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65. Calculating the Probability of Bankruptcy A linear probability model you have
developed finds there are two factors influencing the past bankruptcy behavior of firms: the debt-
to-equity ratio and the sales-to-total assets ratio. Based on past bankruptcy experience, the
linear probability model is estimated as:
PDi = 0.60 (debt/equity) + 0.02 (sales/total assets)
A firm you are thinking of lending to has a sales-to-assets ratio of 1.75 and its expected
probability of default, or bankruptcy, is estimated to be 8.1 percent. Calculate the firm's debt
ratio.
66. Calculating the Probability of Bankruptcy A linear probability model you have
developed finds there are two factors influencing the past bankruptcy behavior of firms: the debt-
to-equity ratio and the profit margin. Based on past bankruptcy experience, the linear probability
model is estimated as:
PDi = 0.02 (debt/equity) + 0.80 (profit margin)
A firm you are thinking of lending to has a debt-to-equity ratio of 110 percent and its expected
probability of default, or bankruptcy, is estimated to be 8 percent. If sales are $2 million, calculate
the firm's net income.
67. Calculating the Probability of Bankruptcy A linear probability model you have
developed finds there are two factors influencing the past bankruptcy behavior of firms: the debt-
to-equity ratio and the profit margin. Based on past bankruptcy experience, the linear probability
model is estimated as:
PDi = 0.03 (debt/equity) + 0.65 (profit margin)
A firm you are thinking of lending to has a debt-to-equity ratio of 105 percent and its expected
probability of default, or bankruptcy, is estimated to be 7 percent. If sales are $3 million, calculate
the firm's net income.
68. Peter's TV Supplies is considering a merger with Jan's Radio Supply Stores. Peter's total
operating costs of producing services are $330,000 for a sales volume (S
P
) of $4.5 million. Jan's
total operating costs of producing services are $30,000 for a sales volume (S
J
) of $550,000.
Suppose that synergies in the production process result in a cost of production for the merged
firms totaling $360,000 for a sales volume of $5,050,000. Calculate the total average cost (TAC)
for the merged firm.
69. Cindy's Computer Corp. is considering a merger with Bobby's Hard Drive, Inc. Cindy's
total operating costs of producing services are $2.1 million for a sales volume (S
C
) of $13 million.
Bobby's total operating costs of producing services are $2.5 million for a sales volume (S
B
) of $7
million. If the two firms merge, calculate the total average cost (TAC) for the merged firm
assuming no synergies.
70. Suppose that the financial ratios of a potential borrowing firm took the following values:
X1
= Net working capital/Total assets = 0.15,
X2
= Retained earnings/Total assets = 0.27,
X3
=
Earnings before interest and taxes/Total assets = 0.28,
X4
= Market value of equity/Book value
of long-term debt = 0.68,
X5
= Sales/Total assets ratio = 0.9. Calculate and interpret the Altman's
Z
-score for this firm.
71. Suppose that the financial ratios of a potential borrowing firm took the following values:
X1
= Net working capital/Total assets = 0.05,
X2
= Retained earnings/Total assets = 0.12,
X3
=
Earnings before interest and taxes/Total assets = 0.17,
X4
= Market value of equity/Book value
of long-term debt = 0.42,
X5
= Sales/Total assets ratio = 0.6. Calculate and interpret the Altman's
Z
-score for this firm.
72. Suppose a linear probability model you have developed finds there are two factors
influencing the past bankruptcy behavior of firms: the debt ratio and the profit margin. Based on
past bankruptcy experience, the linear probability model is estimated as:
PDi = 0.15 (debt ratio) + 0.1 (profit margin)
A firm you are thinking of lending to has a debt ratio of 57 percent and a profit margin of 7.15
percent. Calculate the firm's expected probability of default, or bankruptcy.
73. A linear probability model you have developed finds there are two factors influencing the
past bankruptcy behavior of firms: the equity multiplier and the total asset turnover ratio. Based
on past bankruptcy experience, the linear probability model is estimated as:
PDi = 0.02 (equity multiplier) + 0.01 (total asset turnover)
A firm you are thinking of lending to has an equity multiplier of 3.2 times and a total asset
turnover ratio of 1.95. Calculate the firm's expected probability of default, or bankruptcy.
74. George's Dry Cleaning is considering a merger with Weezzie's Laundry Supply Stores.
George's total operating costs of producing services are $790,000 for sales volume (S
G
) of $4.7
million. Weezzie's total operating costs of producing services are $202,000 for a sales volume
(S
W
) of $2.3 million. For a sales volume of $7 million, calculate the reduction in production costs
the merged firms need to experience such that the total average cost (TAC) for the merged firms
is equal to 12 percent.
75. George's Dry Cleaning is considering a merger with Weezzie's Laundry Supply Stores.
George's total operating costs of producing services are $590,000 for sales volume (S
G
) of $4.7
million. Weezzie's total operating costs of producing services are $152,000 for a sales volume
(S
W
) of $2.3 million. For a sales volume of $7 million, calculate the reduction in production costs
the merged firms need to experience such that the total average cost (TAC) for the merged firms
is equal to 9 percent.
76. Jenny's Day Care is considering a merger with Lionel's Diaper Manufacturers. Jenny's
total operating costs of producing services are $350,000 for sales volume of $1.4 million. Lionel's
total operating costs of producing services are $300,000 for a sales volume of $1.3 million. For a
sales volume of $2.7 million, calculate the reduction in production costs the merged firms need to
experience such that the total average cost (TAC) for the merged firms is equal to 20 percent.
20-73
77. Stubborn Motors, Inc., is asking a price of $10.5 million to be purchased by Rubber Tire
Motor Corp. Rubber Tire currently has total cash flows of $6 million which are growing at 1
percent annually. Managers estimate that because of synergies the merged firm's cash flows will
increase by an additional 4 percent for the first four years following the merger. After the first
four years, incremental cash flows will grow at a rate of 3 percent annually. The WACC for the
merged firms is 9.75 percent. Calculate the NPV of the merger. Should Rubber Tire Motor
Corporation agree to acquire Stubborn Motors for the asking price of $10.5 million?
78. Suppose a linear probability model you have developed finds there are two factors
influencing the past bankruptcy behavior of firms: the debt ratio and the profit margin. Based on
past bankruptcy experience, the linear probability model is estimated as:
PDi = 0.28 (debt ratio) + 0.51 (profit margin)
You know a particular firm has a debt ratio of 46 percent and a probability of default of 18
percent. Calculate the firm's profit margin.
79. A linear probability model you have developed finds there are two factors influencing the
past bankruptcy behavior of firms: the equity multiplier and the total asset turnover ratio. Based
on past bankruptcy experience, the linear probability model is estimated as:
PDi = 0.02 (equity multiplier) + 0.06 (total asset turnover)
A firm has an equity multiplier of 1.1 times and a probability of default of 6.2 percent. Calculate
the firm's total asset turnover ratio.
80. A survey of a local market has provided the following average cost data: Johnson
Construction Corp. (JCC) has assets of $3 million and an average cost of 22 percent. Anderson
Architects (AA) has assets of $4 million and an average cost of 31 percent. Cole Home Builders
(CHB) has assets of $5 million and an average cost of 28 percent. For each firm, average costs
are measured as a proportion of assets. JCC is planning to acquire AA and CHB with the
expectation of reducing overall average costs by eliminating the duplication of services. If JCC
plans to reduce operating costs by $500,000 after the merger, what will the average cost be for
the new firm?
81. The managers of State Bank have been approached by City Bank about a possible
merger. State Bank is asking a price of $171.78 million to be purchased by City Bank. City Bank
currently has total cash flows of $30 million that are growing at 2 percent annually. Managers of
State Bank estimate that because of synergies the merged firm's cash flows will increase by an
additional 6 percent for the first four years following the merger. After the first four years,
managers of State Bank have estimated that incremental cash flows will grow at a rate of 3
percent. The WACC for the merged firms is 11 percent. Managers of City Bank agree that cash
flows should grow at an additional 6 percent for the first four years, but are unsure of the long-
term growth rate in incremental cash flows estimated by City Bank. Calculate the minimum
growth rate needed after the first four years such that City Bank would see this merger as a
positive NPV project.
82. A linear probability model you have developed finds there are two factors influencing the
past bankruptcy behavior of firms: the debt-to-equity ratio and the sales-to-total assets ratio.
Based on past bankruptcy experience, the linear probability model is estimated as:
PDi = 0.52 (debt/equity) + 0.01 (sales/total assets)
A firm you are thinking of lending to has a sales-to-assets ratio of 2.0 and its expected probability
of default, or bankruptcy, is estimated to be 12 percent. Calculate the firm's debt ratio.
83. A linear probability model you have developed finds there are two factors influencing the
past bankruptcy behavior of firms: the debt-to-equity ratio and the profit margin. Based on past
bankruptcy experience, the linear probability model is estimated as:
PDi = 0.01 (debt/equity) + 0.76 (profit margin)
A firm you are thinking of lending to has a debt-to-equity ratio of 121 percent and its expected
probability of default, or bankruptcy, is estimated to be 8.125 percent. If sales are $1 million,
calculate the firm's net income.
