A biotech firm must decide whether to purchase the patent to a new food additive

Question

                    A biotech firm must decide whether to purchase the patent to a new food additive, a low-cal starch substitute. It is estimated that the funds required to bring                     the additive to the market can be as high as $50 million or as low as $25 million. The payoff is uncertain as well: The present value of profits could be as                     high as $500 million or as low as $30 million. The risk free rate is %10, and the standard deviation of rate of return on biotech products is 35%. The patents                     life is estimated at one year                 

                    a) In a worst  2013 case scenario, how much is the patent worth?                 

                    b) In a best   2013 case scenario ,how much is the patent worth?

Please shown Work and watch out for symbolsin your response

Explanation / Answer

Hi,

Please find the answer as follows:

Part A:

Worst Case = 50 million (Highest Cost)

Profits = Revenue - Cost

Revenue = We will take 500 million with 50% probability and 0 million with 50% probability

Profits = .50*(500 - 50) = 225 million

Present Value = 225/(1+Discount Rate) = 225/(1+.10) = 204.55 million

Patent's Worth is 204.55 million

Part B:

Worst Case = 25 million (Lowest Cost)

Profits = Revenue - Cost

Revenue = We will take 500 million with 50% probability and 25 million with 50% probability

Profits = .50*(500 - 25) + .50*(30 - 25) = 240 million

Present Value = 240/(1+Discount Rate) = 240/(1+.10) = 218.18 million

Patent's Worth is 218.18 million

Thanks.

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