Using a modified discriminant function similar to Altman's, Burger Bank estimates the following coefficients for its portfolio of loans: Z = 1.4X₁ + 1.09X₂ + 1.5X₃
Where X₁ = debt to asset ratio; X₂ = net income and X₃ = dividend payout ratio.
Using Z = 1.682 as the cut-off rate, what should be the debt to asset ratio of the firm in order for the bank to approve the loan?

Question

Quizplus · Accepted Answer

We need to solve for X₁ in the equation Z = 1.4X₁ + 1.09X₂ + 1.5X₃, given Z = 1.682 as the cut-off rate: 1.682 = 1.4X₁ + 1.09X₂ + 1.5X₃ Assuming X₂ and X₃ are constant, we can rearrange the equation to solve for X₁: X₁ = (1.682 - 1.09X₂ - 1.5X₃)/1.4 Since we don't have values for X₂ and X₃, we need to consider the worst-case scenario for the debt to asset ratio. According to Altman's original model, a Z-score below 1.81 indicates distress or bankruptcy, so we can assume that the bank would want a higher debt to asset ratio to ensure that the Z-score remains above 1.682. Therefore, we can assume that X₂ and X₃ are at their lowest possible values (i.e. 0). Plugging in X₂ = 0 and X₃ = 0, we get: X₁ = (1.682 - 0 - 0)/1.4 = 1.201 Therefore, the debt to asset ratio should be 120.1%, which is not a valid choice. We need to choose the closest valid answer, which is B) 46.5 percent.

Using a Modified Discriminant Function Similar to Altman's, Burger Bank