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What is Real Option? How to measure it?

Real option: It is an option available for investment like expansion, contraction and abandon etc if the NPV of investment project is positive. So that, the company earn more profit or minimise its loss in different economic conditions.

Type of real options:

Expansion option: It is an option to expand the business investment if the NPV of option is positive.

Abandon option: It is an option to abandon the investment project means sold out the investment at that point where investment incurred loss for investors.

Contraction option: It is an option to contract the investment project if it is not profitable for business anymore. It means the size of investment project is reduce.

Timing option: It is an option to delay or defer the investment project if the market conditions are not favourable for that investment.

Exit option: It is an option to exit from the investment project if company having a loss by adding no further cost on investment.

Switch option: It is an option to switch the investment project with another project which have same value to gain profit if market condition changes.

Option to expand:
Example: Company X wants to expand its business by launching a new product in market which cost Rs.5, 00,000. The risk free rate is 4% and standard deviation is 15%. The present value of investment is Rs.4, 50,000. Find out the value of expansion after two years.

 Solution: Using Binomial model:
U = e sd√t = e0.15*1 = 1.1618
∆t = 1
D = 1/u = 0.8607
P = ert – d/u-d =0.1801/0.3011 = 0.5981
1-p = 0.4019

Value of node B:
= e-rt (pVuu + (1-p)Vud)
=0.96 (0.5981*1, 07,400.65 + 0.4019*0)
= 0.96 (64,236.33 + 0)
= Rs.61, 666.88

 Value of node A:
= 0.96(61,666.88*0.5981 + 0*0.4019)
Value of expansion= Rs.35, 407.64
NPV = Present Value of investment – initial investment + Value of expansion of project
= 5, 00,000 – 5, 15,600 + 35, 407.64
= Rs.19, 807.64

Option to abandon

 Example: Company A had started a new project which is now incurring a loss due to which company has decided to sell it at Rs.5, 90,000. The present value of the project is Rs.6, 60,380 and the initial cost is Rs.720,000. The risk free rate is 3.6% and standard deviation is 20%. Find out if the project is abandon after 3 years is beneficial for the company or not.

Solution: Using Black Scholes model:
D1 = In(S/X) + (r + s.d2/2) t/ s.d*√t
= 0.11269 + 0.168 /0.3464
= 0.8103
D2 = d1 – s.d√t = 0.4639

Using interpolation to find out N(d1) and N(d2):
N(d1) = [(0.8103 – 0.81) / (0.83-0.81)]* (0.7967 – 0.7910) =0.000855
= 0.7910+ 0.000855
= 0.7918
N(d2) = [(0.4639 - 0.46) / (0.48 - 0.46)] * (0.6844 - 0.6772) = 0.001404
= 0.6772 + 0.001404
= 0.6786

Put option = Xe-rt *N(-d2) – SN(-d1)
= 5, 90,000*e-0.036*3 *(1-0.6786) – 6, 60,380(1-0.7918)
= 5, 29,600.28*0.3214 -1, 37,491.116
= Rs.32, 722.41

            NPV = Present Value of investment – initial investment + Value of abandon the project
            = 6, 60,380 – 7, 20,000 + 32,722.41
            = Rs.-26, 897.59

The project gives negative NPV. So, it is not beneficial for company to abandon the investment and sell it at Rs.5, 90,000.
Option to delay:
Example: Company has accepted the project of constructing the dam at the initial cost of Rs.85, 00,000 and the present value of that project is Rs.83, 20,000. The standard deviation is 12% and risk free rate is 4.9%.Find out the NPV if accepted it now and after 2 years NPV.
Solution: Using Binomial model:
U = 1.127
D = 0.887
∆t = 1
P = 0.68
1-p = 0.32

Value of node B:
=e-rt(pVuu+(1-p)Vud)
=0.95 (20, 67,473.28*0.68+0*0.32)
=0.95*(14, 05,881.83+0)
=Rs.13, 35,587.73

Value of node C:
=e-rt (pVdu + (1-p)Vdd)
= 0.95(0.68*0+0.32*0)
= 0.95*0
= Rs.0

Value of node A:
=e-rt (pVu + (1-p)Vd)
= 0.95 (13, 35,587.73*0.68+0.32*0)
=0.95 (9, 08,199.66+0)
=Rs.8, 62,789.68
NPV= present value of investment-initial investment + value of expansion project
= 83, 20,000-85, 00,000 + 8, 62,789.68
=Rs. 6, 82,789.68

The present NPV is negative -Rs50, 000 and after 2 years NPV will be Rs.6,82,789.68. So,2 years delay in project is beneficial for Company.

* You can measure real option with the help of Binomial model or black scholes model.






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