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BRILLIANT’S Analysis of Risk and Uncertainty in Investment Decisions 473

generated by simulation analysis may be used {ZU©`H$Îmm© Ûmam d¡[aE~ëg _| hmoZo dmbo MoÝOog Ho$ à^mdm|
by the decision maker to know the impact of
H$mo OmZZo Ho$ {bE VWm Eogo MoÝOog H$s àmo~o{~{bQ>r OmZZo Ho$
changes in variables and the probability of such
{bE {H$`m OmVm h¡Ÿ&
changes.
There are several techniques of simulation. {gå`wboeZ H$s {d{^ÝZ Q>opŠZŠg h¢ {H$ÝVw CZ_|
However, the Monte Carlo Method of {gå`wboeZ H$s _moÝQ>oH$mbm] ‘oWS> g~go H$m°_Z h¡Ÿ& `h
simulation is the most common. This method _oWS> aoÝS>_ Zå~a Ho$ H$m°ÝgoßQ> na AmYm[aV h¡ VWm
is based on the concept of random numbers
and is useful in the analysis of uncertainty. A{ZpíMVVm Ho$ {díbofU _| Cn`moJr h¡Ÿ&
Steps Involved in Simulation Analysis {gå`wboeZ EZm{b{gg Ho$ Amdí`H$ ñQ>oßg
The simulation analysis involves follow- {gå`wboeZ EZm{b{gg _| {ZåZ{b{IV ñQ>oßg h¢…
ing steps:
(a) Identify the variables which influence cash (a) CZ d¡[aE~ëg H$mo {ZYm©[aV H$aZm Omo H¡$e BZâbmoO
inflows and outflows. For example, when Ed§ AmCQ>âbmoO H$mo à^m{dV H$aVo h¢Ÿ& CXmhaU Ho$
a firm introduces a new product in the
{bE, O~ H$moB© \$_© _mH}$Q> _| Z`m àmoS>ŠQ> bmVr h¡ Vmo
market, these variables are initial invest-
BZ d¡[aE~ëg _| àma§{^H$ BÝdoñQ>_oÝQ>, _mH}$Q> gmBO,
ment, market size, market share, price,
variable costs, fixed costs, product life _mH}$Q> eo`a, àmBg, d¡[aE~b H$m°ñQ>, {\$ŠñS> H$m°ñQ>,
cycle etc. àmoS>ŠQ> bmB\$ gm`H$b Am{X gpå_{bV hm|JoŸ&
(b) Specify the formulae that relate variables. (b) d¡[aE~ëg go g§~§{YV \$m°_y©bo V` H$aZmŸ& CXmhaU
For example, revenue depends on sales Ho$ {bE, aodoÝ`y, goëg dm°ë`y_ Ed§ àmBg na {Z^©a
volume and price, sales volume is given
hmoVr h¡; goëg dm°ë`y_, _mH}$Q> gmBO Ed§ _mH}$Q> _|
by market size and share of the firm in
\$_© Ho$ eo`a na {Z^©a hmoVr h¡Ÿ& Cgr àH$ma, Am°naoqQ>J
market. Similarly, operating cost depends
on variable costs, fixed costs and volume H$m°ñQ>, d¡[aE~b H$m°ñQ>, {\$ŠñS> H$m°ñQ> VWm àmoS>ŠeZ
of production. H$s _mÌm na {Z^©a H$aVr h¡Ÿ&
(c) Indicate the probability distribution for (c) àË`oH$ d¡[aE~ëg H$m àmo~o{~{bQ>r {S>ñQ´>rã`yeZ {ZYm©[aV
each variable. Some variables will have H$aZmŸ& Hw$N> d¡[aE~ëg Xygam| H$s VwbZm _| A{YH$
more uncertainty than others. A{ZpíMV hmo gH$Vo h¢Ÿ&
(d) Develop a computer program that (d) Eogm H$åß`yQ>a àmoJ«m_ S>odbn H$aZm Omo àË`oH$ d¡[aE~b
randomly selects one value from the Ho$ àmo~o{~{bQ>r {S>ñQ´>rã`yeZ _| go H$moB© EH$ d¡ë`y {gboŠQ>
probability distribution of each variable H$a gHo$ VWm BZ d¡ë`yO Ho$ AmYma na àmoOoŠQ> H$s
and uses these values to calculate the NPV H¡$ëHw$boQ> H$a gHo$Ÿ& Bg àH$ma H$åß`yQ>a Ûmam
project’s NPV. A large number of such NPVs
~hþV gr NPV CZHo$ ñQ>¡ÊS>S>© S>o{dEeZ Ho$ gmW
are calculated by computer and stored
H¡$ëHw$coQ> H$aHo$ ñQ>moa H$a Xr OmVr h¡Ÿ& àmoOoŠQ> H$s
along with their standard deviations. The
risk-free rate of return is used for NPV H$mo [añH$-\«$s aoQ> Am°\$ [aQ>Z© go {S>ñH$mCÝQ>
discounting the NPVs of the project which H$a {X`m OmVm h¡ Omo Q>mB_ d¡ë`y Am°\$ _Zr H$mo
reflects only the time value of money. Xem©Vm h¡Ÿ&