This firm is currently operating at 84 percent of capacity. All costs and net working capital vary directly with sales. The tax rate, the profit margin, and the dividend payout ratio will remain constant. How much additional debt is required if no new equity is raised and sales are projected to increase by 12 percent?

Most of the numbers are missing, so I looked for a similar question:

The Steel Mill is currently operating at 84 percent of capacity. Annual sales are $28,400 and net income is $2,250. The firm has current liabilities of $2,700, long-term debt of $9,800, net fixed assets of $16,900, net working capital of $5,000, and owners' equity of $12,100. All costs and net working capital vary directly with sales. The tax rate and profit margin will remain constant. The dividend payout ratio is constant at 40 percent. How much additional debt is required if no new equity is raised and sales are projected to increase by 12 percent?

if the firm is operating at full capacity, then it will need to raise new debt:

EFN = (A/S) x (Δ Sales) - (L/S) x (Δ Sales) - (PM x FS x (1-d))

A/S = $24,600 / $28,400 = 0.866

ΔSales = $28,400 x 12% = $3,408

L/S = $2,700 / $28,400 = 0.095

PM = $2,250 / $28,400 = 0.079

FS = $28,400 x 1.12 = $31,808

(1 - d) = 1 - 40% = 0.6

EFN = (0.866 x $3,408) - (0.095 x $3,408) - (0.079 x $31,808 x 0.6)  = $2,951.33 - $323.76 - $1,507.70 = $1,119.87

but if the firm is operating only at 84% (16% spare capacity), then it will not need to raise new debt:

EFN = (A/S) x (Δ Sales) - (L/S) x (Δ Sales) - (PM x FS x (1-d))

A/S = $7,700 / $28,400 = 0.271

since there is 16% of spare capacity, no new fixed assets will be required

ΔSales = $28,400 x 12% = $3,408

L/S = $2,700 / $28,400 = 0.095

PM = $2,250 / $28,400 = 0.079

FS = $28,400 x 1.12 = $31,808

(1 - d) = 1 - 40% = 0.6

EFN = (0.271 x $3,408) - (0.095 x $3,408) - (0.079 x $31,808 x 0.6)  = $923.57 - $323.76 - $1,507.70 = -$907.89

2,283,000

explanation:

i just had to add it