You are a banker with $2 million cash. A client wants to conduct a LBO (Leverage
ID: 2726452 • Letter: Y
Question
You are a banker with $2 million cash. A client wants to conduct a LBO (Leveraged Buyout: management of a company gain controlling share using outside capital) and ask you how much money can you promise to loan her. She needs a lot of money and is in touch with multiple banks. The return of this loan will be 10% in three months. Pending on last minute negotiation, her final loan need from you will be $200,000 to $600,000 (uniformly distributed) less than the number you promise her. If her final loan request is less than the $2 million you have, you will use the extra cash to purchase 3-month U.S. Treasure Bill and earn 2%. If her final loan need is more than you actually have, you will borrow from a loan shark at 20% for the three months to cover the gap. She is waiting on the line, how much money can you promise her?Explanation / Answer
Mean of the loan variation = (200,000 + 600,000)/2 = $ 400,000
Standard deviation of the loan variation = [(600,000 - 200,000)2 / 12]1/2 = $ 115,470.05
If money promised is greater than $2 million, let the excess money be "M".
The total money promised is $ (2 + M) million. Interest on this money is $ (0.1 + 0.1*M) million.
The interest money should be greater than the interest paid on the money borrowed from loan shark.
So, $ (0.1 + 0.1*M) > $ 0.2 * M
This implies that M < $ 2 million
So, Money that can be promised $ (2 +2) million + Std. deviation of loan variation.
Hence, money promised = $ 4 million + $ 115,470.05 = $ 4,115,470.05
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