Beaudoin Haulage has signed a five-year lease with GMAC on a new dump truck. Lease payments of $4500 are made at the beginning of each month. To purchase the truck, Beaudoin would have had to borrow funds at 8.7% compounded annually. (Do not round intermediate calculations and round your final answer to 2 decimal places.)


a. What initial liability should Beaudoin report on its balance sheet?

$
220000.25

b. How much will the liability be reduced during the first year of the lease?

$

To answer these questions, we need to calculate the present value of the lease payments.

a. To find the initial liability that Beaudoin should report on its balance sheet, we need to calculate the present value of all the lease payments.

The lease payments are $4500 per month and the lease term is five years, so the total number of lease payments is 5 years * 12 months/year = 60 payments.

The interest rate used to calculate the present value is 8.7% compounded annually. Since the lease payments are made at the beginning of each month, we need to adjust the interest rate to a monthly rate. The monthly interest rate is 8.7% / 12 = 0.725% or 0.00725 as a decimal.

Now we can calculate the present value of the lease payments using the formula for the present value of an ordinary annuity:

Present Value = Payment * [1 - (1 + interest rate)^(-number of payments)] / interest rate

Present Value = $4500 * [1 - (1 + 0.00725)^(-60)] / 0.00725

Present Value = $220000.25

Therefore, the initial liability that Beaudoin should report on its balance sheet is $220000.25.

b. To find the reduction in liability during the first year of the lease, we need to calculate the present value of the lease payments made in that year.

The lease payments are $4500 per month, and in the first year, there are 12 payments.

Using the same monthly interest rate of 0.00725, we can calculate the present value of these payments:

Present Value = $4500 * [1 - (1 + 0.00725)^(-12)] / 0.00725

The Present Value gives us the reduction in liability during the first year of the lease.

Therefore, we need to calculate:

$4500 * [1 - (1 + 0.00725)^(-12)] / 0.00725 = $44,730.52

Therefore, the liability will be reduced by $44,730.52 during the first year of the lease.