Question

B [20]
Sparkling Ltd is contemplating the manufacture of pool equipment and must decide whether to build a large or a small plant.
There is a 0.6 probability that the demand for the equipment will be strong and a 0.4 probability that the demand will be weak. If demand is strong and a large plant is built, a profit of R10 million will result. However if demand is weak but the plant is large, profits will amount to R1 million. If Sparkling Ltd builds a small plant and demand is weak, profits of R4million will be made.
If demand is strong and Sparkling Ltd has a small plant, the likelihood of competition is greater. It is estimated that there is a 75% chance that the company will come up against competition under these circumstances. In such a case, Sparkling Ltd could either build another separate small plant in a different area, or expand the existing plant. If Sparkling Ltd decides not to invest in further plant, profits of R6 million are expected, regardless of whether there is any competition.
ADVANCED DIPLOMA IN FINANCIAL MANAGEMENT– ACADEMIC AND ASSESSMENT CALENDAR
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If there is competition, however, either form of expansion is expected to yield a 0.7 probability of a profit of R8 million and a 0.3 probability of a profit of no change in the status quo. If there is no competition, building the separate plant would yield a profit of R9 million with a 0.8 probability and a profit of R7 million with a 0.2 probability. Expanding the existing plant is expected to result in a profit of R7.5 million.
Required:

b) Determine the optimal strategy by means of backward induction. (10)

Answer 1

Mec78 b) Horswes :- The optimal strategy determination by of backward isduction opt 2001 when large plast & de moord is strong The profit Rio xo.6=> R6 millions. If demand is weak = Rixo.4 Roo4 millione Total profit when large plant building Rot R0.4 = R6.4 melling Optim-2 when small plant & demand as strong 1 profit L ③ Expand cristing plant gives when competet som = R8X0.7 t Roxo.3 = Rs. 6 tel. 8 E R 7.4 millions NO competition

poofit Q. Invest in seperate plant gives when competetin • R8x0.7 + R6x0.3 =f5.6 + R2 = Rzeq milling when , no competetion, it will give profit - Raxo.8 + Rxo.2 Rg.6 milling 3 000€ S vest fo7 plant profit Rom @ 25% =R1.5 millions option 3 when small plant k Demand 98 weak, the profit = R4 milliong

In option 2 : The profit reduced to 75% 1:17.4+75) *75% = R1.125 mlectory 2. G.4 +86) *15% = R12 mellsong By observing above facts. Invest in separate plant of the optimal strategy to get highest poofit