April 1999
QT211: QUANTITATIVE ANALYSIS FOR MANAGEMENT

QUESTION 1

Total Marks: 20 Marks

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GRADE A
Sample student's solutions are indicated in green.
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(a) The cashflows for Project S are given below: [3]
 
Year Cashflow
0 ($1,000)
1 $500
2 $400
3 $300
4 $100

What is the Net Present Value (NPV) for Project S if the cost of capital is 10%?
Net present value
= -$1000 + ($500*0.909) + ($400*0.826) + ($300*0.751) + ($100*0.683)
= -$1000 + $454.5 + $330.4 + $225.3 + $68.3
= $78.5

 
(b) A manufacturing process produces cylindrical component parts for the automotive industry. It is important that the process produce parts having a mean diameter of at least 42.8 millimeters. It is known that the population variance is s2 = 2.917. A cylinder is chosen at random and found to have diameter 41.0 millimeters. Calculate the probability that the population mean x.gif (865 bytes) is greater than 42.8 millimeters, stating any assumptions that you make. [5]
s2 = 2.0971    m = 41 millimeters
s2= 1.708
P(x.gif (865 bytes) > 42.8) =  P(Z > 42.8- 41 / 1.708)
                   = P (Z >1.054)
                   = 0.5- 0.351
                   = 0.1469

Therefore, probability of populations mean > 42.8 mil is 0.1469.
Assumptions :
1. Diameter of the ports is normally distributed.
2. The cylinder stated (chosen in random) is a good mean presenting the population.

 
(c) Give one example of each of the following types of sets [1]
(i) A finite set [1]
A finite set : The number of seats in a classroom.

 
(ii) An infinite countable set [1]
An infinite countable set :The number of stars in the sky.

 
(iii) An infinite uncountable set
An infinite uncountable set : The number of real numbers between 0 to 10.

 
(d) Blackburn Rovers, the English professional football club is looking for a new centre forward. The club can buy one of: Michael Owen from Liverpool at a cost of £19 million; Andy Cole from Manchester United at a cost of £9 million; or a promising young player called Tony Grimsey from non-league team Mansfield Road, at a cost of £1 million. Blackburn believe that they will have a probability of 0.8 of winning the league if they buy Michael Owen, a probability of 0.4 of winning the league if they buy Andy Cole, and a probability of 0.1 of winning the league if they buy Tony Grimsey. Winning the league will increase revenue by £25 million. Which player should Blackburn buy to maximize their expected revenue. [7]
Expected monetary value buying Michael Owen
= - £19 M + (0.3 * £25 M)
= £1 million

Expected monetary value buying Andy Cole
= - £9 M + (0.4 * £25 M)
= £1 million

Expected monetary value buying Tony Grimsey
= - £1 M + (0.1 * £25 M)
= £1.5 million

Therefore, Blackburn should buy Tony Grimsey as he has the highest expected value.

 
(e) Give two limitations of simulation techniques. [2]
1. Practical simulation requires the use of computers, and this technique will be useless for firms without computer facilities.

2. Simulation does not provide an optimum solution, it merely indicates the appropriate behaviors base on a given set of inputs.