Final answer:
To calculate the present value of a series of future maintenance costs, we need to consider the constant costs for the first five years and the costs that increase by 10% per year for the second five years, using a 12% discount rate.
Step-by-step explanation:
To calculate the present value of the total repair and maintenance costs of a machine using an interest rate of 12%, we first need to determine the cash flows for each period. For the first five years, the annual cost is constant at $50,000. For the next five years, the cost increases by 10% each year.
The formula for the present value of an annuity (a series of equal payments) for the first five years is PV = PMT × ((1 - (1 + r)^-n) / r), where PMT is the annual payment ($50,000), r is the annual interest rate (12% or 0.12), and n is the total number of periods (5 years).
For the next five years, since the payments are increasing by a fixed percentage annually, we use the present value of a growing annuity: PV = PMT × ((1 - (1 + g)^n) / (r - g)), where PMT is the payment in the first year of this period ($50,000), g is the growth rate (10% or 0.10), and n is the total number of periods (5 years).
After calculating the present value for both periods, we sum them up to get the total present value of the repair and maintenance costs.