Question

You are the CFO of a major pharmaceutical firm. A division manager has presented senior management with an investment opportunity.
The project would require an investment of $95 million today

If the project succeeds, it will be worth $1 billion in a year. You estimate that there is only a 10% chance that the venture would succeed. If it fails, then in a year you will scrap the project and all of your firm’s $95 million investment will be lost.

Whether the venture succeeds or fails is independent of general market conditions.

The risk-free rate is 3%, the expected return of the market is 12%, and the standard deviation of the market return is 20%. Ignore taxes.

What is the NPV of the project?

$775 million

$870 million

$2.1 million

-$95 million

Answer 1

Answer: $2.1 million

Explanation:

It is mentioned the project is independent of the outcome of general market  which means that

=> beta = 0

Using the CAPM formula which is,

r=rt + B* (rm -rf)

=> r = 3% + 0*(12%-3%) = 3%

Expected value of Project in one year = $1 billions * 0.1

Expected value of Project in one year = $100 millions

NPV = Expected value of Project in one year/ (1 + 0.03) - Initial cost

NPV = 100/ (1 + 0.03) - 95

NPV = 97.1 - 95

NPV = $2.1 million

Answer 2

Answer:

$2.1 million

Explanation:

We solve for the expected monetary value at the end of the project:

$\left[\begin{array}{cccc}State&Return&Probability&Weight\\success&1000&0.1&100\\fail&0&0.9&0\\Total&&1&100\\\end{array}\right]$

Then, we have to know at which rate to discount this value so we use CAPM

$Ke= r_f + \beta (r_m-r_f)$

risk free = 0.03

market rate = 0.12

premium market = (market rate - risk free) 0.09

beta(non diversifiable risk) = 0 (independent from the market threfore no correlation.

$Ke= 0.03 + 0 (0.09)$

Ke 0.03000

Now we discount:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $100.00

time  1.00

rate  0.03000

$\frac{100}{(1 + 0.03)^{1} } = PV$  

PV   97.0874

NPV: 97.0874 - 95 = 2.0874 we round up and get 2.10 presnet value (in millions)