11. Over a five-year period, the quarterly change in the price per share of comm
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Question
11. Over a five-year period, the quarterly change in the price per share of common stock for a major oil company ranged from -8% to 12%. A financial analyst wants to learn what can be expected for price appreciation of this stock over the next two years. Using the five-year history as a basis, the analyst is willing to assume that the change in price for each quarter is uniformly distributed between - 8% and 12%. Use simulation to provide information about the price per share for the stock over the coming two-year period (eight quarters). a. Use two-digit random numbers from column 2 of Table 12.2, beginning with 0.52, 0.99, and so on, to simulate the quarterly price change for each of the eight quarters. b. If the current price per share is $80, what is the simulated price per share at the end of the two-year period? c. Discuss how risk analysis would be helpful in identifying the risk associated with a two-year investment in this stock. Each trial in the simulation also requires a value of the parts costandfirst-year demand. Let us now turn to the issue of generating values for the parts cost. The probability distri- bution for the parts cost per uni: is the uniform distribution shown in Figure 12.3. Because this random variable has a different probability distribution than direct labor cost, we use random numbers in a slightly cifferent way to generate values for parts cost. With a uni- fern probability distribution, the following relationship between the random number and the associated value of the parts cost is used: Pars cost = a + (b - a) (12.2) where = random number between 0 and 1 & = smallest value for parts cost b = aigest value for parts cost For PortaCom, the smallest value for the parts cost is $80 and the largest value is $100. Applying equation (12.2) with a = 80 and b = 100 leads to the following formula for gen- erating the parts cost givena random number, r. Parts cost = 80 +r100 - 80) = 8) + 720 (123) Equation (12.3) generates a value for the parts cost. Suppose that a random number of 02680 is obtained. The value forthe parts cost is Paris cast = 80 + 0.2680(20) = 85.36 per unt Suppose that a random number of 1.5842 is generated on the next trial. The value for the parts cost is Paris cost = 80 +0.5842(20) = 91.68 per unt With appropriate choiceso a and b, equation (122) can be used to generae values for any uniform probability distribution. Table 12.5 shows the generation of 1) values for the parts cost per unit. Finally, we need a random number procedure for generating the first-year demand. Because first-year demand is normally disrbuted with a mean of 15,000 units and a standard deviation of 4500 units (see Figure 1244, we need a procedure for generating random values fromExplanation / Answer
a)
The quarterly change in price per share has gone up from -8% to 12%.
The difference between the two is 20% or 0.20
Quarter
Random Number
Random number * 0.20
Quarterly Price Change
1
0.52
0.10
0.0240
2
0.99
0.20
0.1180
3
0.12
0.02
-0.0560
4
0.15
0.03
-0.0500
5
0.50
0.10
0.0200
6
0.77
0.15
0.0740
7
0.40
0.08
0.0000
8
0.52
0.10
0.0240
(b)
Quarter
Quarterly Price Change
Price/Share at end of period
1
0.0240
81.92
2
0.1180
91.59
3
-0.0560
86.46
4
-0.0500
82.13
5
0.0200
83.78
6
0.0740
89.98
7
0.0000
89.98
8
0.0240
92.14
c
)here it is examined by two year investment by comparing its previous year data and and approripriate steps had taken
Quarter
Random Number
Random number * 0.20
Quarterly Price Change
1
0.52
0.10
0.0240
2
0.99
0.20
0.1180
3
0.12
0.02
-0.0560
4
0.15
0.03
-0.0500
5
0.50
0.10
0.0200
6
0.77
0.15
0.0740
7
0.40
0.08
0.0000
8
0.52
0.10
0.0240
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