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
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