Final answer:
Calculate the present value of hiring employees for 3 years and compare it to the net cost of buying and operating a machine, taking into account the resale value and the effective monthly interest. The maximum machine price is where the cost equals the present value of employee costs.
Step-by-step explanation:
To evaluate the maximum price that it would make sense to pay for a machine, compared to hiring employees, we need to consider the net present value (NPV) of both options over a 3 year period, taking into account employee costs and effective monthly interest. The cost of hiring 10 employees at the end of each month for 3 years at $4,750 per employee is a repeating cost, so we calculate this as an annuity. The formula to calculate the present value of an annuity is PVA = PMT [((1-(1+r)^-n)/r)], where PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments. Plugging in the given values, PMT equals $47,500, r equals 0.6% or 0.006 in decimal form, and n equals 36 months (3 years). Calculating gives us the present value of the labor costs over the 3 year period.
Similarly, to calculate the net cost of the machine, we take the initial cost of the machine and subtract the present value of the $100,000 we receive after selling it at the end of 3 years. The present value of $100,000 received in 3 years can be calculated using the formula PV = FV / (1+r)^n, with FV equal to $100,000, r to 0.006, and n to 36. With these calculations, we can figure out the maximum initial price of the machine where the cost of purchasing and operating the machine equals the NPV of hiring employees. This is the price at which it would become indifferent between the two options. Beyond this price, hiring employees would be the cheaper option.