Corporate Finance

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Corporate Finance

Note that the value of the option is more than its intrinsic value (50 – 40 = 10) because of time value.
A call option should be exercised if the stock price exceeds the strike price at expiration. That is if S > X.
For the sake of convenience let’s express it as a ratio. The option has value if S/X > 1. If S/X is less than 1,
the option should not be exercised as it is out of the money.
The variability (per unit of time) of returns is measured by variance. Multiplying the variance per unit of
time by amount of time to maturity gives the cumulative variance. The higher the cumulative variance, the
more valuable is the option. The Black–Scholes value of a European call option as a percentage of value of
underlying asset is available in a table form to make our life simple. A portion of the same is given here:

Option value (percent)

Share price/PV of Annual^ σ^ × Square root of time

exercise price 0.25 0.5 0.75 1.0

0.5 0 3 10 19

0.6 0 5 14 24

0.7 1 8 18 28

0.8 3 12 22 32

0.9 6 16 26 35

1.0 10 20 29 38

Consider the following data.

Stock price = Rs 50

Annual volatility = 25 percent

r= 5 percent

Exercise price = Rs 60

T= 4 years

PV of exercise price = 60/(1.05)^4 = Rs 49.36

Share price/PV(X) = 50/49.36 = 1.01

σ ( 4 ) = 25 percent × 2 = 50 percent

The cell at the intersection of row 6 and column 2, 20 percent, gives the call option value as a percentage
of value of underlying asset.

Option value = 20 percent of stock price = 0.2 × Rs 50 = Rs 10.

REAL OPTIONS

The traditional DCF methodology is based on the assumption that managers make an investment and then
wait to see what happens.

Cash flows

Investment