Corporate Finance

A Real Option’s Perspective of Capital Budgeting 
 245

As an assignment test whether the put–call parity held for the ACC stock assuming a suitable annual risk
free rate.^2

VALUATION OF OPTIONS

The Black-Scholes model is widely used in pricing options. The Black-Scholes formula values a European
call or put option as follows:

Value of call = S e(b-r)T N (d 1 ) – X e-rT N (d 2 )

Value of put = –S e(b-r)T N (–d 1 ) + X e-rT N (–d 2 )

where

S= stock price

X= strike price or exercise price,

b= cost of carry defined as risk-free rate – dividend yield (q),

T= time to maturity in years, and

σ^2 = variance in returns from the underlying stock.

d 1 =

()

T

TbXS

σ

ln (/ σ++^2 /2)

d 2 = d 1 – σ T

The function N (parameter) used in the formula is a mathematical notation for the cumulative normal
distribution function.

An Example

A call option has the following properties:

S= Rs 50

X= Rs 40

Rf= 5 percent

q= 3 percent

b = r – q = 0.05 – 0.03 = 0.02

T = 5 years

σ= 30 percent = 0.3

e= 2.7183, a constant

d 1 =

53.0

ln( 5 0/4 .0()0 02 ++ 3.0^2 /25)

= 0.8171

d 2 = 0.8171 – 0 3. 5 = 0.5582

N (d 1 )= N (0.8171) = 0.7931

N (d 2 )= N (0.1463) = 0.5582

Value of call = Se(b – r)T N (d 1 ) – X e–rT N (d 2 )

= 50 e(0.02 – 0.05)5 0.7931 – 40 e–0.05 × 5 0.5582 = Rs 16.74

(^2) Convert the annual rate into a compound daily rate.