Real options
Real options (Black-Scholes Option Pricing Model)
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Contents:
Referenced syllabus: B2, B4 (d)
Terminologies
When appraising projects, the traditional NPV measure may not well incorporate the value of uncertainties, such as:
To value these uncertainties, option comes in.
Types of options: (Real Options)
Description |
Option types |
|
Option to delay |
This allows the business to defer the project. This is often found when the business has exclusive right to the product or market. |
Call option |
Option to expand |
This allows the business to make further investments. This is usually found that the original project NPV is negative, but by considering the expansion option value, the whole project NPV would become positive. |
Call option |
Option to abandon |
This allows the business the right to cease the project during its life and sell its cash flows. For example, a business may sell the venture to the investor at a specified period of time. |
Put option |
Option to redeploy (switch) |
This allows the business the right to switch the productive assets to another project. This is suitable when switching value is higher than the switching costs. |
Put option to switch; Call option to start the new project. |
Call option and put option
Option styles
The whole project value
Project value= Traditional value (NPV) + Option value*
*Option value
Factors affecting option value:
Call option value |
Put option value |
|
Market price |
|
|
Exercise price |
|
|
Time to expiry |
|
|
Volatility |
|
|
Interest rate |
Black Scholes Option Pricing Model Formulae (Given)
c= Call option value
Pa= Future cash flows from the investment
Pe =Project investment costs incurred
e= 2.7183 (exponential constant which is developed by scientist)
r= Risk free rate (not cost of capital)
t= Years remaining before costs incurred (for example, if the investment begins in 2 years’ time, t=2 not 24 months)
Put Option Formulae: (Given)
In Excel
Step 1 – lay out the five elements:
Pa
Pe
S (standard deviation)
r
t
Step 2 – use the Excel functions:
Functions |
Command |
Natural log |
=LN() |
Exponential (e) |
=exp() |
d1 |
=(ln(pe/pe)+(r+0.5*s^2)*t)/(s*sqrt(t)) |
d2 |
=d1-s*(sqrt(t)) |
Nd1 |
=normsdist(d1) |
Nd2 |
=normsdist(d2) |
Step 3 – show in the excel: (example):
B |
C |
D |
E |
F |
|
1 |
Pa |
100 |
d1 |
=((ln(C1/C2)+(C4+0.5*(C3^2)*C5)/(C3*sqrt(C5) |
|
2 |
Pe |
95 |
d2 |
=F1-(C3*sqrt(C5)) |
|
3 |
S |
0.5 |
N(d1) |
=normsdist(F1) |
|
4 |
r |
0.1 |
N(d2) |
=normsdist(F2) |
|
5 |
t |
0.25 |
Call |
=(C1*F3)-(C2*F4*exp(-C4*C5)) |
|
Put |
=F5-B1+B2*exp(-B4*B5) |
Current exam
In the exam, you do not need to learn the Excel formulae of how BSOP model is calculated. However, you can directly click ‘BSOP Calculator’ and input numbers into the ‘Variables’ cells’. The final answer is automatically generated.
Example:
Black Scholes Option Pricing model
Characteristics of Black Scholes Option Pricing model:
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Categories: : Advanced Financial Management (AFM)