Final answer:
To calculate the present value of the machine, we sum the present value of the initial down payment and the present value of the annuity payments over the 10-year period.
Step-by-step explanation:
To determine the present value of a machine when a company puts $25,000 down and will pay $5,000 every year for the life of the machine (10 years) at an interest rate of 10% compounded annually, we calculate the present value of the initial down payment and the annual payments separately.
The present value of the down payment (PVD) is simply its own value, as it is a payment made at the present time: PVD = $25,000.
The annuity payments can be calculated using the present value of an annuity formula: PVA = Pmt × [(1 - (1 + r)^-n) / r], where Pmt is the annual payment, r is the annual interest rate, and n is the number of payments. Here, Pmt = $5,000, r = 0.10, and n = 10.
After calculating the present value of the annuity (PVA), we can find the total present value of the machine by adding the present value of the down payment to the present value of the annuity payments: Total PV = PVD + PVA.