\"Recall the formula to calculate the break-even volume from Chapter 8 as a func

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 2465 and standard deviation 127. The selling price p follows a beta distribution with Alpha = 5, Beta = 3, A = 34, and B = 92. The variable cost follows a beta distribution with Alpha = 4, Beta = 6, A = 20, and B = 32. (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 * 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

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