Expected NPV and real options (help)

Hello, :slight_smile:

Assume that you are the CFO Godin Corporation. You are considering an R&D project with an initial investment in pharmaceutical research in order to produce a neurobiological health product. If this investment is successful, you should make further investments in development: that is, various kinds of clinical testing. The drug can be evaluated in a single trial phase. Finally, if the health product proves to be safe and efficient, you will then have to make investments to produce and market it.
The initial outlay of this project that mainly consists in R&D costs is worth of $7 million and has to be paid at date 0. If this initial research phase is undertaken, there are three possible outcomes. The probability that each of the outcomes really occurs has been estimated from similar research projects in the past. More precisely, there is a 9% probability to create a highly efficient neurobiological health product, there is also a 16% probability to find a moderately efficient one and there is a 75% probability that the R&D phase fails.
If the initial research phase is successful, you will have to invest at date 1 in the development phase that will cost $30 million. If this development phase is undertaken there are two possible outcomes. Either your neurobiological health product will pass the safety tests of the Food and Drug Administration (FDA) (with an estimated probability of 45%) or it will fail them (with a 55% probability). Those probabilities hold whatever the efficiency of the health product. Notice that if the product fails to pass the safety tests, the project will not generate any Cash-Flows.
Finally, if your neurobiological health product has passed the safety tests of the FDA, you can produce and market it. A consulting company has estimated that a highly efficient health product would allow you to get, starting at period 3, a yearly FCF of $55 million for perpetuity. A moderately efficient health product would only allow you to get, starting at period 3, a yearly FCF of $30 million for perpetuity. Whatever the efficiency of your health product, in order to produce and market your health product, you will have to build factories and facilities. Those costs are worth off $250 million and have to be incurred at date 2.
You have estimated that the cost of capital for this project is 10% and that it will remain constant over all the period.
As a consequence, you have the following five potential outcomes if you invest in the project:
• Either the R&D phase fails,
• Or the R&D phase is successful and you create a highly efficient neurobiological health product that would successfully pass the safety tests of the FDA,
• Or the R&D phase is successful and you create a highly efficient neurobiological health product that fails to pass the safety tests of the FDA,
• Or the R&D phase is successful and you create a moderately efficient neurobiological health product that would successfully pass the safety tests of the FDA,
• Or the R&D phase is successful and you create a moderately efficient neurobiological health product that fails to pass the safety tests of the FDA.

  1. Compute the expected NPV of the project without real options. You may consider all the scenarios; compute the Present Value of the Cash-Flows for each scenario and finally, the expected NPV.
  2. Compute the expected NPV of the project including real options. The Real option embedded in this project is the possibility not to invest the $30 millions at date 1 at the development phase if the expected NPV of a moderately efficient neurobiological health product is negative (including the probabilities of the scenarios 4 and 5: i.e. that it passes the FDA test or not).

Here is it what I did :
CaptureSSSSSSSSSS
a) If The R&D phase fails : PV = 0 and NPV=0
b) If the R&D phase is successful and you create a highly efficient neurobiological health product that would successfully pass the safety tests of the FDA : PV = (55/10%)/(1.1)²= 454.5455M
c) If the R&D phase is successful and you create a highly efficient neurobiological health product that fails to pass the safety tests of the FDA : PV = 0
d) If the R&D phase is successful and you create a moderately efficient neurobiological health product that would successfully pass the safety tests of the FDA: PV= (30/10%)/(1.1)²=247.9339M

So the NPV1 of a highly efficient neurobiological health product is : 454.5455 - 250 - 30= 174.5455M
The NP1 of moderately efficient neurobiological health product is : 247.9339 - 250 - 30 = -32.0661M
Expected NP1 of the project is : (174.54559%) + (-32066116%)+(0*75%) = -51290.05M
NP0 is : -7- (51290.05/1.1) = -46634.31M. I’m not sure if what I did is correct

  1. I’m completely lost on the 2nd question. Could you please help me. Thanks in advance :slight_smile:

Good luck to everyone in the exam :slight_smile:

In this type of problem, you want to draw a tree diagram, so this is shown in the picture above. You see a timeline that starts at year 0 and extends to infinity. From years 0 to 1 there are three paths. The top path, labeled ‘H’, is for the highly efficient case. The middle path, labeled ‘M’, is for the moderately efficient case. The bottom path is for the case the R&D phase fails.

Notice that I used positive numbers to mean cost, so you have a positive cost of 7 million at time 0, a positive cost of 30 million at time 1, and a positive cost of 250 million at time 2.

First, there is no choice and we have to spend the money along any path regardless if it is profitable or not. We have to follow the path BACKWARDS.

Starting from the TOP of the tree, you get a cash flow of -55 million from years 3 on wards. This is a perpetuity. Recall from interest theory that the present value of this amount at time 2 (NOT 3) is -55/.1 million, or -550 million. If you combine with the cost of 250 million at time 2, your net cost at time 2 is -300 million (or, equivalently, your NPV at that time is 300 million).
To find the NPV at time 1, you have to take the present value of the expected amount you would get at time 2. Luckly, they gave you the probabilities to you, and the alternative path has an NPV of 0 at time 2 (since you won’t spend another 250 million if it doesn’t pass the FDA test).

The present value of the cost at time 1 is then
-300*.45/1.1 = -122.72727272… million
and the net cost at time 1 is -300*.45/1.1 + 30 = -92.72727272… million
(or equivalently, the NPV at time 1 is 92.72727272 million for the H path)

Following the same steps above but for the M path, and assuming I didn’t make a mistake, the net cost at time 1 should be 9.545454…million
(or equivalently, the NPV at time 1 is -9.54545454… million for the M path)

To find the net cost at time 0, we need to take the present value of the expected cost, and add the cost of 7 million incurred at time 0.
That’s (.09 * -92.72727272… + .16 * 9.54545454…) / 1.1 + 7
= about .80165 million in costs
(or, equivalently, an NPV of -.80165 million)

If, instead, we could choose not to spend 30 million if the product turns out to be moderately effective (and by extension, avoid the risk of paying 250 million at time 2), then the cost instead becomes
(.09 * -92.72727272…) / 1.1 + 7 = about -.58678 million
(or, equivalently, an NPV of .58678 million)


In summary, and assuming I didn’t make a calculator mistake,
NPV without Real Option: -$0.80165 million
NPV with Real Option: $0.58678 million