Final answer:
The present value of the maintenance costs for the equipment, which are expected to occur at the end of year 8 and amount to $9,750, is approximately $3,188.66 when discounted at a 15% cost of debt.
Step-by-step explanation:
To calculate the present value (PV) of maintenance for new equipment that a company is considering purchasing, you should discount the future maintenance costs back to the present. Given the maintenance cost is $9,750 expected to be incurred at the end of year 8, with a cost of debt at 15%, the formula to calculate the present value is PV = C / (1 + r)^t, where C is the future cost, r is the discount rate (cost of debt), and t is the time in years until the payment.
The present value of maintenance is thus calculated as follows:
PV = $9,750 / (1 + 0.15)^8
PV = $9,750 / (1.15)^8
PV = $9,750 / (3.059023)
PV = $3,188.66 approximately
The PV of $3,188.66 represents the value of the future maintenance costs in today's dollars, taking into account the time value of money. The cost of debt (15%) acts as the discount rate applied to the future cost to account for the opportunity cost of spending money now versus later. Moreover, the tax rate and CCA rate do not need to be considered for this calculation, as they do not directly influence the discounting of a single future payment for maintenance.