(1+10%)^5 = 12.42;

t6= 20/(1+10%)^6 =11.29; t7= 20/(1+10%)^7 = 10.26

NPV = -1,500 + 18.18 + 16.53+ 15.03 + 13.66 + 12.42 + 11.29 + 10.26 = $-1402.63

Project investment starting after 1 year (t1):

t1= -1,500/(1+10%)^1 = -1,363.64; t2= 20/(1+10%)^2 = 16.53; t3=20/(1+10%)^3 = 15.03; t4= 20/(1+10%)^4 = 13.66; t5= 20/(1+10%)^5 = 12.42;

t6= 20/(1+10%)^6 =11.29; t7= 20/(1+10%)^7 = 10.26

NPV = -1,363.64 + 16.53+ 15.03 + 13.66 + 12.42 + 11.29 + 10.26 = $-1284.45

Calcultion of increase or decrease in project’s expected NPV is as per below,

t1 - t0

Scenario 1: $813.99 - $1,177.63 = $-363.64 (there is a decrease of NPV if the project starts after 1 year i.e decrease in NPV or profit).

Scenario 2: $-1,284.45 - $-1,402.63 = $118.18 (there is an increase in NPV if the project starts after 1 year i.e decrease in negative NPV or loss).