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The investment criterion $X > I(1+r)$ remains valid even when a project is financed with borrowed capital. In this scenario, the term $I(1+r)$ represents the total loan repayment amount, including both the principal ($I$) and interest, after one year. Consequently, a project funded by a loan is deemed profitable only if its future payoff, $X$, is sufficient to cover the full repayment of the loan.

Investment Profitability with Borrowed Funds

Given the following scenario, determine whether the manufacturing firm should undertake the project. Justify your decision with a calculation.

Investment Decision for a New Machine

A company finances a $10,000 project with a one-year loan at a 4% annual interest rate. If the project's future return is exactly $10,400, the company should proceed with the investment because it breaks even.

A company is considering a project with an initial cost of $150,000. To fund this, the company will take out a one-year loan for the full amount at an annual interest rate of 5%. What is the minimum future return the project must generate by the end of the year to be considered profitable? Explain your reasoning and show your calculation.

Minimum Profitable Return Calculation

A manufacturing firm plans to purchase a new piece of equipment for $50,000. To finance this, the firm will take out a one-year loan for the full amount at an annual interest rate of 8%. The firm projects that the new equipment will generate a total future return of $53,500 by the end of the year, at which point the loan must be fully repaid. Based on this information, should the firm proceed with the investment?

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