Questions: Colter Steel has 4,650,000 in assets. Assume short-term interest rates are 10 percent and long-term rates are 4 percentage points lower than short-term rates. Earnings before interest and taxes are 990,000. The tax rate is 40 percent. If long-term financing is perfectly matched (synchronized) with long-term asset needs, and the same is true of short-term financing, what will earnings after taxes be?

To determine the earnings after taxes, we need to follow these steps:

1. Calculate the interest expenses for both short-term and long-term financing.

   • Short-term financing is used for temporary current assets. The interest rate for short-term financing is 10%.
   • Long-term financing is used for permanent current assets and fixed assets. The interest rate for long-term financing is 4 percentage points lower than the short-term rate, which is \(10\% - 4\% = 6\%\).

2. Calculate the interest expense for each type of financing:

   • Short-term interest expense: \[ \text{Short-term interest expense} = \text{Temporary current assets} \times \text{Short-term interest rate} = \$1,300,000 \times 0.10 = \$130,000 \]

   • Long-term interest expense: \[ \text{Long-term interest expense} = (\text{Permanent current assets} + \text{Fixed assets}) \times \text{Long-term interest rate} \] \[ = (\$1,515,000 + \$1,835,000) \times 0.06 = \$3,350,000 \times 0.06 = \$201,000 \]

3. Calculate total interest expense: \[ \text{Total interest expense} = \text{Short-term interest expense} + \text{Long-term interest expense} = \$130,000 + \$201,000 = \$331,000 \]

4. Calculate earnings before taxes (EBT): \[ \text{EBT} = \text{Earnings before interest and taxes (EBIT)} - \text{Total interest expense} = \$990,000 - \$331,000 = \$659,000 \]

5. Calculate earnings after taxes (EAT): \[ \text{EAT} = \text{EBT} \times (1 - \text{Tax rate}) = \$659,000 \times (1 - 0.40) = \$659,000 \times 0.60 = \$395,400 \]

Therefore, the earnings after taxes are \(\$395,400\).