# Question

This problem utilizes information from Problem 10- 9 and requires that the LBO valuation model be constructed. Randy was happy with the anticipated results from the acquisition of Flanders Inc., but he wanted to do some exploratory analysis of the risks involved in the acquisition so that he might be able to anticipate the risks inherent in the investment. He planned to construct a spreadsheet model using the industry- standard LBO valuation model ( using information from Problem 10- 9) and then identify the key sources of risk in the model, constructing what he felt were reasonable characterizations of the probability distributions for each of these variables. Specifically, Randy decided on the following variables (value drivers) and distributional characterizations:

Mark Flanders estimated EBITDA growth to be 10% per year, but this rate is far from certain. Randy decided that he would set the most likely growth rate to be 10%, but he would use a triangular distribution with a minimum value of 0% and a maximum of 15% to characterize the annual rate of growth in EBITDA over the planning period. Randy felt that the rate of growth each year would be related to what happened in the subsequent year, so he decided to impose a .80 correlation on the growth rates for successive years. That is, the correlation between the rate of growth in 2018 and 2017 is estimated to be .80, and so forth.

Another key determinant of the value of the Flanders acquisition is the exit multiple that Clear stone will encounter in five years when it sells the firm. Randy has estimated that they will be able to exit at the same multiple (five) at which they purchase Flanders Inc.; however, this variable is subject to uncertainty. Based on Clear stone’s past experience, Randy estimates a 10% chance of the exit multiple being as low as three times EBITDA, a 20% chance of it being four, a 40% chance of it being five, a 20% chance of it being six, and a 10% chance of it being as high as seven.

a. After incorporating Randy’s two assumptions about the uncertainties in the acquisition of Flanders Inc., what is the mean and median rate of return on Clear stone’s investment in the firm’s equity?

b. What is the probability that the Flanders acquisition will yield a rate of return to Clear stone that is below the firm’s target of 40%?

Mark Flanders estimated EBITDA growth to be 10% per year, but this rate is far from certain. Randy decided that he would set the most likely growth rate to be 10%, but he would use a triangular distribution with a minimum value of 0% and a maximum of 15% to characterize the annual rate of growth in EBITDA over the planning period. Randy felt that the rate of growth each year would be related to what happened in the subsequent year, so he decided to impose a .80 correlation on the growth rates for successive years. That is, the correlation between the rate of growth in 2018 and 2017 is estimated to be .80, and so forth.

Another key determinant of the value of the Flanders acquisition is the exit multiple that Clear stone will encounter in five years when it sells the firm. Randy has estimated that they will be able to exit at the same multiple (five) at which they purchase Flanders Inc.; however, this variable is subject to uncertainty. Based on Clear stone’s past experience, Randy estimates a 10% chance of the exit multiple being as low as three times EBITDA, a 20% chance of it being four, a 40% chance of it being five, a 20% chance of it being six, and a 10% chance of it being as high as seven.

a. After incorporating Randy’s two assumptions about the uncertainties in the acquisition of Flanders Inc., what is the mean and median rate of return on Clear stone’s investment in the firm’s equity?

b. What is the probability that the Flanders acquisition will yield a rate of return to Clear stone that is below the firm’s target of 40%?

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