Leonardo, a senior executive at the Las Vegas Home Bank, either offers only low-

Question

Leonardo, a senior executive at the Las Vegas Home Bank, either offers only low-risk prime mortgages or a combination of prime and riskier subprime mortgages. If he provides only prime mortgages, the bank's profit is $320 million with certainty. If he sell both prime and subprime mortgages, the bank earns $1 comma 600 million with a 25 % probability or minus $640 million with a 75 % probability, because subprime loans carry a high risk of default. Before, Leonardo received 1 % of the bank's profit if it was positive and nothing (but got to keep his job) if it was negative. Under his new contract, Leonardo receives a salary of $2.4 million a year and 0.25 % of the bank's profit. If the bank suffers a loss, Leonardo is fired, so that he loses his salary and receives no bonus. Assume Leonardo is risk neutral. Show that shareholders' expected earnings are higher with the new compensation scheme than with the original one. With the original compensation scheme, shareholders' expected earnings (the bank's profit before paying Leonardo's salary) are $___________million.(Enter your response as a whole number and include a minus sign if necessary.) With the new compensation scheme, shareholders' expected earnings (the bank's profit before paying Leonardo's salary) are $_______ million. (Enter your response as a whole number and include a minus sign if necessary.)

Explanation / Answer

Under Prime loans leonardo providing only the Low risk loans.

These loans together giving the profit to the bank about $320 millin.

The above $320 million profit was after payment to Leonardo of his 1%.

Now if we want to know what are the total profits before paying to the leonard share ?

Given $320 millin equals to the 99% of total profits , if we add back the 1% of leoanrdo's share then we will arrive total profits before share.

==> $320/99% = $323.2323 million

A)the bank's profit before paying Leonardo's salary is $323.2323 million.

B)With the new compensation scheme, shareholders' expected earnings (the bank's profit before paying Leonardo's salary) are $____-80___ million.

Answer) Bank profit when Prime and subprime loans provided.      
Probability       Loss or Profit       New Profit/Loss
25%               1600                  400
75%               -640              -480
                                   -80

Since under the new schme bank overally incurring losses of $80 million .

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