Final answer:
The increase in the value of Bellwood Company after taking a loan according to the trade-off theory cannot be conclusively estimated without additional input about how the borrowed funds will be utilized and their effect on the company's profitability and risk profile.
Step-by-step explanation:
According to the trade-off theory, the value increase for Bellwood Company after taking a loan of $3.1 million at an 8% interest rate, with repayment in equal installments over the next two years, and taxed at a rate of 24%, cannot be determined without additional information about the projects or investments the loan will finance and how these will affect the company's cash flows and risk. If the loan is utilized in value-creating projects that yield returns above the cost of debt, the value of the company may increase due to the tax shield offered by the interest deduction. However, if the return on the new investment is less than the cost of capital, the company's value would decrease.
The trade-off theory suggests that firms balance the benefits of debt, such as the tax shield, against financial distress costs. These components should be evaluated to determine the change in company value. Without specific data on how the borrowed funds will impact the company's profitability or the exact cost of financial distress, the question cannot be answered quantitatively.