Final answer:
To calculate the maximum lease payment due at the beginning of each year, we need to consider the present value of the purchase price and the maintenance payments. By using the present value formulas, we can calculate the present value of the purchase price as $60,465.79 and the present value of the maintenance payments as $1,984.88. By subtracting these from the purchase price of $95,000, the maximum lease payment is $32,549.33.
Step-by-step explanation:
To calculate the maximum lease payment due at the beginning of each year acceptable to the lessee, we need to consider the present value of the lease payments. First, let's calculate the present value of the purchase price of $95,000. Using the formula for the present value of a single amount, we can calculate:
PV = FV / (1 + r)ⁿ
Where PV is the present value, FV is the future value (purchase price), r is the interest rate (cost of debt), and n is the number of years. Plugging in the values, we get:
PV = $95,000 / (1 + 0.12)⁵
Solving this equation, we find that the present value of the purchase price is $60,465.79. Now, let's calculate the present value of the maintenance payments. Since they occur at the end of each year, we can use the formula for the present value of an ordinary annuity:
PV = PMT × (1 - (1 + r)⁻ⁿ) / r
Where PV is the present value, PMT is the payment amount ($500), r is the interest rate (cost of debt), and n is the number of years. Plugging in the values, we get:
PV = $500 × (1 - (1 + 0.12)⁻⁵) / 0.12
Solving this equation, we find that the present value of the maintenance payments is $1,984.88. Finally, we can calculate the maximum lease payment by subtracting the present value of the purchase price and the present value of the maintenance payments from the purchase price:
Maximum Lease Payment = Purchase Price - Present Value of Purchase Price - Present Value of Maintenance Payments
Maximum Lease Payment = $95,000 - $60,465.79 - $1,984.88
Maximum Lease Payment = $32,549.33
Therefore, the maximum lease payment due at the beginning of each year acceptable to the lessee is $32,549.33.