August 22, 2014
Previously we have discussed IP valuation methodsconsidering the fact that all relevant decisions related to the usage of IP (like development of product using the IP) is done at current moment. There will not be any change in decision irrespective of the change in market condition, industry condition, cost of product development etc. But in reality that is not that case, IP owner has the flexibility to change the decision related to usage of IP in future depending on the above factors. For this reason option pricing method provides much more accurate result on IP valuation.
Let us first see what option is:
An option gives buyer right, but not obligation, to buy (call option) or to sell (put option) a financial asset (say share of a company) at an agreed price (strike price) during a certain period of time or on a specific date (exercise date). In European option the right for buy and sell can be executed only on the specific date where as in American option the right can be executed anytime before the exercise date. For this buyer pays a certain amount to the seller which is called price of the option.
On the exercise date, if the share price is more than the exercise price, buyer of call option will exercise the option and will make profit. But if the share price is below the exercise price, then the buyer will not exercise the option. Considering the price which buyer has paid to the seller to purchase the option below is the payoff.
Exercise price = K
Share price at the date of exercise = ST
Payoff of the buyer of call option = ST – K, when ST> K
(Without adjusting the price of option) = 0, when ST ≤ K
Payoff of the buyer of put option = 0, when ST> K
(Without adjusting the price of option) = K – ST, when ST ≤ K
The pricing of option is determined by Black – Scholes model,
Price for call option c = S0N(d1) – Ke-rTN(d2) where
d1 = [ln (S0/K) + (r + σ2/2)T] / σ√T
d2 = d1 – σ√T = = [ln (S0/K) + (r – σ2/2)T] / σ√T
Where S0 = Today’s stock price
r = continuously compounded risk free rate
σ = stock price volatility
T = option maturity period
K = exercise period
N(x) = cumulative probability distribution for a standardized normal distribution
Price of put option = Ke-rTN(-d2) – S0N(d1)
Now let us see one scenario where a company wants to invest and develop an IP.
The investment has following stages
Also other assumptions are
Now, if we use traditional NPV analysis them
Expected NPV of the project = -450 + 800 – 400 x e-0.1 = USD (-12K). As the expected NPV is negative the firm decided not to invest.
But the investment formanufacturing and testing of the prototype can be treated as option. The company has the flexibility of abandon the prototype manufacturing and testing in one year if the expected payoff from the IP decreases. Hence it can be treated as option where
K = USD 400K, S0 = USD 800K, r = 10%, σ = 80%
So price of the option will be = USD 475K
[d1 = (0.693 + 0.42) / 0.8 = 1.39, d2 = (0.693 – 0.22) / 0.8 = 0.59, N(d1) = 0.92, N(d2) = 0.72]
So the expected NPV of the project is = -450 + 475 = USD 25K. As the expected NPV is positive, the firm can decide to invest.
The probability of abandon = 1 – N(d2) = 1 – 0.72 = 0.28 = 28%
In the above example we have seen how option pricing can accommodate future uncertainty and can provide more accurate valuation compared to traditional discounting cash flow method. In the next blog we will discuss more examples of application of option pricing on IP valuation and how an IP investor can decide on buying/ selling/ developing an IP depending on the valuation of IP.