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BRILLIANT’S Analysis of Risk and Uncertainty in Investment Decisions 475

DECISION TREE APPROACH / {S>[gOZ Q´>r En«moM

Q.55. Describe the decision tree approach with the help of an example. How is this technique
useful in capital budgeting? / {S>[gOZ Q´>r EàmoM H$m EH$ CXmhaU H$s ghm`Vm go dU©Z H$s{OE&
H¡${nQ>b ~OqQ>J _| `h VH$ZrH$ H¡$go Cn`moJr h¢?

Decision Tree Approach {S>grOZ Q´>r AàmoM
Many times, a firm has to take a sequen- H$B© ~ma \$_© H$mo bJmVa {ZU©` boZo hmoVo h¢Ÿ& O~
tial decision. The decision is said to be sequen- dV©_mZ {ZU©`, nyd© _| {bE JE [ZU©` go à^m{dV hmoVm h¡
tial when the present decision is affected by Ed§ ^{dî` Ho$ {ZU©` H$mo à^m{dV H$aVm hmoŸ{ZU©` V~
the decisions taken in the past and it will affect
{gŠdopÝe`b H$hbmVo h¢ & ì`dhm[aH$Vm _|, H¡${nQ>b ~OqQ>J
the future decisions also. In practice, capital gå~ÝYr {ZU©` ^{dî` Ho$ BÝdoñQ>_oÝQ> g§~§Yr {ZU©`m| H$mo
budgeting decision also has implications for à^m{dV H$aVo h¢Ÿ& Bg{bE {H$gr àmoOoŠQ> H$m _yë`m§H$Z
future investment decisions. Therefore, evalu-
H$aZo Ho$ {bE {gŠdopÝe`b {S>grOZ _oqH$J àmogog H$s
ation of a project frequently requires a sequen-
Amdí`H$Vm hmoVr h¡Ÿ& Ohm± ñdrH¥${V-AñdrH¥${V g§~§Yr {ZU©`
tial decision making process where the Accept-
Reject Decision is made in several stages. At {d{^ÝZ ñQ>oOog _| {b`m OmVm hmoŸ& àË`oH$ ñQ>oO na EH$ go
each stage, there may be more than one option Á`mXm {dH$ën CnbãY hmo gH$Vo h¢ VWm àË`oH$ ~ma \$_©
available and the firm may have to decide H$mo `h {ZU©` H$aZm n‹S> gH$Vm h¡ {H$ H$m¡Z-gm {dH$ën
everytime that which option is to be selected. MwZm OmEŸ&
For example, a firm is planning to launch CXmhaU Ho$ {bE, EH$ \$_© EH$ Z`m àmoS>ŠQ> bm±M
a new product and to install a plant with H$aZo H$s ßbmqZJ H$a ahr h¡ VWm CgHo$ {bE à{V_mh
capacity of 8,000 units per month. The firm is 8,000 `y{ZQ²>g H$m CËnmXZ H$aZo H$s H¡$no{gQ>r dmbm
hopeful that the entire production will be sold. ßbm§Q> ñWm{nV H$aZm MmhVr h¡Ÿ& \$_© `h Anojm H$aVr h¡
However, if due to any reason, the demand is {H$ gånyU© CËnmXZ H$m {dH«$` hmo OmEJmŸ& hmbm§{H$ {H$gr
not generated even to achieve the break even H$maU go {S>_mÊS> OZaoQ> Zht hþB© VWm ~«oH$-B©dZ bodb
level, the firm will face a heavy loss. In this VH$ ^r Zht nhþ±Mm Om gH$m Vmo \$_© H$mo ~hþV A{YH$
situation, it is better for the firm to first install ZwH$gmZ hmo gH$Vm h¡Ÿ& Bg pñW{V _| \$_© Ho$ {bE ~ohVa
a pilot project and go for test marketing. `h h¡ {H$ dh nhbo EH$ nm`boQ> àmoOoŠQ> BÝñQ>m°b H$ao VWm
Management believes that there is 70% chance Q>oñQ> _mH}$qQ>J H$aoŸ& _¡ZoO_oÝQ> H$m {dídmg h¡ {H$ nm`boQ>
that the pilot production and test marketing
will be successful. In case of success, firm can àmoS>ŠeZ VWm Q>oñQ> _mH}$qQ>J g\$b hmoZo H$s g§^mdZm 70%
build the plant costing ` 150 million. The plant h¡Ÿ& `{X g\$bVm {_bVr h¡ Vmo \$_© ` 150 {_{b`Z H$m
will generate an annual cash inflow of ` 30 ßbm§Q> bJm gH$Vr h¡Ÿ& `h ßbm§Q> à{Vdf© ` 30 {_{b`Z H$m
million for 20 years if the demand is high or an dm{f©H$ H¡$e-BZâbmo AJbo 20 dfm] VH$ OZaoQ> H$aoJm
annual cash inflow of ` 20 million if the demand `{X {S>_mÊS> hmB© ahVr h¡ `m ` 20 {_{b`Z H$m EÝ`wAb
is moderate. High demand has a probability of H¡$e BZâbmo OZaoQ> H$aoJm `{X {S>_mÊS> _m°S>aoQ> ahVr h¡Ÿ&
0.6; moderate demand has a probability of 0.4. hmB©-{S>_mÊS> H$s àmo~o{~{bQ>r 0.6 h¡ O~{H$ _m°SaoQ> {S>_mÊS>
To analyze such situations where sequential H$s àmo~o{~{bQ>r 0.4 h¡Ÿ& Bg àH$ma H$s {gMwEeZ H$m {díbofU
decision making is involved, decision-tree H$aZo _| Ohm± {gŠdopÝe`b {S>grOZ _oqH$J H$s Amdí`H$Vm
analysis is helpful. h¡, {S>grOZ Q´>r EZm{b{gg ~hþV Cn`moJr h¡Ÿ&