MNO, Inc., a publicly traded manufacturing firm in the United States, has provided the following financial information in its application for a loan.

Assets                                                               Liabilities and Equity

Cash                                               $ 20           Accounts Payable                        $ 30

Accounts Receivables                    $ 90           Notes Payable                             $ 90

Inventory                                        $ 90           Accruals                                      $ 30

                                                                                   Long Term Debt                         $150

Plant and equipment                      $500           Equity                                         $400

Total Assets                                  $700           Total Liabilities & Equity           $700

Also assume sales = $500, cost of goods sold = $360, taxes = $56, interest payments = $40, net income = $44, the dividend payout ratio is 50 percent, and the market value of equity is equal to the book value.

a.  What is the Altman discriminant function value for MNO, Inc.? Recall that:

Net working capital = Current assets minus current liabilities.

Current assets = Cash + accounts receivable + inventories.

Current liabilities = Accounts payable + accruals + notes payable.

EBIT = Revenues - Cost of goods sold - depreciation.

Taxes = (EBIT - Interest)(tax rate).

Net income = EBIT - interest - taxes.

Retained earnings = Net income (1 - dividend payout ratio)

Altman's discriminant function is given by: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

Assume prior retained earnings are zero.

X1 = (200 -30 -30 -90)/ 700 = .0714          X1 = Working capital/total assets (TA)

X2 = 22 / 700 = .0314                                 X2 = Retained earnings/TA

X3 = 140 / 700 = .20                                   X3 = EBIT/TA

X4 = 400 / 150 = 2.67                                 X4 = Market value of equity/long term debt

X5 = 500 / 700 = .7143                               X5 = Sales/TA

Z  = 1.2(0.07) + 1.4(0.03) + 3.3(0.20) + 0.6(2.67) + 1.0(0.71) = 3.104

=    .0857   +  .044    +    .66      +   1.6     +   .7143  = 3.104

b.  Should you approve MNO, Inc.'s application to your bank for a $500 capital expansion loan?

Since the Z-score of 3.104 is greater than 1.81, ABC Inc.'s application for a capital expansion loan should be approved.

c. If sales for MNO were $300, the market value of equity was only half of book value, and the cost of goods sold and interest were unchanged, what would be the net income for MNO? Assume the tax credit can be used to offset other tax liabilities incurred by other divisions of the firm. Would your credit decision change?

ABC's net income would be -$100 without taking into account text credits. Note, that ABC's tax liability is -$56,000. If we assume that ABC uses this tax credit against other tax liabilities, then:

X1 = (200 - 30 - 30 - 90) / 700 = .0714

X2 = -44 / 700 =  -0.0629

X3 = -60 / 700 =  -0.0857

X4 = 200 / 150 =   1.3333

X5 = 300 / 700 =   0.4286

Since ABC's Z-score falls to $.9434 < 1.81, credit should be denied.

MY question is Why the retained earning is -44, and not -156*0.5? How to calculate the new retained earning in c.