Final answer:
Lear, Inc's earnings after taxes, given the financing plan and a 30% tax rate, amount to $105,875 after accounting for both long-term and short-term interest expenses.
Step-by-step explanation:
To determine Lear, Inc's earnings after taxes under the specified financing plan, we first need to calculate the interest expenses on both long-term and short-term financing. Lear plans to finance all $680,000 of its capital assets and half of its permanent current assets ($215,000) with long-term financing at 10 percent. The total amount financed long-term is $680,000 + $215,000 = $895,000. The annual long-term interest expense will be 10% x $895,000 = $89,500.
Lear also plans to finance the remaining half of its permanent current assets and all other current assets with short-term financing at 5 percent. The remaining permanent current assets financed short-term are $215,000 and the non-permanent current assets are $570,000 ($1,000,000 total current assets - $430,000 permanent current assets). So, the total short-term financing is $215,000 + $570,000 = $785,000, with an annual interest expense of 5% x $785,000 = $39,250.
The total interest expense is $89,500 + $39,250 = $128,750. Now, we can calculate the earnings before taxes (EBT) which are $280,000 - $128,750 = $151,250. Finally, we can determine the earnings after taxes by applying the 30% tax rate: $151,250 x (1 - 0.3) = $105,875.