Rabbit Inc. has an asset with a fair market value of $ 450,000 that it wants to lease. Rabbit's wants to recover its net investment in the leased asset and earn an 8%. The asset will revert back to Rabbit's at the end of a 5-year lease term and it is expected that the residual value of the asset will be $ 20,000 at the end of the lease. If Rabbit wants to charge rent semi-annually starting at the beginning of the lease, what amount should the lease payments be (rounded to whole dollars)?
A) $ 51,745
B) $ 62,096
C) $ 101,200
D) $ 104,367

Question

Quizplus · Accepted Answer

To find the lease payment, we use the formula for the present value of an annuity due since payments are made at the beginning of each period. The present value of the lease payments plus the present value of the residual value must equal the fair market value of the asset. The formula for the present value of an annuity due is PV = PMT * [(1 - (1 + r)^-n) / r] * (1+r), where PMT is the payment, r is the semi-annual interest rate (8% annual rate divided by 2), and n is the total number of payments (5 years * 2 payments per year = 10 payments). Additionally, we must account for the present value of the residual value, which is $20,000 discounted back 5 years at the semi-annual rate. First, calculate the semi-annual rate: 8% / 2 = 4% or 0.04 as a decimal.Next, calculate the present value of the residual value: $20,000 / (1 + 0.04)^(5*2) = $20,000 / 1.48024 ≈ $13,516.The total amount Rabbit Inc. wants to recover is the fair market value minus the present value of the residual value: $450,000 - $13,516 = $436,484.Using the formula for the present value of an annuity due, we solve for PMT, considering the present value we just calculated needs to be recovered through the lease payments.Rearranging the formula to solve for PMT gives us PMT = PV / {[(1 - (1 + r)^-n) / r] * (1+r)}.Plugging in the numbers: PMT = $436,484 / {[(1 - (1 + 0.04)^-10) / 0.04] * (1+0.04)} ≈ $51,745.Therefore, the correct lease payment amount is $51,745, rounded to whole dollars.