Final answer:
To calculate the most J company would be willing to spend on a project offering $20,000 annual cost savings for 5 years, the present value of these savings at an 8% required rate of return is calculated to be $86,242.60.
Step-by-step explanation:
The student is asking how much J company would be willing to spend on a project that provides annual cost savings of $20,000 for 5 years, considering the company has an 8% required rate of return. To determine the maximum investment for these cost savings, we need to calculate the present value of these future cost savings by discounting them at the required rate of return. The present value (PV) is found using the formula for the present value of an annuity: PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt is the annual payment, r is the rate of return, and n is the number of periods.
Applying this formula, we calculate:
PV = $20,000 * [(1 - (1 + 0.08)^-5) / 0.08]
PV = $20,000 * [4.31213]
PV = $86,242.60
Therefore, the most that J company should be willing to spend on the project is $86,242.60, given their 8% required rate of return.