Question

You can buy a machine for $100,000 that will produce a net income, after operating expenses, of $10,000 per year. if you plan to keep the machine for four years, what must the market. (resale) value be at the end of four years to justify the investment? you must make a 12% annual return on your investment

Answer 1

To determine the justified resale value of a machine to achieve a 12% return, calculate the present value of the income produced over four years and adjust the resale value accordingly, ensuring the total net present value equals zero.

Step-by-step explanation:

The question asks what the market or resale value of a machine should be after four years to justify an investment that requires a 12% annual return, assuming the machine produces a net income of $10,000 per year. To calculate this, we use the concept of net present value (NPV).

The NPV includes both the income generated by the machine over the four years and the future resale value of the machine, discounted at the desired rate of return, which in this case is 12%. The investment’s initial cost is $100,000.

To find the required resale value, we perform the following steps:

1. Calculate the present value of the $10,000 annual net income over four years using a 12% discount rate.
2. Subtract this value from the initial investment cost of $100,000 to find the shortfall that must be made up by the sale.
3. Calculate the present value of the required resale value (the future value we are solving for) using the same 12% rate.
4. Adjust the resale value to ensure the total NPV equals zero, which would mean the investment has achieved a 12% return.

This problem is typically solved through financial formulas or a financial calculator, as it involves the present value and future value of money.