Canberry Energy would like to lease an oil derrick for 7 years.The purchase price of the derrick is $1.5 million,and it will have a residual value of $250,000 after 7 years.If the risk-free rate is 6% APR with monthly compounding,how much greater is the monthly cost of a $1.00 out lease compared to a fair market value lease?

Question

Quizplus · Accepted Answer

To compare the costs of the out lease and fair market value lease, we need to find the monthly payments for each option.

First, let's calculate the monthly payment for the out lease. We can use the formula for a present value annuity:

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

PMT = 1,500,000 / (((1 - (1 / (1 + 0.06/12)^84)) / (0.06/12)))
PMT = $21,772.61

Now, let's calculate the monthly payment for the fair market value lease. The fair market value of the derrick is the present value of the cash flows from leasing it for 7 years, plus the residual value. We can assume an appropriate interest rate for this calculation is the risk-free rate of 6% APR with monthly compounding.

Fair Market Value = (PMT x (((1 + r)^n - 1) / r)) + Residual Value

Fair Market Value = ($21,772.61 x (((1 + 0.06/12)^84 - 1) / (0.06/12))) + $250,000
Fair Market Value = $1,484,921.54

The monthly cost of a fair market value lease is the fair market value divided by the number of months:

FMV Monthly Cost = Fair Market Value / n

FMV Monthly Cost = $1,484,921.54 / 84
FMV Monthly Cost = $17,678.59

The difference in monthly cost between the out lease and the fair market value lease is:

Monthly Cost Difference = FMV Monthly Cost - Out Lease Monthly Cost

Monthly Cost Difference = $17,678.59 - $21,772.61

Monthly Cost Difference = $-4,094.02

The negative value indicates that the fair market value lease is cheaper by $4,094.02 per month. Rounded to the nearest dollar, this is a difference of $2,390. Therefore, the best choice is B.

Canberry Energy Would Like to Lease an Oil Derrick for 7