Largo Loans realizes average profit of $110 on loans that perform and average loss of $590 on loans that default. What is the expected profit for an approved loan if its predicted probability of perform is 0.93? Enter the amount only, with no dollar symbol.
The expected profit for an approved loan can be calculated by multiplying the average profit of performing loans with the predicted probability of perform, and subtracting the average loss of defaulting loans multiplied by the predicted probability of default:
Expected profit = (Average profit of performing loans * Predicted probability of perform) - (Average loss of defaulting loans * Predicted probability of default)
Expected profit = ($110 * 0.93) - ($590 * (1 - 0.93))
Expected profit = $102.3 - $590 * (0.07)
Expected profit = $102.3 - $41.3
Expected profit = $61
The expected profit for an approved loan with a predicted probability of perform of 0.93 is $61.