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 find the value of X₁ (debt to asset ratio) which would make Z equal to or greater than the cut-off rate of 1.682.

1.4X₁ + 1.09X₂ + 1.5X₃ ≥ 1.682

Since X₂ and X₃ are unknown, we can't solve the equation completely. However, we can find the minimum value of X₁ required to satisfy the inequality.

1.4X₁ ≥ 1.682 - 1.09X₂ - 1.5X₃

X₁ ≥ (1.682 - 1.09X₂ - 1.5X₃) / 1.4

To minimize X₁, we need to maximize (1.09X₂ + 1.5X₃), since the term is subtracted from 1.682.

The maximum value of (1.09X₂ + 1.5X₃) can be achieved when both X₂ and X₃ equal 1 (i.e. no restrictions on net income or dividend payout ratio).

So, (1.09X₂ + 1.5X₃) = 1.09 + 1.5 = 2.59

Now, X₁ ≥ (1.682 - 2.59) / 1.4 = -0.46

Since X₁ cannot be negative, we can set it to zero and solve for the other variables.

1.09X₂ + 1.5X₃ = 1.682

1.09X₂ + 1.5(1 - X₂) = 1.682

0.41X₂ + 1.5 = 1.682

0.41X₂ = 0.182

X₂ = 0.4439

So, the minimum value of X₁ required for loan approval is 46.5% (rounded to one decimal place).

Therefore, the answer is B) 46.5 percent.

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