Your private equity firm is considering making an offer to buy a small yogurt fi

Question

Your private equity firm is considering making an offer to buy a small yogurt firm with the intent of reselling it after streamlining its operations. The problem is that you don’t know the exact current value of the firm. You are sure that it is equally likely to be worth anywhere in the range of $150 million to $600 million dollars (a uniform distribution). You also know that if your offer exceeds the value of the firm the current owners will sell. Given your track record of enhancing the value of existing firms, you are confident that you can increase the value of the firm by $50 million. What is the highest offer you can make without expecting to lose money on average? (Give only the numerical answer with no dollar sign. Write $100 million as 100.)

Explanation / Answer

Ans: 425

Current value of firm is following a uniform distribution with minimum value of $150 mn and maximum of $600mn. So the average expected value of the firm will be (150+600)/2=$375 mn.

Since you know, you can increase the firm value by $50 mn. Therefore, you can sell the firm at expected average price of 375+50=425 mn dollor. Highest bidding without expecting any loss will be 425.

for uniform distribution mean is =(a+b)/2

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