HP 12C Financial 12C Depreciation, Black-ScholesFormula for Valuing European Options, 254 Appendix E: Formulas Used

254 Appendix E: Formulas Used

Black-Scholes Formula for Valuing European Options

P	= current asset price.
r%	= risk-free rate (continuous, per time unit).
s%	= volatility (continuous, per time unit).
T	= term of option (same time unit as r% and s%).
X	= exercise price of option.
N(z)	= probability that a unit normal random variable is less than z.
Call Value	= P × N(d1) – Q × N(d2)
Put Value	= Call Value + Q – P
where	:
d1	= LN(P/Q)/v + v/2, d2-= d1 – v
Q	= Xe( – T × r % / 1 0 0 ) , v=s%/100× T

Depreciation

L= asset’s useful life expectancy.

SBV = starting book value.

SAL = salvage value.

FACT = declining-balance factor expressed as a percentage.

j= period number.

DPNj	= depreciation expense during period j.
RDVj	= remaining depreciable value at end of period j
	= RDVj–1– DPNj where RDV0 = SBV – SAL
RBVj	= remaining book value = RBVj–1– DPNj where RBV0 = SBV
Y1	= number of months in partial first year.

File name: hp 12c pt_user's guide_English_HDPMF123E27	Page: 254 of 275
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