Assume the prevailing interest rate is 12% per annum. A 4-year lease agreement requires you to pay $1,000 up front, followed by payments of $800, $600, and $500 at the end of each of the
Following three years, respectively. What would the payment on a 4-year lease with a constant
Annual payment have to offer for you to be indifferent between the two lease options? Assume
That the first payment on the constant annual payment lease will be made at the end of the first
Year, and round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

First, we need to find the present value of the payments on the original lease:

PV = 1000 + 800/(1+0.12)^1 + 600/(1+0.12)^2 + 500/(1+0.12)^3
PV = $1,669.05

Next, we need to find the annual payment on a constant annual payment lease that also has a present value of $1,669.05. We can use the annuity formula:

PV = PMT * [(1 - (1+r)^(-n)) / r]

Where PV = present value, PMT = annual payment, r = interest rate per period, and n = number of periods.

Rearranging for PMT:

PMT = PV * (r / (1 - (1+r)^(-n)))

Using the values given in the problem, we can plug in and solve:

PMT = 1669.05 * (0.12 / (1 - (1+0.12)^(-4)))
PMT = $838.95

Rounding to the nearest dollar, the annual payment needed to make the two lease options equivalent is $839. Therefore, the best choice is A. To compare the two lease options, we need to calculate the present value of the payments in each option and compare them.

For the given lease agreement, the present value of the payments is:

PV = $1,000 + $800/(1 + 12%)^1 + $600/(1 + 12%)^2 + $500/(1 + 12%)^3
PV = $1,000 + $712.05 + $476.19 + $340.14
PV = $2,528.38

To calculate the annual payment required to make the two options equivalent, we can use the present value equation for an annuity:

PV = PMT x [1 - (1 + r)^-n] / r

Where PV is the present value of the annuity, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, we want to solve for PMT, so we rearrange the equation:

PMT = PV x r / [1 - (1 + r)^-n]

Plugging in the values given, we get:

PMT = $2,528.38 x 12% / [1 - (1 + 12%)^-4]
PMT = $839.15

Therefore, the constant annual payment lease would need to offer a payment of $839 to make the two options equivalent. Since option A is closest to this amount, A is the best choice.

Assume the Prevailing Interest Rate Is 12% Per Annum