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Recall the formula to calculate the break-even volume from Chapter 8 as a functi

ID: 376668 • Letter: R

Question

Recall the formula to calculate the break-even volume from Chapter 8 as a function of the fixed cost F, the selling price p, and the variable cost v. This question requires you to calculate the expected break-even volume when there is uncertainty. The fixed cost F follows a normal distribution with mean 2464 and standard deviation 132. The selling price p follows a beta distribution with Alpha = 3, Beta = 4, A = 29, and B = 91. The variable cost follows a beta distribution with Alpha = 6, Beta = 2, A = 14, and B = 27. (A and B in the beta distribution represent the minimum and maximum, respectively.) Use SIPMath to simulate the break-even volume with 100000 trials. What is the expected break-even volume?

Explanation / Answer

FC VC SP
mean          2,465 alpha 4 5
SD             127 beta 6 3
A 20 34

FC + VC * units = Sell price * units (when we break even)

units = FC / (SP - VC)

For simulating the fixed cost (following normal with mean 2465 and sd 127), in excel write the formula norm.inv(rand(),2465,127)

For the variable cost, write the formula beta.inv(rand(),4,6, 20,32)

For the selling price, write the formula beta.inv(rand(),5,3, 34,92)

fourth column will have units as FC/ (SP - VC). drag the 4 columns to 100,000 observations. 100,000 simulations yielded the average units as 57

50 sample simulations as shown below

SIM selling price variable cost fixed cost units
1                     64                      27          2,447               65
2                     62                      28          2,251               66
3                     68                      25          2,603               61
4                     89                      23          2,208               33
5                     76                      27          2,489               51
6                     76                      28          2,468               51
7                     70                      24          2,379               52
8                     75                      27          2,584               54
9                     81                      24          2,475               44
10                     75                      23          2,537               48
11                     77                      26          2,478               49
12                     73                      23          2,502               50
13                     69                      23          2,600               56
14                     74                      28          2,446               53
15                     57                      23          2,659               78
16                     59                      24          2,334               67
17                     75                      23          2,397               46
18                     71                      24          2,629               55
19                     57                      29          2,475               86
20                     68                      28          2,508               63
21                     79                      24          2,090               38
22                     63                      26          2,461               67
23                     51                      27          2,436            100
24                     85                      24          1,966               32
25                     71                      23          2,293               48
26                     66                      24          2,250               53
27                     69                      25          2,515               56
28                     63                      24          2,449               61
29                     82                      26          2,551               45
30                     68                      28          2,581               64
31                     66                      24          2,415               58
32                     64                      27          2,620               70
33                     50                      24          2,421               94
34                     54                      23          2,382               77
35                     75                      23          2,500               48
36                     73                      23          2,643               53
37                     65                      22          2,540               59
38                     90                      23          2,615               39
39                     71                      25          2,323               50
40                     52                      23          2,437               85
41                     69                      25          2,683               61
42                     60                      23          2,571               70
43                     74                      24          2,512               50
44                     71                      26          2,420               54
45                     69                      28          2,323               57
46                     74                      22          2,430               46
47                     70                      24          2,433               53
48                     73                      27          2,390               52
49                     68                      23          2,503               56
50                     72                      25          2,347               50